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Factor completely 6u^2-19U+15

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1 Answer

Hi Sabrina,

Since 6u2-19u+15 is a quadratic equation with a leading coefficient that's not equal to one, we have to first multiply the leading coefficient, 6 with the constant, 15. We have 6*15 = 90. We then figure what numbers multiply to 90 and add up to the middle coefficient, -19 and those would be -9 and -10. There are several methods to proceed from this point and I'll choose my favorite: plug the two numbers we just found into two binomials with 6u as the first number:

(6u-9)(6u-10).

Next, find their GCFs and write them as denominators under both binomials:

[(6u-9)/3] [(6u-10)/2]

Simplify and you're done:

(6u-9)/3 = 2u-3 and (6u-10)/2 = 3u-5. So our answer is (2u-3)(3u-5)

It's always a good idea to check your answer by FOILing it.