Question

Factor: 9x2 - 144x + 64
(3x + 4)(3x - 8)
(3x + 8)2
(3x - 8)2
prime

can you help me find the factors of the product taht add to e -144?

Answer 1

What is 9*64?

Answer 2

576

Answer 3

@whpalmer4 ?

Answer 4

Okay, so can you think of two numbers that multiply to 576 and add to -144?

Answer 5

Actually, what is the final object of this exercise? Are you trying to determine the properties the parabola, or are you trying to find the (x-a)(x-b) form?

Answer 6

i dont know

Answer 7

are those answer choices below the polynomial?

Answer 8

yes

Answer 9

I think you can probably reason this one out without finding the factors, given that you have choices.

If you multiply out \[(x+a)(x+b) = x^2 + ax + bx + ab\]If both a and b are positive, then the last term is positive, and the middle term as well. That eliminates one of the answer choices.

If you multiply out \[(x-a)(x+b) = x^2 - ax -bx + ab\]If you have difference like this, the last term is positive, and the middle term is negative. That fits the pattern, so that might be it: you could multiply that one out for real and see what you get.

If you multiply out \[(x+a)(x-b) = x^2 + ax - bx -ab\]here we get a negative final term, which doesn't match our problem, so that eliminates another answer choice.

That leaves the "prime" answer. It's either this or the other one you haven't eliminated, but you know how to check the other one.

Answer 10

thanks