: Divide the polynomials using Long Division. Show your solution.
1. x3 + 4x2 - 6x + 3 divided by x - 31. x3 + 4x2 - 6x + 3 divided by x - 3
2. 2x4 - 11x2 + 4 divided by x + 2
3. 4x6 - 3x + 1 divided by x - 1
Answers
Answered by
1
Step-by-step explanation:
Here, g(x)=3x−1. To apply Remainder theorem, (3x−1) should be converted to (x−a) form.
∴3x−1=
3
1
(3x−1)=x−
3
1
∴g(x)=(x−
3
1
)
By remainder theorem, r(x)=p(a)=p(
3
1
)
p(x)=x
3
−6x
2
+2x−4⇒p(
3
1
)=(
3
1
)
3
−6(
3
1
)
2
+2(
3
1
)−4
=
27
1
−
9
6
+
3
2
−4=
27
1−18+18−108
=
27
−107
∴ the remainder p(
3
1
)=−
27
107
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