help plss and explain!! If 7x^2 – mx-12 is equal to (7x + n)(x-6), where m and n are constants, find the value of m.

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help plss and explain!!

If 7x^2 – mx-12 is equal to (7x + n)(x-6), where m and n are constants, find the value of m.

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Philomena 5 years 2021-07-18T16:26:42+00:00 1 Answers 20 views 0

Answers ( )

  1. thnahdat
    0
    2021-07-18T16:27:59+00:00
    Reply

    Answer:

    m=40

    Problem:

    If 7x^2 – mx-12 is equal to (7x + n)(x-6), where m and n are constants, find the value of m.

    Step-by-step explanation:

    We want to find n amd m such that

    (7x+n)(x-6)=7x^2-mx-12.

    Since (ax+b)(cx+d)=acx^2+(ad+bc)x+bd, then we need or should have the following:

    (7x)(x)=7x^2

    (7×-6+n×1)x=-mx

    (n)(-6)=-12

    The bottom equation tells us n=2 since 2(-6)=-12.

    The first equation is already true.

    Now we must solve (7×-6+n×1)x=-mx with n=2 for m.

    That is we need to solve 7×-6+2×1=-m

    Simplify and done -m=-42+2=-40 so m=40.

    Let’s do a check

    7x^2 – mx-12 is equal to (7x + n)(x-6)

    7x^2-40x-12 is equal to (7x+2)(x-6)

    (7x+2)(x-6)=7x(x)+7x(-6)+2(x)+2(-6)

    (7x+2)(x-6)=7x^2-42x+2x-12

    (7x+2)(x-6)=7x^2-40x-12 and that is what we wanted.

    Another way:

    We want (7x+n)(x-6)=7x^2-mx-12 to be true for all x.

    So if x=0 or for x=1, we want the equation to be true.

    Insert x=0. This gives (n)(-6)=-12 which implies n=2.

    (7x+2)(x-6)=7x^2-mx-12

    Insert x=1. This gives (7+2)(1-6)=7-m-12.

    Simplify both sides: 9(-5)=-m-5

    Continue to simplify left side: -45=-m-5

    Add 5 on both sides: -40=-m

    Multiply both sides by -1: 40=m

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