How do you find all the zeros of f(x) = 4(x-3)(x+6)^3 f(x)=4(x−3)(x+6)3?

1 Answer
Jacobi J.
Jan 2, 2018

x=3x=3 and x= -6x=−6 are zeroes to this polynomial function. Try plugging the zeroes into the function and f(x)f(x) will evaluate to 0.

Explanation:

Zeroes of a function are values that make f(x)=0f(x)=0. If three terms are being multiplied and the product is 0, at least one of the terms has to be equal to 0.

Let's set x-3x−3 equal to zero:

x-3=0x−3=0

  • Add 3 to both sides

=>x=3⇒x=3 (this is one of our zeroes)

Let's set (x+6)^3(x+6)3 equal to zero

(x+6)^3=0(x+6)3=0

  • Take the cube root of both sides (cube root of zero is zero)

=>x+6=0⇒x+6=0

  • Subtract 6 from both sides

=>x= -6⇒x=−6 (this is our second zero to our function)

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