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Question

When 3x3+2x2x+4 is divided by 3+2x the remainder is 18.


A

True

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B

False

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Solution

The correct option is A

True


P(x)=3x3+2x2x+4

If P(x) is divided by (xa), then the remainder is P(a)

2x+3=0x=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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