Question

Hi guys can you help me factor these two equations?

Answer 1

Problem # 1

Not Factored: (5x^2 - 13x - 6)
Factored: (5x + 2 )(x - 3)

There is no real "work" to be shown for this, you can see that
1) Seperating 5x^2 into 5x and x will get you the equation in the form:
 (5x     ) (x      )  = 5x^2 +

2) To complete this factor you need to guess which two numbers will add together to give you - 13x and multiply to form -6 (from the original unfactored equation). The numbers that will do this are 2 and 3

3) You can plug in negative or positives of those numbers to make sure they give you the exact results you need.

For example testing -2 and 3 you will get: (5x - 2) (x + 3 ) = 5(x^2) - 2x + 15x - 6 = 5x^2 +13x - 6.  This is NOT the same as the unfactored equation. So you know -2 and 3 is the wrong choice. Choosing 2 and -3 will give you the answer instead.

As i said, there's no actual "work" to show this, you have to make guesses and try to factor it.

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Problem # 2

Not Factored: 4x^4 - 28x^3 + 48x^2
Factored: 4x^2 (x^2 - 7x + 12) =
                4x^2 (x  - 3) (x - 4)

To solve this, you factor out the 4x^2 from the entire equation. Then you can further factor the quadratic equation by seperating x^2 into (x    )(x    ) and guessing for which numbers will add to -7x and multiply to 12