Answer: Choice E
multiply to give a*c and add to get b
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This is known as the AC factoring method based on how you multiply the first and last coefficients (a and c) and use that product to figure out which factors add to the middle coefficient.
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An example:
6x^2 + 35x + 50
We have a = 6, b = 35, c = 50
Multiply a and c and we get: a*c = 6*50 = 300
We need to find factors of 300 that pair up and add to 35
Through trial and error you should find,
15 * 20 = 300
15 + 20 = 35
The two numbers are therefore 15 and 20.
So we break 35x into 15x+20x and use the factor by grouping method
6x^2 + 35x + 50
6x^2 + 15x + 20x + 50
(6x^2 + 15x) + (20x + 50)
3x(2x + 5) + 10(2x + 5)
(3x + 10)(2x + 5)
We see that 6x^2 + 35x + 50 factors to (3x + 10)(2x + 5)
Use the FOIL method or the box method or distribution to help see that (3x + 10)(2x + 5) expands back to 6x^2 + 35x + 50.
