using synthetic division or remainder theorem, find the value of the polynomial for the given value of x.
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Answer:
EXAMPLE
Evaluate
3
x
2
−
9
x
+
7
3x2−9x+7 when
1.
x
=
3
x=3
2.
x
=
−
1
x=−1
Solution
1.
x
=
3
x=3
3
x
2
−
9
x
+
7
3x2−9x+7
Substitute
3
3 for
x
x
3
(
3
)
2
−
9
(
3
)
+
7
3(3)2−9(3)+7
Simplify the expression with the exponent.
3
⋅
9
−
9
(
3
)
+
7
3⋅9−9(3)+7
Multiply.
27
−
27
+
7
27−27+7
Simplify.
7
7
2.
x
=
−
1
x=−1
3
x
2
−
9
x
+
7
3x2−9x+7
Substitute
−
1
−1 for
x
x
3
(
−
1
)
2
−
9
(
−
1
)
+
7
3(−1)2−9(−1)+7
Simplify the expression with the exponent.
3
⋅
1
−
9
(
−
1
)
+
7
3⋅1−9(−1)+7
Multiply.
3
+
9
+
7
3+9+7
Simplify.
19
19