jacobrios15:

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)

1 month ago
Angle:

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)

1 month ago
jacobrios15:

ok

1 month ago
jacobrios15:

ive never heard of any of that

1 month ago
Angle:

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

1 month ago
jacobrios15:

ok

1 month ago
Angle:

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

1 month ago
jacobrios15:

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

1 month ago
Angle:

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

1 month ago
jacobrios15:

ok thanks

1 month ago