Write in Standard Form (x-3)(x+2)(x-5)

$(x - 3) (x + 2) (x - 5)$

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 $(x - 3) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$(x (x + 2) - 3 (x + 2)) (x - 5)$

Apply the distributive property.

$(x \cdot x + x \cdot 2 - 3 (x + 2)) (x - 5)$

Apply the distributive property.

$(x \cdot x + x \cdot 2 - 3 x - 3 \cdot 2) (x - 5)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $2$ to the left of $x$ .

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

Multiply $- 3$ by $2$ .

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

Subtract $3 x$ from $2 x$ .

$(x^{2} - x - 6) (x - 5)$

Step 4

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

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

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 $1$ .

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

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

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

Add $2$ and $1$ .

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

Move $- 5$ to the left of $x^{2}$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 5$ by $- 1$ .

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

Multiply $- 6$ by $- 5$ .

$x^{3} - 5 x^{2} - x^{2} + 5 x - 6 x + 30$

Simplify by adding terms.

Subtract $x^{2}$ from $- 5 x^{2}$ .

$x^{3} - 6 x^{2} + 5 x - 6 x + 30$

Subtract $6 x$ from $5 x$ .

$x^{3} - 6 x^{2} - x + 30$

Write in Standard Form (x-3)(x+2)(x-5)

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