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11 May, 04:27

4x2 - 14x + 6

x3 - 7x2 + 12x

What is the GCF of the terms in the numerator and denominator? Rewrite the expression by factoring out any common

factors.

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Answers (1)
  1. 11 May, 06:46
    0
    Answer is given below.

    Step-by-step explanation:

    let us solve the numerator first

    =4x²-14x+6

    =2 (2x²) + 2 (-7x) + 2 (3)

    = GCF of the terms of the numerator is 2.

    denominator

    x³-7x²+12x

    x (x²) + x (-7x) + x (12)

    GCF of the terms of the denominator is x.

    factorise the numerator

    4x²-14x+6

    4x²-2x-12x + 6 (by splitting the middle term; the numbers should produce the product 4*6 and when the no. s are added they should give - 14)

    (4x²-2x) + (-12x+6)

    2x (2x-1) - 6 (2x-1)

    (2x-6) (2x-1)

    factors are

    (2x-6), (2x-1)

    denominator

    this can also be done by splitting the middle term

    x³-7x²+12x

    x³-3x²-4x²+12x

    (x³-3x²) + (-4x²+12x)

    x² (x-3) - 4x (x-3)

    (x²-4x) (x-3)

    factors are

    (x²-4x), (x-3)
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