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If $g(t) = 8t^2 + 15t - 33$ , use synthetic division to find $g(-3)$ .

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Evaluate polynomials using synthetic division

Full solution

Q. If

g(t) = 8t^2 + 15t - 33

, use synthetic division to find

g(-3)

.

Write Coefficients and Value: First, we write down the coefficients of $g(t)$ which are $8$ , $15$ , and $-33$ , and the value we are evaluating, which is $-3$ .
Set up Synthetic Division: Set up the synthetic division: $\newline$ $-3$ | $8$ $15$ $-33$ $\newline$ | $-24$ $27$ $\newline$ ---------------- $\newline$ $8$ $-9$ $-6$
Bring Down Leading Coefficient: Bring down the leading coefficient to the bottom row. $\newline$ $-3$ | $8$ $15$ $-33$ $\newline$ | $-24$ $27$ $\newline$ ---------------- $\newline$ $8$ $-9$ $-6$
Multiply and Add: Multiply $-3$ by $8$ and add the result to $15$ , then write the result below the $15$ . $\newline$ $-3 \;|\; 8 \; 15 \; -33$ $\newline$ $\;\;\;|\;\;\;\;\;\;\; -24 \; 27$ $\newline$ $----------------$ $\newline$ $\;\;\; 8 \; -9 \; -6$
Calculate $g(-3)$ : Multiply $-3$ by $-9$ and add the result to $-33$ , then write the result below the $-33$ .
$-3$ | $8$ $15$ $-33$
| $-24$ $-3$ $0$
----------------
$8$ $-9$ $-3$ $3$
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