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Is it possible to factor this problem?

14x(squared)-23x+8

Sorry couldn't find carrot symbol. And factor this as much as possible. Please and thanks.

2 Answers

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  • 7 years ago
    Favorite Answer

    It's usually above the 6...So shift and 6 keys together

    Consider the product of the x^2 coefficient and the constant

    8 * 14 = 112

    look at the factors of 112

    8 and 14, but their sum is 22

    4 and 28, but sum is 32

    2 and 56, their sum is 58

    7 and 16, their sum is 23 --- this is the one we're looking for!

    Sum, because 8 is +8, and a positive times a positive is positive and negative times a negative is a positive. If the sign of the constant was a negative, we'd loom at the difference.

    and because the coefficient in from of the x factor is negative, they both have to be negative (ie -7 and -16)

    so: 14x^2 -7x -16x + 8

    ==> 7x((2x -1) - 8(2x -1)

    ==> (2x-1)(7x -8)

    Multiply out ==> 14x^2 -16x -7x + 8 = 14x^2 - 23x + 8 which is what we started with.

  • 7 years ago

    14x^2-23x+8 = 14x^2-16x - 7x+8

    = 2x(7x-8) -1(7x - 8) = (2x-1)(7x-8)

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