Find the value of p for which f(x)=2 3 -p 2+6x-3p is exactly divisible by (x+2).
Answers
Answer:
Step-by-step explanation:
p ( 3 ) will be the remainder of both polynomials
f(x)=2 3 -p 2+6x-3p
The remainder for the first polynomial
p ( 3 ) = x^3 + px^2 + x + 6
= ( 3 )^3 + p ( 3 )^2 + ( 3 ) + 6 .
= 27 + 9p + 3 + 6
= 9p + 36
so the remainder is 9p + 36
The remainder for the second polynomial us given by
p ( 3 ) = 2x^3 - x^2 + ( P + 3 )x - 6
= 2 ( 3 )^3 - ( 3 )^2 + ( P + 3 )3 - 6
= 2 × 27 - 9 + 3p + 9 - 6
= 54 - 6 + 3p
= 3p + 48
The remainders are given same
so we get equation
9p + 36 = 3p + 48
9p - 3p = 48 - 36
6p = 12
p = 12/6
p = 2
so the value of p is 2
Answer:
Given polynomial x
3
−px
2
+6x−p divided by x−p
If divided by x−p then x−p=0 or x=p
Replace x by p we get
q(x)=x
3
−px
2
+6x−p
q(p)=(p)
3
−p(p)
2
+6(p)−p
⇒q(p)=p
3
−p
3
+6p−p
⇒q(p)=5p.
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