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

1 Answer
Jan 2, 2018

Answer:

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

Explanation:

Zeroes of a function are values that make #f(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-3# equal to zero:

#x-3=0#

  • Add 3 to both sides

#=>x=3# (this is one of our zeroes)

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

#(x+6)^3=0#

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

#=>x+6=0#

  • Subtract 6 from both sides

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