+1094 If (x - 3)(4x + 9) = ax^2 + bx + c, then find a + b + c.
When you see a factored form going into a quadratic, what do you do? Of course, you multiply!
(x - 3)(4x + 9)
How do you multiply, you ask? Remember 5th grade, when the teacher taught all about the distributive property? This is just like that: you take one variable from one group, and multiply it with the other two from the other group.
x * 4x = 4x^2
x * 9 = 9x
-3 * 4x = -12x
-3 * 9 = -27
So, now that we multiplied, what do we do? Did you just say, Combine Like Terms? If you did.....you are correct! So...combine we go:
Degree 2: 4x^2
Degree 1: 9x - 12x = -3x
Constant: -27
Together, this is 4x^2 - 3x - 27.
But, that is not what we are looking for, right? We want to find a + b + c. Is that hard? No:
4 - 3 - 27 = -26
There you go, you have the answer.
The takeaway:
Whenever you see that something should be expanded, EXPAND IT! (unless you could use the binomial theorem or specified)
:)
