what number should be subtracted from 2x^3-5x^2+5x so that the resulting polynomial has 2x-3
Answers
Answered by
24
Step-by-step explanation:
Let
p(x)=2x
3
−5x
2
+5x
g(x)=2x−3
and the number to be subtracted from p(x) be a, then
p
′
(x)=p(x)−a=2x
3
−5x
2
+5x−a
Consider, g(x)=0⇒2x−3=0⇒x=
2
3
∴ By factor theorem,
For g(x) to be a factor of p
′
(x)
p(
2
3
)=0
⇒2(
2
3
)
3
−5(
2
3
)
2
+5(
2
3
)−a=0
⇒
4
27
−
4
45
−
2
15
−a=0
⇒
4
27−45−30
=a
⇒a=
4
−48
=−12
Hence, −12 should be subtracted from p(x) for g(x) to be its factor.
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