Use the Factor Theorem to determine whether is a factor of .
Specifically, evaluate at the proper value, and then determine whether is a factor.

is a factor of
is not a factor of

Ask by Mcguire Garza. in the United States

Mar 25,2025

Question

Use the Factor Theorem to determine whether is a factor of .
Specifically, evaluate at the proper value, and then determine whether is a factor.

is a factor of
is not a factor of

Ask by Mcguire Garza. in the United States

Mar 25,2025

UpStudy AI · Accepted Answer

1. We first evaluate $$ P(1) $$ using the polynomial
   $$
   P(x)=2x^3-4x^2-x+19.
   $$
   
2. Substitute $$ x=1 $$ into $$ P(x) $$:
   $$
   P(1)=2(1)^3-4(1)^2-1+19.
   $$
   
3. Simplify each term:
   $$
   2(1)^3=2,\quad -4(1)^2=-4,\quad -1=-1,\quad \text{and} \quad+19=+19.
   $$
   
4. Combine the terms:
   $$
   P(1)=2-4-1+19=16.
   $$
   
5. Since $$ P(1) \neq 0 $$, by the Factor Theorem, $$ x-1 $$ is not a factor of $$ P(x) $$.

Thus, the answers are:
$$
P(1)=16
$$
$$
x-1 \text{ is not a factor of } P(x).
$$
$$ P(1) = 16 $$ $$ x-1 $$ is not a factor of $$ P(x) $$

Use the Factor Theorem to determine whether is a factor of .
Specifically, evaluate at the proper value, and then determine whether is a factor.

is a factor of
is not a factor of

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Use the Factor Theorem to determine whether is a factor of . Specifically, evaluate at the proper value, and then determine whether is a factor. is a factor of is not a factor of

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Use the Factor Theorem to determine whether is a factor of .
Specifically, evaluate at the proper value, and then determine whether is a factor.

is a factor of
is not a factor of