Question

find the factors for x³ + 3x² - 4x -12​

Answer 1

Answer:

(x+3)(x+2)(x−2)

Step-by-step explanation:

Factor x3+3x2−4x−12

x3+3x2−4x−12

=(x+3)(x+2)(x−2)

Answer 2

Given:

$x^3\;+\;3x^2\;-\;4x\;-12$

To find:

The factors of $x^3\;+\;3x^2\;-\;4x\;-12$

Step-by-step explanation:

Let us consider $x\;=\;-1$

$f(x)\;=\;x^3\;+\;3x^2\;-\;4x\;-12$

$f(x)=(-1)^3+3(-1)^2-4(-1)-12$

$f(x)=\;-1+3+4-12=-6$

So, $(x+1)$ is not a factor

Let us consider $x=-2$

$f(x)=(-2)^3+3(-2)^2-4(-2)-12$

$f(x)=-8+12+8-12\;=\;0$

So, $(x+2)$ is a factor of $f(x)$

When we divide $f(x)$ by $(x+2)$

⇒ Quotient = $x^2+x-6$

⇒ $x^2-2x+3x-6$

⇒ $x(x-2)\;+\;3(x-2)$

⇒ $(x-2)\;(x+3)$

Answer:

Therefore, the factors of $x^3\;+\;3x^2\;-\;4x\;-12$ are $(x+2)\;(x-2)\;(x+3)$