Question

I NEED HELP ASAP PLEASE!!

Describe how to factor the polynomial that is a difference of two squares completely. Identify the zeros of the equation and the x-intercepts. (4x^2 - 9)

Answer 1

(2x-3) (2x+3)

zeros, x intercepts: -3/2, 3/2

Explanation:

4x^2 -9

We know the difference of squares is a^2 -b^2

This factors into (a-b) (a+b)

Let 4x^2 =a^2

Taking the square root

2x =a

Let b^2 =9

Taking the square root

b= 3

(4x^2-9 ) = (2x-3) (2x+3)

To find the zeros, we set the equation equal to zero

(4x^2-9 ) = (2x-3) (2x+3) =0

Using the zero product property

2x-3 =0 and 2x+3 =0

2x-3+3 = 0+3 2x+3-3 = 0-3

2x=3 2x=-3

Divide by 2

2x/2 = 3/2 2x/2 = -3/2

x = 3/2 x = -3/2

These are the zeros of the equation (which are also the x intercepts)