SOLUTION: I haven't been at school for almost two weeks and when I came back I had to take a math test on stuff I was not taught. I tried to do the best I could but I made a 49. The teacher

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Question 871202: I haven't been at school for almost two weeks and when I came back I had to take a math test on stuff I was not taught. I tried to do the best I could but I made a 49. The teacher said I could make it up by correcting the questions I got incorrect. For the problem I'm about to ask you about, I tried to solve all the answers three times for each choice and I still couldn't receive the correct answer. I finally put down "B" because it was the solution I got the farthest on.
Question:
Which of the following shows a quadratic expression and its factored form?

Answer choices:
A. Quadratic form: 4xsquared-3xsquared+1; Factored form: 4(x-3)(x+1)
B. Quadratic form: 5xsquared-10x-15; Factored form: 5(x-1)(x+3)
C. Quadratic form: -3xsquared-2x-8; Factored form: -3(x-4)(x+2)
D. Quadratic form: -2xsquared+18; Factored form: -2(x-3)(x+3)
Could you also provide a reason on why you chose the answer you got please?
Found 2 solutions by Fombitz, ewatrrr:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You need to learn the FOIL Method.
That's how you get from factors to quadratic.
Example:
%28x-3%29%28x%2B1%29
First: x%2Ax=x%5E2
Outer:x%281%29=x
Inner:-3%28x%29=-3x
Last:-3%281%29=-3
Now add it up.
%28x-3%29%28x%2B1%29=x%5E2%2Bx-3x-3
%28x-3%29%28x%2B1%29=x%5E2-2x-3
So now quickly checking, since the last two entries of the factors are (-3)(1), the constant term of the quadratic is (-3).
So now for each answer, what is the constant terms (remember there is a multiplier in front of each set of factors).
A.4%28-3%29%281%29=-12
B.5%28-1%29%283%29=-15
C.-3%28-4%29%282%29=24
D.-2%28-3%29%283%29=18
Check against the quadratic equation.
A.1%3C%3E-12
B.-15=-15 Possible
C.-8%3C%3E24
D.18=18 Possible
OK, now look at the x term, the coefficient of x is always twice the sum of the last two entries of the factor. Look at those for the possible answers from before. Again remember the multiplier in front of the factors.
B.5%282%28-1%2B3%29%29=5%282%282%29%29=20
D.-2%282%28-3%2B3%29%29=-2%282%280%29%29=0
Now compare again with the quadratic equations looking for the x term.
B. -10%3C%3E20
D.0=0 Here's your answer.
highlight%28-2x%5E2%2B18=-2%28x-3%29%28x%2B3%29%29
It's good practice to work the FOIL method forwards and backwards until you become comfortable using it.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

F	First terms

O	Outside terms

I	Inside terms

L	Last terms

A. For Ex: 4(x-3)(x+1) = 4(x^2 - 2x - 3) does NOT = 4x^2 - 3x + 1

B. Incorrect 5(x^2 - 2x - 3) = 5(x -3)(x+1) 

C. Obviously Incorrect: -3(x-4)(x+2) = -3(x^2 -2x - 8) does NOT = -3x^2 -2x - 8

D. -2x^2 + 18 = -2(x^2-9) = -2(x-3)(x+3)  YES!!!