Question

find one of the factors when (a+3)^2 - 3(a+3)-18 is factored completely?

a.a+6
b.a+3
c.a-6
d.a-2

Answer 1

a^2 + 9 - 3a - 9 - 18

solve :)

Answer 2

?

Answer 3

Doing a slight change of variable, if we let x = a + 3, then the equation becomes;\[x^2-3x-18\]Now we need to think of two numbers that multiply to -18, and add up to -3.

Answer 4

-6 , 3?

Answer 5

Right :) so we now have:\[x^2-3x-18=(x-6)(x+3)\], but originally we had x = a+3, so putting that back in gives:\[(x-6)(x+3)=(a+3-6)(a+3+3)=(a-3)(a+6)\]

Answer 6

Note: we really didnt have to do the variable substitution. Whenever you have things like:\[a(junk)^2+b(junk)+c=0\], and whatever is inside the parenthesis is the same, you can always treat it like:\[ax^2+bx+c=0\], factor it, and replace x with the junk.