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

$g (x) = - 2 (3 x + 1) (x + 2) (x - 3)$

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

$g (x) = a x^{2} + b x + c$

Simplify by multiplying through.

Apply the distributive property.

$g (x) = (- 2 (3 x) - 2 \cdot 1) (x + 2) (x - 3)$

Multiply.

Multiply $3$ by $- 2$ .

$g (x) = (- 6 x - 2 \cdot 1) (x + 2) (x - 3)$

Multiply $- 2$ by $1$ .

$g (x) = (- 6 x - 2) (x + 2) (x - 3)$

Expand $(- 6 x - 2) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$g (x) = (- 6 x (x + 2) - 2 (x + 2)) (x - 3)$

Apply the distributive property.

$g (x) = (- 6 x \cdot x - 6 x \cdot 2 - 2 (x + 2)) (x - 3)$

Apply the distributive property.

$g (x) = (- 6 x \cdot x - 6 x \cdot 2 - 2 x - 2 \cdot 2) (x - 3)$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$g (x) = (- 6 (x \cdot x) - 6 x \cdot 2 - 2 x - 2 \cdot 2) (x - 3)$

Multiply $x$ by $x$ .

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

Multiply $2$ by $- 6$ .

$g (x) = (- 6 x^{2} - 12 x - 2 x - 2 \cdot 2) (x - 3)$

Multiply $- 2$ by $2$ .

$g (x) = (- 6 x^{2} - 12 x - 2 x - 4) (x - 3)$

Subtract $2 x$ from $- 12 x$ .

$g (x) = (- 6 x^{2} - 14 x - 4) (x - 3)$

Expand $(- 6 x^{2} - 14 x - 4) (x - 3)$ by multiplying each term in the first expression by each term in the second expression.

$g (x) = - 6 x^{2} x - 6 x^{2} \cdot - 3 - 14 x \cdot x - 14 x \cdot - 3 - 4 x - 4 \cdot - 3$

Simplify terms.

Simplify each term.

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

Move $x$ .

$g (x) = - 6 (x \cdot x^{2}) - 6 x^{2} \cdot - 3 - 14 x \cdot x - 14 x \cdot - 3 - 4 x - 4 \cdot - 3$

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

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

$g (x) = - 6 (x \cdot x^{2}) - 6 x^{2} \cdot - 3 - 14 x \cdot x - 14 x \cdot - 3 - 4 x - 4 \cdot - 3$

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

$g (x) = - 6 x^{1 + 2} - 6 x^{2} \cdot - 3 - 14 x \cdot x - 14 x \cdot - 3 - 4 x - 4 \cdot - 3$

Add $1$ and $2$ .

$g (x) = - 6 x^{3} - 6 x^{2} \cdot - 3 - 14 x \cdot x - 14 x \cdot - 3 - 4 x - 4 \cdot - 3$

Multiply $- 3$ by $- 6$ .

$g (x) = - 6 x^{3} + 18 x^{2} - 14 x \cdot x - 14 x \cdot - 3 - 4 x - 4 \cdot - 3$

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

Move $x$ .

$g (x) = - 6 x^{3} + 18 x^{2} - 14 (x \cdot x) - 14 x \cdot - 3 - 4 x - 4 \cdot - 3$

Multiply $x$ by $x$ .

$g (x) = - 6 x^{3} + 18 x^{2} - 14 x^{2} - 14 x \cdot - 3 - 4 x - 4 \cdot - 3$

Multiply $- 3$ by $- 14$ .

$g (x) = - 6 x^{3} + 18 x^{2} - 14 x^{2} + 42 x - 4 x - 4 \cdot - 3$

Multiply $- 4$ by $- 3$ .

$g (x) = - 6 x^{3} + 18 x^{2} - 14 x^{2} + 42 x - 4 x + 12$

Simplify by adding terms.

Subtract $14 x^{2}$ from $18 x^{2}$ .

$g (x) = - 6 x^{3} + 4 x^{2} + 42 x - 4 x + 12$

Subtract $4 x$ from $42 x$ .

$g (x) = - 6 x^{3} + 4 x^{2} + 38 x + 12$

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

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