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Nonlinear Functions

SAT Math· difficulty 5/5

A degree-3 polynomial has x-intercepts at x=−1,2,4x = -1, 2, 4 and passes through (0,8)(0, 8). What is the leading coefficient?

  • A

    22

  • B

    11

    check_circle
  • C

    −1-1

  • D

    12\dfrac{1}{2}

Explanation

f(x)=a(x+1)(x−2)(x−4)f(x) = a(x+1)(x-2)(x-4). f(0)=a(1)(−2)(−4)=8a=8⇒a=1f(0) = a(1)(-2)(-4) = 8a = 8 \Rightarrow a = 1.

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