Question

x^3-13x- 12 factors using synthetic division​

Answer 1

Answer:

$\Large\boxed{(X+1)(X+3)(X-4)}$

Step-by-step explanation:

Given:

To solve this problem, first you have to find the factors of x³-13x-12 from left to right numbers into the solution.

Solutions:

First, you have to use rational root formula.

$\Large\boxed{\textnormal{RATIONAL ROOT FORMULA}}$

A₀=12

Aₙ=1

Dividers of a₀:

$\displaystyle 1, 2, 3, 4, 5, 6, 12$

Dividers of aₙ:

$\displaystyle 1$

Make sure to use rational numbers.

$\displaystyle \pm\frac{1,2,3,4, 6, 12}{1}$

Factor it out of x+1.

$\displaystyle (X+1)\frac{x^3-13x-12}{x+1}$

Solve.

$\displaystyle \:\frac{x^3-13x-12}{x+1}\quad \frac{x^3-13x-12}{x+1}=x^2+\frac{-x^2-13x-12}{x+1}=x^2-x+\frac{-12x-12}{x+1}$

Divide the numbers from left to right.

$\displaystyle \frac{-12x-12}{x+1}:\quad \frac{-12x-12}{x+1}=-12$

$\displaystyle X^2-X-12$

Factor it out.

Solve. (Refine/simplify.)

Used distributive property.

$\Large\boxed{\textnormal{DISTRIBUTIVE PROPERTY}}$

$\displaystyle A(B+C)=AB+AC$

$\displaystyle \left(x^2+3x\right)+\left(-4x-12\right)$

Factor it out by the x+3x.

$\displaystyle xx+3x=x(x+3)$

Factor it out by the -4 or -4x-12.

$\displaystyle x\left(x+3\right)-4\left(x+3\right)$

Then, common term of x+3.

$\displaystyle (x+3)(x-4)$

$\Large\boxed{(X+1)(X+3)(X-4)}$

Hence, the correct answer is (x+1)(x+3)(x-4).