Question

I really need help with this please show work

Jay factored the 4 term polynomial x^3 - 9x + 2x^2 - 18 and decided that the complete factorization was (x+2) (x^2 - 9)

Before turning in his paper, he checked his final factorization by multiplying out his factors and was sure that he had found the correct factors. When his teacher graded his paper, she marked his answer as incorrect, but gave him one more chance to show the correct factorization.

a) What was Jay's mistake?

b) Show/describe EACH step in factoring the 4 term expression correctly and completely:

x^3 - 9x +2x^2 - 18

Answer 1

x^3 - 9x + 2x^2 - 18

It's a bit odd to write the polynomial this way. Let's sort by degree.

x^3 + 2x^2 -9x - 18

That's less confusing. Let's check Jay's factorization:

(x+2) (x^2 - 9) = x^3 + 2x^2 - 9x - 18

Seems correct.

(a) Jay's problem is that he still has more factoring to do. The second factor he has is the difference of two squares:

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

(b)

Let's factor f(x) = x^3 - 9x + 2x^2 - 18

Playing around with some small numbers we find

f(-2) = 0

so (x + 2) is a factor.

x^3 + 2x^2 -9x - 18

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

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

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