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Use synthetic division to find the quotient and remainder when
f(x)=5x^(4)-6x^(3)-5x^(2)-4x-3 is divided by
g(x)=x+9.

Use synthetic division to find the quotient and remainder when $f(x)=5 x^{4}-6 x^{3}-5 x^{2}-4 x-3$ is divided by $g(x)=x+9$ .

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Transformations of functions

Full solution

Q. Use synthetic division to find the quotient and remainder when

f(x)=5 x^{4}-6 x^{3}-5 x^{2}-4 x-3

is divided by

g(x)=x+9

.

Identify divisor: Identify the divisor for synthetic division. We are dividing by $x + 9$ , so we use $-9$ as the divisor in synthetic division.
Set up division: Set up the synthetic division. Write down the coefficients of $f(x)$ : $5$ , $-6$ , $-5$ , $-4$ , $-3$ . Place $-9$ to the left outside the division bracket.
Begin synthetic division: Begin synthetic division. Bring down the leading coefficient, $5$ , directly below the line.
Multiply and add: Multiply $-9$ by the number just written below the line $5$ , which gives $-45$ . Write this under the next coefficient $-6$ and add, resulting in $-51$ .
Repeat process: Repeat the process: Multiply $-9$ by $-51$ , giving $459$ . Add this to $-5$ , resulting in $454$ .
Continue division: Continue the process: Multiply $-9$ by $454$ , giving $-4086$ . Add this to $-4$ , resulting in $-4090$ .
Final step: Final step in synthetic division: Multiply $-9$ by $-4090$ , giving $36810$ . Add this to $-3$ , resulting in $36807$ .

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