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Let’s check out your problem:
If
g
(
t
)
=
8
t
2
+
15
t
−
33
g(t) = 8t^2 + 15t - 33
g
(
t
)
=
8
t
2
+
15
t
−
33
, use synthetic division to find
g
(
−
3
)
g(-3)
g
(
−
3
)
.
View step-by-step help
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Math Problems
Precalculus
Evaluate polynomials using synthetic division
Full solution
Q.
If
g
(
t
)
=
8
t
2
+
15
t
−
33
g(t) = 8t^2 + 15t - 33
g
(
t
)
=
8
t
2
+
15
t
−
33
, use synthetic division to find
g
(
−
3
)
g(-3)
g
(
−
3
)
.
Write Coefficients and Value:
First, we write down the coefficients of
g
(
t
)
g(t)
g
(
t
)
which are
8
8
8
,
15
15
15
, and
−
33
-33
−
33
, and the value we are evaluating, which is
−
3
-3
−
3
.
Set up Synthetic Division:
Set up the synthetic division:
\newline
−
3
-3
−
3
|
8
8
8
15
15
15
−
33
-33
−
33
\newline
|
−
24
-24
−
24
27
27
27
\newline
----------------
\newline
8
8
8
−
9
-9
−
9
−
6
-6
−
6
Bring Down Leading Coefficient:
Bring down the leading coefficient to the bottom row.
\newline
−
3
-3
−
3
|
8
8
8
15
15
15
−
33
-33
−
33
\newline
|
−
24
-24
−
24
27
27
27
\newline
----------------
\newline
8
8
8
−
9
-9
−
9
−
6
-6
−
6
Multiply and Add:
Multiply
−
3
-3
−
3
by
8
8
8
and add the result to
15
15
15
, then write the result below the
15
15
15
.
\newline
−
3
∣
8
15
−
33
-3 \;|\; 8 \; 15 \; -33
−
3
∣
8
15
−
33
\newline
∣
−
24
27
\;\;\;|\;\;\;\;\;\;\; -24 \; 27
∣
−
24
27
\newline
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
----------------
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
\newline
8
−
9
−
6
\;\;\; 8 \; -9 \; -6
8
−
9
−
6
Calculate
g
(
−
3
)
g(-3)
g
(
−
3
)
:
Multiply
−
3
-3
−
3
by
−
9
-9
−
9
and add the result to
−
33
-33
−
33
, then write the result below the
−
33
-33
−
33
.
−
3
-3
−
3
|
8
8
8
15
15
15
−
33
-33
−
33
|
−
24
-24
−
24
−
3
-3
−
3
0
0
0
----------------
8
8
8
−
9
-9
−
9
−
3
-3
−
3
3
3
3
{
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