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Algebra/Algebraic Expression

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Question
How do I factorize 2y²-7y+6? Thank you.

Answer
Note that 2 = 1*2 and note that 6 = 1*6 or 6 = 2*3.

If 1,6 is tried, the middle would be -1*1 - 2*6 = -12 or -1*6 - 3*2 = -12.
If we use 2,3 we get -1*2 - 2*3 = 2-6 = -8 or -1*3 - 2*2 = -7, which is it.

This means it is (2y-3)(y-2).
Note that 2y*y = 2y², -3(-2) = 6, and 2y(-2) - 3(y) = -4y - 3y = -7y.

Looking back at the original, this is what you get.

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