Find the Degree f(x)=(x+3)(x-1)^3

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

Step 1

Simplify and reorder the polynomial.

Use the Binomial Theorem.

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

Simplify each term.

Multiply $- 1$ by $3$ .

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

Raise $- 1$ to the power of $2$ .

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

Multiply $3$ by $1$ .

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

Raise $- 1$ to the power of $3$ .

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

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

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

Simplify terms.

Simplify each term.

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

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

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

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

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

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

Add $1$ and $3$ .

$x^{4} + x (- 3 x^{2}) + x (3 x) + x \cdot - 1 + 3 x^{3} + 3 (- 3 x^{2}) + 3 (3 x) + 3 \cdot - 1$

Rewrite using the commutative property of multiplication.

$x^{4} - 3 x \cdot x^{2} + x (3 x) + x \cdot - 1 + 3 x^{3} + 3 (- 3 x^{2}) + 3 (3 x) + 3 \cdot - 1$

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

Move $x^{2}$ .

$x^{4} - 3 (x^{2} x) + x (3 x) + x \cdot - 1 + 3 x^{3} + 3 (- 3 x^{2}) + 3 (3 x) + 3 \cdot - 1$

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

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

$x^{4} - 3 (x^{2} x^{1}) + x (3 x) + x \cdot - 1 + 3 x^{3} + 3 (- 3 x^{2}) + 3 (3 x) + 3 \cdot - 1$

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

$x^{4} - 3 x^{2 + 1} + x (3 x) + x \cdot - 1 + 3 x^{3} + 3 (- 3 x^{2}) + 3 (3 x) + 3 \cdot - 1$

Add $2$ and $1$ .

$x^{4} - 3 x^{3} + x (3 x) + x \cdot - 1 + 3 x^{3} + 3 (- 3 x^{2}) + 3 (3 x) + 3 \cdot - 1$

Rewrite using the commutative property of multiplication.

$x^{4} - 3 x^{3} + 3 x \cdot x + x \cdot - 1 + 3 x^{3} + 3 (- 3 x^{2}) + 3 (3 x) + 3 \cdot - 1$

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

Move $x$ .

$x^{4} - 3 x^{3} + 3 (x \cdot x) + x \cdot - 1 + 3 x^{3} + 3 (- 3 x^{2}) + 3 (3 x) + 3 \cdot - 1$

Multiply $x$ by $x$ .

$x^{4} - 3 x^{3} + 3 x^{2} + x \cdot - 1 + 3 x^{3} + 3 (- 3 x^{2}) + 3 (3 x) + 3 \cdot - 1$

Move $- 1$ to the left of $x$ .

$x^{4} - 3 x^{3} + 3 x^{2} - 1 \cdot x + 3 x^{3} + 3 (- 3 x^{2}) + 3 (3 x) + 3 \cdot - 1$

Rewrite $- 1 x$ as $- x$ .

$x^{4} - 3 x^{3} + 3 x^{2} - x + 3 x^{3} + 3 (- 3 x^{2}) + 3 (3 x) + 3 \cdot - 1$

Multiply $- 3$ by $3$ .

$x^{4} - 3 x^{3} + 3 x^{2} - x + 3 x^{3} - 9 x^{2} + 3 (3 x) + 3 \cdot - 1$

Multiply $3$ by $3$ .

$x^{4} - 3 x^{3} + 3 x^{2} - x + 3 x^{3} - 9 x^{2} + 9 x + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$x^{4} - 3 x^{3} + 3 x^{2} - x + 3 x^{3} - 9 x^{2} + 9 x - 3$

Simplify by adding terms.

Combine the opposite terms in $x^{4} - 3 x^{3} + 3 x^{2} - x + 3 x^{3} - 9 x^{2} + 9 x - 3$ .

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

$x^{4} + 3 x^{2} - x + 0 - 9 x^{2} + 9 x - 3$

Add $x^{4} + 3 x^{2} - x$ and $0$ .

$x^{4} + 3 x^{2} - x - 9 x^{2} + 9 x - 3$

Subtract $9 x^{2}$ from $3 x^{2}$ .

$x^{4} - 6 x^{2} - x + 9 x - 3$

Add $- x$ and $9 x$ .

$x^{4} - 6 x^{2} + 8 x - 3$

Step 2

The largest exponent is the degree of the polynomial.

$4$

Find the Degree f(x)=(x+3)(x-1)^3

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