Find the Degree, Leading Term, and Leading Coefficient k(x)=2(x-3)^2(x+1)^3(x+2)

$k (x) = 2 {(x - 3)}^{2} {(x + 1)}^{3} (x + 2)$

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

Rewrite ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

$k (x) = 2 ((x - 3) (x - 3)) {(x + 1)}^{3} (x + 2)$

Expand $(x - 3) (x - 3)$ using the FOIL Method.

Apply the distributive property.

$k (x) = 2 (x (x - 3) - 3 (x - 3)) {(x + 1)}^{3} (x + 2)$

Apply the distributive property.

$k (x) = 2 (x \cdot x + x \cdot - 3 - 3 (x - 3)) {(x + 1)}^{3} (x + 2)$

Apply the distributive property.

$k (x) = 2 (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3) {(x + 1)}^{3} (x + 2)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$k (x) = 2 (x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3) {(x + 1)}^{3} (x + 2)$

Move $- 3$ to the left of $x$ .

$k (x) = 2 (x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3) {(x + 1)}^{3} (x + 2)$

Multiply $- 3$ by $- 3$ .

$k (x) = 2 (x^{2} - 3 x - 3 x + 9) {(x + 1)}^{3} (x + 2)$

Subtract $3 x$ from $- 3 x$ .

$k (x) = 2 (x^{2} - 6 x + 9) {(x + 1)}^{3} (x + 2)$

Apply the distributive property.

$k (x) = (2 x^{2} + 2 (- 6 x) + 2 \cdot 9) {(x + 1)}^{3} (x + 2)$

Simplify.

Multiply $- 6$ by $2$ .

$k (x) = (2 x^{2} - 12 x + 2 \cdot 9) {(x + 1)}^{3} (x + 2)$

Multiply $2$ by $9$ .

$k (x) = (2 x^{2} - 12 x + 18) {(x + 1)}^{3} (x + 2)$

Use the Binomial Theorem.

$k (x) = (2 x^{2} - 12 x + 18) (x^{3} + 3 x^{2} \cdot 1 + 3 x \cdot 1^{2} + 1^{3}) (x + 2)$

Simplify each term.

Multiply $3$ by $1$ .

$k (x) = (2 x^{2} - 12 x + 18) (x^{3} + 3 x^{2} + 3 x \cdot 1^{2} + 1^{3}) (x + 2)$

One to any power is one.

$k (x) = (2 x^{2} - 12 x + 18) (x^{3} + 3 x^{2} + 3 x \cdot 1 + 1^{3}) (x + 2)$

Multiply $3$ by $1$ .

$k (x) = (2 x^{2} - 12 x + 18) (x^{3} + 3 x^{2} + 3 x + 1^{3}) (x + 2)$

One to any power is one.

$k (x) = (2 x^{2} - 12 x + 18) (x^{3} + 3 x^{2} + 3 x + 1) (x + 2)$

Expand $(2 x^{2} - 12 x + 18) (x^{3} + 3 x^{2} + 3 x + 1)$ by multiplying each term in the first expression by each term in the second expression.

$k (x) = (2 x^{2} x^{3} + 2 x^{2} (3 x^{2}) + 2 x^{2} (3 x) + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Simplify terms.

Simplify each term.

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$k (x) = (2 (x^{3} x^{2}) + 2 x^{2} (3 x^{2}) + 2 x^{2} (3 x) + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$k (x) = (2 x^{3 + 2} + 2 x^{2} (3 x^{2}) + 2 x^{2} (3 x) + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Add $3$ and $2$ .

$k (x) = (2 x^{5} + 2 x^{2} (3 x^{2}) + 2 x^{2} (3 x) + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Rewrite using the commutative property of multiplication.

$k (x) = (2 x^{5} + 2 \cdot (3 x^{2} x^{2}) + 2 x^{2} (3 x) + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$k (x) = (2 x^{5} + 2 \cdot (3 (x^{2} x^{2})) + 2 x^{2} (3 x) + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$k (x) = (2 x^{5} + 2 \cdot (3 x^{2 + 2}) + 2 x^{2} (3 x) + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Add $2$ and $2$ .

$k (x) = (2 x^{5} + 2 \cdot (3 x^{4}) + 2 x^{2} (3 x) + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $2$ by $3$ .

$k (x) = (2 x^{5} + 6 x^{4} + 2 x^{2} (3 x) + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Rewrite using the commutative property of multiplication.

$k (x) = (2 x^{5} + 6 x^{4} + 2 \cdot (3 x^{2} x) + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$k (x) = (2 x^{5} + 6 x^{4} + 2 \cdot (3 (x \cdot x^{2})) + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$k (x) = (2 x^{5} + 6 x^{4} + 2 \cdot (3 (x \cdot x^{2})) + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$k (x) = (2 x^{5} + 6 x^{4} + 2 \cdot (3 x^{1 + 2}) + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Add $1$ and $2$ .

