Question

How do I rewrite this function as a group of factors:

f(x) = g^2 - 81

* I need the steps mainly

Answer 1

hint:

a^2 - b^2 = (a-b)(a+b)

This is the difference of squares factoring rule

Answer 2

I think the factors are (g + 9) (g- 9) but I do not know how to get to them.

Answer 3

it might help to rewrite

g^2 - 81

as

g^2 - 9^2

Answer 4

then use the rule: a^2 - b^2 = (a-b)(a+b)

Answer 5

I'll try to explain it the way my teacher taught me. So you know a polynomial function looks like this

f(x)= x^2+x+n

(where n is the numeral)

in order to find the factors, you take n and multiply it with the coefficient of the x^2. Take for example, x^2+4x+4

4 x 1 = 4 (what, when added together gives you the middle coefficient of 4 and multiplies to become 4?)

2 and 2

so we have (x+2)(x+2) as factors.

in this case, your function is f(g) = g^2 - 81

the middle coefficient is 0.

you want to take 1 x -81 =-81 (what multiplied together gives you -81 but when added together gives you 0?)

-9 & 9. So, the factors are:

(g-9)(g+9)

Does that make sense?

Answer 6

So after I rewrite it as g^2 - 9^2 I just plug it into (a-b)(a+b) for my answer?

Answer 7

correct, in this case, a = g and b = 9

Answer 8

so..

a^2 - b^2 = (a-b)(a+b)

turns into

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