Question

Simplify (x − 4)(x2 − 2x − 3).

x3 − 6x2 + 5x + 12
x3 + 6x2 − 11x + 12
x3 + 6x2 − 11x − 12
x3 − 6x2 + 5x − 12

Answer 1

A.) x3 - 6x2 + 5x + 12

Explanation:

FOIL (First, Outer, Inner, Last)

(x-4)(x2-2x-3)

Distribute the x to everything in the other parentheses

x * x2 = x3 x * -2x = -2x^2 x * -3 = -3x

Distribute the -4 to everything in the other parentheses

-4 * x2 = -4x^2 -4 * -2x = 8x -4 * -3 = 12

Combine like terms

x3 + -2x^2 - 3x - 4x^2 + 8x + 12

x3 - 6x2 + 5x + 12

Answer 2

Answer: FIRST OPTION

Explanation:

You must keep on mind that, according the exponents properties, when you multiply two powers with equal base, you must add the exponents.

Then:

- Apply the distributive property as you can see below:

`(x*x^2)-(x*2x)-(x*3)-(4*x^2)+(4*2x)+(4*3)=x^3-2x^2-3x-4x^2+8x+12`

-Add like terms, then you obtain:

`x^3-2x^2-3x-4x^2+8x+12\\x^3-6x^2+5x+12`