ACT Math · Polynomial and rational functions

What are the zeros of f(x) = (2x - 6)(x + 4)?

What are the zeros of f(x)=(2x−6)(x+4)f(x) = (2x - 6)(x + 4)?

Answer and explanation

Answer: F: x = 3, -4

The zeros of a product are the values that make a factor zero. Setting 2x−6=02x-6=0 gives 2x=62x=6, so x=3x=3. Setting x+4=0x+4=0 gives x=−4x=-4. The zeros are 33 and −4-4, choice F. Choice H (6,−46,-4) forgets to divide by 22 in the first factor. Choice G (−3,4-3,4) has the signs of both zeros reversed. Choice J (3,43,4) reverses only the sign of the second. Check: f(3)=0⋅7=0f(3)=0\cdot7=0 and f(−4)=(−14)(0)=0f(-4)=(-14)(0)=0. A factor (x+4)(x+4) gives a zero at −4-4, not 44.

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