Mathematics

Question

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Let f(x) = 36x^5 − 44x^4 − 28x^3 and g(x) = 4x^2. Find f(x)/g(x) .
A. 9x^2 − 11x − 7
B. 9x^2 + 11x + 7
C. 9x^3 − 11x^2 − 7x
D. 9x^3 + 11x^2 + 7x

2 Answer

  • Answer:

    C. 9x³ − 11x² − 7x

    Step-by-step explanation:

    [tex]f(x)=36x^5-44x^4-28x^3\\\\g(x)=4x^2\\\\\dfrac{f(x)}{g(x)}=\dfrac{36x^5-44x^4-28x^3}{4x^2}\\\\\dfrac{f(x)}{g(x)}=\dfrac{(4x^2)(9x^3)-(4x^2)(11x^2)-(4x^2)(7x)}{4x^2}\\\\\dfrac{f(x)}{g(x)}=\dfrac{(4x^2)(9x^3-11x^2-7x)}{4x^2}\qquad\text{cancel}\ 4x^2\\\\\dfrac{f(x)}{g(x)}=9x^3-11x^2-7x[/tex]

  • Answer:option C is the correct answer

    Step-by-step explanation:

    f(x) = 36x^5 − 44x^4 − 28x^3

    g(x) = 4x^2

    We want to determine f(x)/g(x). It becomes

    (36x^5 − 44x^4 − 28x^3) /(4x^2)

    Looking at the numerator, each term in the numerator can divide the term in the denominator without remainder. it means that the term in the denominator is a common factor of the numerator and thus, 4x^2 can be factorized out of the numerator. It becomes

    4x^2(9x^3 − 11x^2 − 7x) /(4x^2)

    4x^2 in the numerator cancels out 4x^2 in the denominator. It becomes

    9x^3 − 11x^2 − 7x

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