Question

Factor completely.

5x2 - 45
a-5(x + 3)(x - 3)
b-5(x2 - 45)
c-5(x - 9)(x + 9)
d-(5x + 9)(x - 5)

Answer 1

Here's the reasoning behind this:

the "Greatest Common Factor" or "GCF" of (5) and (45) is (5)

this means that
5x^2 - 45 = 5*(x^2 - 9)

then, there is a formula that looks like this (a^2 - b^2) = (a - b)(a + b)
in our case, (x^2 - 9) = (x^2 - 3^2) = (x - 3)(x + 3)

Answer 2

ok

Answer 3

ive never heard of any of that

Answer 4

it is a specific case of the Distributive Property
(a - b)(a + b) = a*(a + b) - b*(a + b) = a*a + a*b - b*a - b*b = a^2 - b^2

Answer 5

ok

Answer 6

so with those steps we get that 5x^2 - 45 = 5*(x^2 - 9) = 5*(x - 3)(x + 3)

Answer 7

in the end shouldnt it be (x+3)(x-3)

Answer 8

oh yeah mhmm

things that are multiplied like that can be flipped around without any problems

it's like how 2 times 5 is the same as 5 times 2

Answer 9

ok thanks