Question
When 3x3+2x2−x+4 is divided by 3+2x the remainder is −18.
Answer: Option A
:
A
P(x)=3x3+2x2−x+4
If P(x) is divided by (x−a), then the remainder is P(a)
2x+3=0⇒x=−32
So, the remainder is the value of polynomial at −32
Substituting x=−32 in p(x)
p(−32)=3(−32)3+2(−32)2−(−32)+4
p(−32)=3(−278)+2(94)−(−32)+4
p(−32)=−818+92+32+4
p(−32)=−81+36+12+328
p(−32)=−81+808
p(−32)=−18
∴ The remainder is −18.
Thus, the given statement is true.
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:
A
P(x)=3x3+2x2−x+4
If P(x) is divided by (x−a), then the remainder is P(a)
2x+3=0⇒x=−32
So, the remainder is the value of polynomial at −32
Substituting x=−32 in p(x)
p(−32)=3(−32)3+2(−32)2−(−32)+4
p(−32)=3(−278)+2(94)−(−32)+4
p(−32)=−818+92+32+4
p(−32)=−81+36+12+328
p(−32)=−81+808
p(−32)=−18
∴ The remainder is −18.
Thus, the given statement is true.
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