Claudia wants to test if the binomial 3x−6 is a factor of P(x)=3x3−9x2+9x−6.
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).
Match the blanks in the previous three sentences with the word, number, or phrase that correctly completes each sentence.
12
−2
2
−278
−84
0
is not
is
First, she evaluates P(_) using the binomial 3x−6. After simplifying correctly, she is left with a remainder of _(_)_. Based on the remainder, she correctly concludes that 3x−6 _(_) a factor of P(x).
Match the blanks in the previous three sentences with the word, number, or phrase that correctly completes each sentence.
P(-2)
0
is not
To determine if the binomial 3x - 6 is a factor of P(x) = 3x^3 - 9x^2 + 9x - 6, Claudia follows these steps:
1. She evaluates P(_[blank 1]_):
To evaluate P(x), substitute 3x - 6 into the expression:
P(3x - 6) = 3(3x - 6)^3 - 9(3x - 6)^2 + 9(3x - 6) - 6.
2. After simplifying correctly, she is left with a remainder of _[blank 2]_:
Claudia simplifies the expression P(3x - 6) and divides it by 3x - 6. The resulting remainder is _[blank 2]_.
3. Based on the remainder, she correctly concludes that 3x - 6 _[blank 3]_ a factor of P(x):
If the remainder is equal to zero, then 3x - 6 is a factor; otherwise, it is not a factor.
Now, to match the blanks with the correct answers:
Blank 1: 12
Blank 2: 0
Blank 3: is
see
https://www.jiskha.com/questions/1811130/what-is-the-number-of-distinct-possible-rational-roots-of-the-polynomial