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Use synthetic division to determine whether or not
(x+4) is a factor of
(-4x^(3)+21x^(2)-4x-5).

Quotient:
◻ help (formulas)
Remainder:
◻ help (numbers)

Use synthetic division to determine whether or not $(x+4)$ is a factor of $\left(-4 x^{3}+21 x^{2}-4 x-5\right)$ . $\newline$ - Quotient: $\square$ help (formulas) $\newline$ - Remainder: $\square$ help (numbers)

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Complex conjugate theorem

Full solution

Q. Use synthetic division to determine whether or not

(x+4)

is a factor of

\left(-4 x^{3}+21 x^{2}-4 x-5\right)

.

\newline

- Quotient:

\square

help (formulas)

\newline

- Remainder:

\square

help (numbers)

Replace with root: To use synthetic division, replace $(x+4)$ with its root, which is $-4$ . Set up synthetic division with $-4$ and the coefficients of the polynomial $-4x^3+21x^2-4x-5$ .
Set up synthetic division: Write down the coefficients: $-4$ , $21$ , $-4$ , $-5$ . Bring down the first coefficient, $-4$ , to the bottom row.
Write down coefficients: Multiply $-4$ by the root, which is $-4$ , and write the result under the second coefficient. $\newline$ $-4 \times -4 = 16$ .
Multiply and write result: Add the second coefficient, $21$ , and the result from the previous step, $16$ , to get $37$ . Write $37$ in the bottom row.
Add and write result: Multiply the root, $-4$ , by $37$ and write the result under the third coefficient. $\newline$ $-4 \times 37 = -148$ .
Multiply and write result: Add the third coefficient, $-4$ , and the result from the previous step, $-148$ , to get $-152$ . Write $-152$ in the bottom row.
Add and write result: Multiply the root, $-4$ , by $-152$ and write the result under the fourth coefficient. $\newline$ $-4 \times -152 = 608$ .
Multiply and write result: Add the fourth coefficient, $-5$ , and the result from the previous step, $608$ , to get $603$ . Write $603$ in the bottom row. This is the remainder.
Add and write result: If the remainder is $0$ , then $(x+4)$ is a factor of the polynomial. $\newline$ Since the remainder is $603$ , which is not $0$ , $(x+4)$ is not a factor of the polynomial.

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