Claudia wants to test if the binomial 3x−6 is a factor of P(x)=3x^3−9x^2+9x−6.

Question

First, she evaluates P(_[blank 1]_). After simplifying correctly, she is left with a remainder of _[blank 2]_. Based on the remainder, she correctly concludes that 3x−6 _[blank 3]_ a factor of P(x).

i need help filling in the blanks

Answer 1

No. The binomial 3x-6 would not be a factor. The factored form of P(x)=3x^3−9x^2+9x−6 is P(x)=3(x-2)(x^2-x+1)

Answer 2

(3x^3−9x^2+9x−6) / (3x-6)

all the 3's cancel

(x^3 - 3x^2 + 3x - 2) / (x - 2)

remainder is zero

3x-6 is a factor

Answer 3

thank you