Question

Select all of the roots of x3 2x2 – 16x– 32. –1 –2 –4 1 4 5

Answer 1

Answer:

The roots are -2,-4 and 4

B, C and E are correct.

Step-by-step explanation:

Given: $x^3+2x^2-16x-32$

We are given a cubic polynomial. We have to find the roots of the polynomial. Roots are the x-intercept of polynomial.

First we will set the polynomial to 0 and solve for x

$x^3+2x^2-16x-32=0$

$x^2(x+2)-16(x+2)=0$

$(x+2)(x^2-16)=0$

$(x+2)(x+4)(x-4)=0$                               $\because a^2-b^2=(a+b)(a-b)$

Now, we will set each factor to zero and solve for x

$x+2=0\ \ \ \ x+4=0\ \ \ \ \ \ \ x-4=0$

$x=-2,-4,4$

Hence, The roots are -2,-4 and 4

Answer 2

In order to find the roots of the cubic equations by graphing you have to follow those steps

we have

$x^3+2x^2-16x-32$

we know that

The roots of the function are the values of x when the value of the function is equal to zero

Using a graphing tool

see the attached figure

The roots are

$x=-4\ x=-2\ x=4$

therefore

the answer is

$x=-4\ x=-2\ x=4$