$k (x) = (2 x^{5} + 6 x^{4} + 2 \cdot (3 x^{3}) + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $2$ by $3$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} \cdot 1 - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $2$ by $1$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x \cdot x^{3} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 (x^{3} x) - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $x^{3}$ by $x$ .

Raise $x$ to the power of $1$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 (x^{3} x) - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{3 + 1} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Add $3$ and $1$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 12 x (3 x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Rewrite using the commutative property of multiplication.

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 12 \cdot (3 x \cdot x^{2}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 12 \cdot (3 (x^{2} x)) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 12 \cdot (3 (x^{2} x)) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 12 \cdot (3 x^{2 + 1}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Add $2$ and $1$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 12 \cdot (3 x^{3}) - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $- 12$ by $3$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 36 x^{3} - 12 x (3 x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Rewrite using the commutative property of multiplication.

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 36 x^{3} - 12 \cdot (3 x \cdot x) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 36 x^{3} - 12 \cdot (3 (x \cdot x)) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $x$ by $x$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 36 x^{3} - 12 \cdot (3 x^{2}) - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $- 12$ by $3$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 36 x^{3} - 36 x^{2} - 12 x \cdot 1 + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $- 12$ by $1$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 36 x^{3} - 36 x^{2} - 12 x + 18 x^{3} + 18 (3 x^{2}) + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $3$ by $18$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 36 x^{3} - 36 x^{2} - 12 x + 18 x^{3} + 54 x^{2} + 18 (3 x) + 18 \cdot 1) (x + 2)$

Multiply $3$ by $18$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 36 x^{3} - 36 x^{2} - 12 x + 18 x^{3} + 54 x^{2} + 54 x + 18 \cdot 1) (x + 2)$

Multiply $18$ by $1$ .

$k (x) = (2 x^{5} + 6 x^{4} + 6 x^{3} + 2 x^{2} - 12 x^{4} - 36 x^{3} - 36 x^{2} - 12 x + 18 x^{3} + 54 x^{2} + 54 x + 18) (x + 2)$

Simplify by adding terms.

Subtract $12 x^{4}$ from $6 x^{4}$ .

$k (x) = (2 x^{5} - 6 x^{4} + 6 x^{3} + 2 x^{2} - 36 x^{3} - 36 x^{2} - 12 x + 18 x^{3} + 54 x^{2} + 54 x + 18) (x + 2)$

Subtract $36 x^{3}$ from $6 x^{3}$ .

$k (x) = (2 x^{5} - 6 x^{4} - 30 x^{3} + 2 x^{2} - 36 x^{2} - 12 x + 18 x^{3} + 54 x^{2} + 54 x + 18) (x + 2)$

Add $- 30 x^{3}$ and $18 x^{3}$ .

$k (x) = (2 x^{5} - 6 x^{4} - 12 x^{3} + 2 x^{2} - 36 x^{2} - 12 x + 54 x^{2} + 54 x + 18) (x + 2)$

Subtract $36 x^{2}$ from $2 x^{2}$ .

$k (x) = (2 x^{5} - 6 x^{4} - 12 x^{3} - 34 x^{2} - 12 x + 54 x^{2} + 54 x + 18) (x + 2)$

Add $- 34 x^{2}$ and $54 x^{2}$ .

$k (x) = (2 x^{5} - 6 x^{4} - 12 x^{3} + 20 x^{2} - 12 x + 54 x + 18) (x + 2)$

Add $- 12 x$ and $54 x$ .

$k (x) = (2 x^{5} - 6 x^{4} - 12 x^{3} + 20 x^{2} + 42 x + 18) (x + 2)$

Expand $(2 x^{5} - 6 x^{4} - 12 x^{3} + 20 x^{2} + 42 x + 18) (x + 2)$ by multiplying each term in the first expression by each term in the second expression.

$k (x) = 2 x^{5} x + 2 x^{5} \cdot 2 - 6 x^{4} x - 6 x^{4} \cdot 2 - 12 x^{3} x - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Simplify terms.

Simplify each term.

Multiply $x^{5}$ by $x$ by adding the exponents.

Move $x$ .

$k (x) = 2 (x \cdot x^{5}) + 2 x^{5} \cdot 2 - 6 x^{4} x - 6 x^{4} \cdot 2 - 12 x^{3} x - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Multiply $x$ by $x^{5}$ .

Raise $x$ to the power of $1$ .

$k (x) = 2 (x \cdot x^{5}) + 2 x^{5} \cdot 2 - 6 x^{4} x - 6 x^{4} \cdot 2 - 12 x^{3} x - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$k (x) = 2 x^{1 + 5} + 2 x^{5} \cdot 2 - 6 x^{4} x - 6 x^{4} \cdot 2 - 12 x^{3} x - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Add $1$ and $5$ .

