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Let’s check out your problem:
If
p
(
w
)
=
9
w
2
+
22
w
−
30
p(w) = 9w^2 + 22w - 30
p
(
w
)
=
9
w
2
+
22
w
−
30
, use synthetic division to find
p
(
−
2
)
p(-2)
p
(
−
2
)
.
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Math Problems
Precalculus
Evaluate polynomials using synthetic division
Full solution
Q.
If
p
(
w
)
=
9
w
2
+
22
w
−
30
p(w) = 9w^2 + 22w - 30
p
(
w
)
=
9
w
2
+
22
w
−
30
, use synthetic division to find
p
(
−
2
)
p(-2)
p
(
−
2
)
.
Set up synthetic division:
Set up synthetic division with
−
2
-2
−
2
outside the division box and the coefficients of
p
(
w
)
p(w)
p
(
w
)
inside:
9
9
9
,
22
22
22
,
−
30
-30
−
30
.
Bring down leading coefficient:
Bring down the leading coefficient,
9
9
9
, to the bottom row.
Multiply and write result:
Multiply
−
2
-2
−
2
by
9
9
9
and write the result,
−
18
-18
−
18
, under the second coefficient,
22
22
22
.
Add coefficients:
Add the second coefficient,
22
22
22
, and the number just written,
−
18
-18
−
18
, to get
4
4
4
. Write this under the line.
Multiply and write result:
Multiply
−
2
-2
−
2
by the number just written,
4
4
4
, to get
−
8
-8
−
8
. Write this under the third coefficient,
−
30
-30
−
30
.
Add coefficients:
Add the third coefficient,
−
30
-30
−
30
, and the number just written,
−
8
-8
−
8
, to get
−
38
-38
−
38
. Write this under the line.
Find value of
p
(
−
2
)
p(-2)
p
(
−
2
)
:
The number at the bottom right,
−
38
-38
−
38
, is the value of
p
(
−
2
)
p(-2)
p
(
−
2
)
.
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