Question

HELP PLEASE!! Write the polynomial in factored form and find the zeros. 2x^3 - 10x^2 - 12x

A. 2x(x+1)(x-6);x=0,-1,6

B. 2x(x-1)(x+6);x=0,-1,6

C. 2x(x+1)(x-6);x=0,1,-6

D. 2x(x-1)(x+6);x=0,1,-6

Answer 1

A. 2x(x+1)(x-6);x=0,-1,6

Explanation:

Take out 2x and factorise:

2x(x² - 5x - 6)

We can factorise (x² - 5x - 6)

What two numbers multiply to make -6 and add to give -5? That is -6 and 1 which is written as:

(x - 6)(x + 1)

Now the fully factorised polynomial is:

2x(x - 6)(x + 1)

Equate each of them to 0

2x = 0, x - 6 = 0, x + 1 = 0

Solve for x

x = 0, x = 6, x = -1