$k (x) = 2 x^{6} + 2 x^{5} \cdot 2 - 6 x^{4} x - 6 x^{4} \cdot 2 - 12 x^{3} x - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Multiply $2$ by $2$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{4} x - 6 x^{4} \cdot 2 - 12 x^{3} x - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Multiply $x^{4}$ by $x$ by adding the exponents.

Move $x$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 (x \cdot x^{4}) - 6 x^{4} \cdot 2 - 12 x^{3} x - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Multiply $x$ by $x^{4}$ .

Raise $x$ to the power of $1$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 (x \cdot x^{4}) - 6 x^{4} \cdot 2 - 12 x^{3} x - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{1 + 4} - 6 x^{4} \cdot 2 - 12 x^{3} x - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Add $1$ and $4$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 6 x^{4} \cdot 2 - 12 x^{3} x - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Multiply $2$ by $- 6$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 x^{3} x - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 (x \cdot x^{3}) - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Multiply $x$ by $x^{3}$ .

Raise $x$ to the power of $1$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 (x \cdot x^{3}) - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 x^{1 + 3} - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Add $1$ and $3$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 x^{4} - 12 x^{3} \cdot 2 + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Multiply $2$ by $- 12$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 x^{4} - 24 x^{3} + 20 x^{2} x + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 x^{4} - 24 x^{3} + 20 (x \cdot x^{2}) + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 x^{4} - 24 x^{3} + 20 (x \cdot x^{2}) + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 x^{4} - 24 x^{3} + 20 x^{1 + 2} + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Add $1$ and $2$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 x^{4} - 24 x^{3} + 20 x^{3} + 20 x^{2} \cdot 2 + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Multiply $2$ by $20$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 x^{4} - 24 x^{3} + 20 x^{3} + 40 x^{2} + 42 x \cdot x + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 x^{4} - 24 x^{3} + 20 x^{3} + 40 x^{2} + 42 (x \cdot x) + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Multiply $x$ by $x$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 x^{4} - 24 x^{3} + 20 x^{3} + 40 x^{2} + 42 x^{2} + 42 x \cdot 2 + 18 x + 18 \cdot 2$

Multiply $2$ by $42$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 x^{4} - 24 x^{3} + 20 x^{3} + 40 x^{2} + 42 x^{2} + 84 x + 18 x + 18 \cdot 2$

Multiply $18$ by $2$ .

$k (x) = 2 x^{6} + 4 x^{5} - 6 x^{5} - 12 x^{4} - 12 x^{4} - 24 x^{3} + 20 x^{3} + 40 x^{2} + 42 x^{2} + 84 x + 18 x + 36$

Simplify by adding terms.

Subtract $6 x^{5}$ from $4 x^{5}$ .

$k (x) = 2 x^{6} - 2 x^{5} - 12 x^{4} - 12 x^{4} - 24 x^{3} + 20 x^{3} + 40 x^{2} + 42 x^{2} + 84 x + 18 x + 36$

Subtract $12 x^{4}$ from $- 12 x^{4}$ .

$k (x) = 2 x^{6} - 2 x^{5} - 24 x^{4} - 24 x^{3} + 20 x^{3} + 40 x^{2} + 42 x^{2} + 84 x + 18 x + 36$

Add $- 24 x^{3}$ and $20 x^{3}$ .

$k (x) = 2 x^{6} - 2 x^{5} - 24 x^{4} - 4 x^{3} + 40 x^{2} + 42 x^{2} + 84 x + 18 x + 36$

Add $40 x^{2}$ and $42 x^{2}$ .

$k (x) = 2 x^{6} - 2 x^{5} - 24 x^{4} - 4 x^{3} + 82 x^{2} + 84 x + 18 x + 36$

Add $84 x$ and $18 x$ .

$k (x) = 2 x^{6} - 2 x^{5} - 24 x^{4} - 4 x^{3} + 82 x^{2} + 102 x + 36$

The degree of a polynomial is the highest degree of its terms.

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$2 x^{6} \to 6$

$- 2 x^{5} \to 5$

$- 24 x^{4} \to 4$

$- 4 x^{3} \to 3$

$82 x^{2} \to 2$

$102 x \to 1$

$36 \to 0$

The largest exponent is the degree of the polynomial.

$6$

The leading term in a polynomial is the term with the highest degree.

$2 x^{6}$

The leading coefficient of a polynomial is the coefficient of the leading term.

The leading term in a polynomial is the term with the highest degree.

$2 x^{6}$

The leading coefficient in a polynomial is the coefficient of the leading term.

$2$

List the results.

Polynomial Degree: $6$

Leading Term: $2 x^{6}$

Leading Coefficient: $2$

Find the Degree, Leading Term, and Leading Coefficient k(x)=2(x-3)^2(x+1)^3(x+2)

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