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Let’s check out your problem:
If
h
(
t
)
=
11
t
2
−
26
t
−
3
h(t) = 11t^2 - 26t - 3
h
(
t
)
=
11
t
2
−
26
t
−
3
, use synthetic division to find
h
(
3
)
h(3)
h
(
3
)
.
View step-by-step help
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Math Problems
Precalculus
Evaluate polynomials using synthetic division
Full solution
Q.
If
h
(
t
)
=
11
t
2
−
26
t
−
3
h(t) = 11t^2 - 26t - 3
h
(
t
)
=
11
t
2
−
26
t
−
3
, use synthetic division to find
h
(
3
)
h(3)
h
(
3
)
.
Set Up Synthetic Division:
We need to set up synthetic division with
3
3
3
as the root we're testing.
\newline
Write down the coefficients of
h
(
t
)
h(t)
h
(
t
)
:
11
11
11
,
−
26
-26
−
26
, and
−
3
-3
−
3
.
Place Root and Coefficients:
Place the root (
3
3
3
) on the left side and the coefficients on the right side to start synthetic division.
Bring Down First Coefficient:
Bring down the first coefficient (
11
11
11
) as is.
Multiply and Write Result:
Multiply the root
3
3
3
by the number we just brought down
11
11
11
and write the result
33
33
33
under the next coefficient
−
26
-26
−
26
.
Add Numbers in Second Column:
Add the numbers in the second column
(
−
26
+
33
)
(-26 + 33)
(
−
26
+
33
)
to get
7
7
7
. Write this number below the line.
Multiply and Write Result:
Multiply the root
3
3
3
by the new number we got
7
7
7
and write the result
21
21
21
under the next coefficient
−
3
-3
−
3
.
Add Numbers in Third Column:
Add the numbers in the third column
(
−
3
+
21
)
(-3 + 21)
(
−
3
+
21
)
to get
18
18
18
. Write this number below the line.
Find Remainder:
The number at the bottom (
18
18
18
) is the remainder, which represents the value of
h
(
3
)
h(3)
h
(
3
)
.
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