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If (x - 3)(4x + 9) = ax^2 + bx + c, then find a + b + c.

 Sep 2, 2020
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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)

 

:)

 Sep 2, 2020

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