Question

Which value of z will allow both polynomials to be factored? Explain your answer.

x² - 6x + z
x² + 6x + z

Answer 1

z = 9 will allow both polynomials to be factored.

Explanation:

Perfect square binomials:

For perfect square binomials, we have that:

`(x \pm a)^2 = x^2 \pm 2ax + a^2`

x² - 6x + z

x² + 6x + z

First term of the binomial is x, and the second is:

`2ax = \pm 6x`

`2a = \pm 6`

`a = \pm (6)/(2)`

`a = \pm 3`

Value of z:

The final term is a squared, so:

`a = (\pm 3)^2 = 9`

z = 9 will allow both polynomials to be factored.