Solve g(x)=(x-2)(x+1)(x-3)(x+4)

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

Evaluate

$$\left(x-3\right)\left(x-2\right)\left(x+1\right)\left(x+4\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x-2 by each term of x+1.

$$\left(x^{2}+x-2x-2\right)\left(x-3\right)\left(x+4\right)$$

Combine x and -2x to get -x.

$$\left(x^{2}-x-2\right)\left(x-3\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of x^{2}-x-2 by each term of x-3.

$$\left(x^{3}-3x^{2}-x^{2}+3x-2x+6\right)\left(x+4\right)$$

Combine -3x^{2} and -x^{2} to get -4x^{2}.

$$\left(x^{3}-4x^{2}+3x-2x+6\right)\left(x+4\right)$$

Combine 3x and -2x to get x.

$$\left(x^{3}-4x^{2}+x+6\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of x^{3}-4x^{2}+x+6 by each term of x+4.

$$x^{4}+4x^{3}-4x^{3}-16x^{2}+x^{2}+4x+6x+24$$

Combine 4x^{3} and -4x^{3} to get 0.

$$x^{4}-16x^{2}+x^{2}+4x+6x+24$$

Combine -16x^{2} and x^{2} to get -15x^{2}.

$$x^{4}-15x^{2}+4x+6x+24$$

Combine 4x and 6x to get 10x.

$$x^{4}-15x^{2}+10x+24$$

Expand

$$x^{4}-15x^{2}+10x+24$$

Solution Steps

Apply the distributive property by multiplying each term of x-2 by each term of x+1.

$$\left(x^{2}+x-2x-2\right)\left(x-3\right)\left(x+4\right)$$

Combine x and -2x to get -x.

$$\left(x^{2}-x-2\right)\left(x-3\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of x^{2}-x-2 by each term of x-3.

$$\left(x^{3}-3x^{2}-x^{2}+3x-2x+6\right)\left(x+4\right)$$

Combine -3x^{2} and -x^{2} to get -4x^{2}.

$$\left(x^{3}-4x^{2}+3x-2x+6\right)\left(x+4\right)$$

Combine 3x and -2x to get x.

$$\left(x^{3}-4x^{2}+x+6\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of x^{3}-4x^{2}+x+6 by each term of x+4.

$$x^{4}+4x^{3}-4x^{3}-16x^{2}+x^{2}+4x+6x+24$$

Combine 4x^{3} and -4x^{3} to get 0.

$$x^{4}-16x^{2}+x^{2}+4x+6x+24$$

Combine -16x^{2} and x^{2} to get -15x^{2}.

$$x^{4}-15x^{2}+4x+6x+24$$

Combine 4x and 6x to get 10x.

$$x^{4}-15x^{2}+10x+24$$