Maths Help?

You are given a polynomial function f(x) and ask for you to “check whether the binomial (2x + 3) is a factor of f(x) or not” What do you do? Explain. 

2 Answers

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  • 1 month ago

    Set the binomial to zero and solve for x:

    2x + 3 = 0

    2x = -3

    x = -3/2

    If 2x+3 is a factor, then f(-3/2) will equal zero. Calculate f(-1.5) and see if it is zero or not, then you'll know.

    f(-3/2) = 0 --> (2x + 3) is a factor

    f(-3/2) ≠ 0 --> (2x + 3) is NOT a factor.

  • 1 month ago

    Since the zero if (2x + 3) is -3/2, if the polynomail has -3/2 as a zero, then (2x + 3) is a factor.

    Showing this with another made up binomial:

    (2x + 3)(3x² + 2x - 3)

    6x³ + 4x² - 6x + 9x² + 6x - 9

    6x³ + 13x² - 9

    Testing x = -3/2

    6(-3/2)³ + 13(-3/2)² - 9

    6(-27/8) + 13(9/4) - 9

    3(-27/4) + 13(9/4) - 9

    -81/4 + 117/4 - 9

    36/4 - 9

    9 - 9

    0

    So this shows that if -3/2 is a root to the polynomial, (2x + 3) will be a factor of it.

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