Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.
\[
-x^{3}+2 x-4 ; x+2
\]

Is $x+2$ a factor of $-x^{3}+2 x-4$ ?
Yes
No

Answer

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Answer

$\boxed{\text{Yes}}$

Steps

Step 1 ：The Factor Theorem states that a polynomial $f(x)$ has a factor $(x - k)$ if and only if $f(k) = 0$.

Step 2 ：To check if $(x + 2)$ is a factor of the polynomial $-x^3 + 2x - 4$, we need to find the value of the polynomial when $x = -2$ (since $x + 2 = 0$ when $x = -2$).

Step 3 ：Substitute $x = -2$ into the polynomial: $f(-2) = -(-2)^3 + 2*(-2) - 4 = -(-8) - 4 - 4 = 8 - 4 - 4 = 0$.

Step 4 ：Since $f(-2) = 0$, by the Factor Theorem, $(x + 2)$ is a factor of the polynomial $-x^3 + 2x - 4$.

Step 5 ：$\boxed{\text{Yes}}$

Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.\[-x^{3}+2 x-4 ; x+2\] Is $x+2$ a factor of $-x^{3}+2 x-4$ ?YesNo

Answer

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Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.
\[
-x^{3}+2 x-4 ; x+2
\]

Is $x+2$ a factor of $-x^{3}+2 x-4$ ?
Yes
No