Write in Standard Form (x-3)(x-4)(x+1)(x-2)

$(x - 3) (x - 4) (x + 1) (x - 2)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Expand $(x - 3) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$(x (x - 4) - 3 (x - 4)) (x + 1) (x - 2)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 4$ to the left of $x$ .

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

Multiply $- 3$ by $- 4$ .

$(x^{2} - 4 x - 3 x + 12) (x + 1) (x - 2)$

Subtract $3 x$ from $- 4 x$ .

$(x^{2} - 7 x + 12) (x + 1) (x - 2)$

Step 4

Expand $(x^{2} - 7 x + 12) (x + 1)$ by multiplying each term in the first expression by each term in the second expression.

$(x^{2} x + x^{2} \cdot 1 - 7 x \cdot x - 7 x \cdot 1 + 12 x + 12 \cdot 1) (x - 2)$

Step 5

Simplify terms.

Simplify each term.

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

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

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

$(x^{2} x^{1} + x^{2} \cdot 1 - 7 x \cdot x - 7 x \cdot 1 + 12 x + 12 \cdot 1) (x - 2)$

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

$(x^{2 + 1} + x^{2} \cdot 1 - 7 x \cdot x - 7 x \cdot 1 + 12 x + 12 \cdot 1) (x - 2)$

Add $2$ and $1$ .

$(x^{3} + x^{2} \cdot 1 - 7 x \cdot x - 7 x \cdot 1 + 12 x + 12 \cdot 1) (x - 2)$

Multiply $x^{2}$ by $1$ .

$(x^{3} + x^{2} - 7 x \cdot x - 7 x \cdot 1 + 12 x + 12 \cdot 1) (x - 2)$

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

Move $x$ .

$(x^{3} + x^{2} - 7 (x \cdot x) - 7 x \cdot 1 + 12 x + 12 \cdot 1) (x - 2)$

Multiply $x$ by $x$ .

$(x^{3} + x^{2} - 7 x^{2} - 7 x \cdot 1 + 12 x + 12 \cdot 1) (x - 2)$

Multiply $- 7$ by $1$ .

$(x^{3} + x^{2} - 7 x^{2} - 7 x + 12 x + 12 \cdot 1) (x - 2)$

Multiply $12$ by $1$ .

$(x^{3} + x^{2} - 7 x^{2} - 7 x + 12 x + 12) (x - 2)$

Simplify by adding terms.

Subtract $7 x^{2}$ from $x^{2}$ .

$(x^{3} - 6 x^{2} - 7 x + 12 x + 12) (x - 2)$

Add $- 7 x$ and $12 x$ .

$(x^{3} - 6 x^{2} + 5 x + 12) (x - 2)$

Step 6

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

$x^{3} x + x^{3} \cdot - 2 - 6 x^{2} x - 6 x^{2} \cdot - 2 + 5 x \cdot x + 5 x \cdot - 2 + 12 x + 12 \cdot - 2$

Step 7

Simplify terms.

Simplify each term.

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

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

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

$x^{3} x^{1} + x^{3} \cdot - 2 - 6 x^{2} x - 6 x^{2} \cdot - 2 + 5 x \cdot x + 5 x \cdot - 2 + 12 x + 12 \cdot - 2$

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

$x^{3 + 1} + x^{3} \cdot - 2 - 6 x^{2} x - 6 x^{2} \cdot - 2 + 5 x \cdot x + 5 x \cdot - 2 + 12 x + 12 \cdot - 2$

Add $3$ and $1$ .

$x^{4} + x^{3} \cdot - 2 - 6 x^{2} x - 6 x^{2} \cdot - 2 + 5 x \cdot x + 5 x \cdot - 2 + 12 x + 12 \cdot - 2$

Move $- 2$ to the left of $x^{3}$ .

$x^{4} - 2 \cdot x^{3} - 6 x^{2} x - 6 x^{2} \cdot - 2 + 5 x \cdot x + 5 x \cdot - 2 + 12 x + 12 \cdot - 2$

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

Move $x$ .

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

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

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

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

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

$x^{4} - 2 x^{3} - 6 x^{1 + 2} - 6 x^{2} \cdot - 2 + 5 x \cdot x + 5 x \cdot - 2 + 12 x + 12 \cdot - 2$

Add $1$ and $2$ .

$x^{4} - 2 x^{3} - 6 x^{3} - 6 x^{2} \cdot - 2 + 5 x \cdot x + 5 x \cdot - 2 + 12 x + 12 \cdot - 2$

Multiply $- 2$ by $- 6$ .

$x^{4} - 2 x^{3} - 6 x^{3} + 12 x^{2} + 5 x \cdot x + 5 x \cdot - 2 + 12 x + 12 \cdot - 2$

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

Move $x$ .

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

Multiply $x$ by $x$ .

$x^{4} - 2 x^{3} - 6 x^{3} + 12 x^{2} + 5 x^{2} + 5 x \cdot - 2 + 12 x + 12 \cdot - 2$

Multiply $- 2$ by $5$ .

$x^{4} - 2 x^{3} - 6 x^{3} + 12 x^{2} + 5 x^{2} - 10 x + 12 x + 12 \cdot - 2$

Multiply $12$ by $- 2$ .

$x^{4} - 2 x^{3} - 6 x^{3} + 12 x^{2} + 5 x^{2} - 10 x + 12 x - 24$

Simplify by adding terms.

Subtract $6 x^{3}$ from $- 2 x^{3}$ .

$x^{4} - 8 x^{3} + 12 x^{2} + 5 x^{2} - 10 x + 12 x - 24$

Add $12 x^{2}$ and $5 x^{2}$ .

$x^{4} - 8 x^{3} + 17 x^{2} - 10 x + 12 x - 24$

Add $- 10 x$ and $12 x$ .

$x^{4} - 8 x^{3} + 17 x^{2} + 2 x - 24$

Write in Standard Form (x-3)(x-4)(x+1)(x-2)

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