Math, asked by shabaj7976, 1 year ago

find the remainder when p(x)=4x^3-12x^2+14x-3 is divided by g(x) = x-1/2

Answers

Answered by Anonymous
39

Answer:

By remainder theorem, we know that p(x) when divides by

 \boxed{ \sf g(x) =  \bigg(x -  \frac{1}{2}  \bigg)} \\

gives a remainder equal to

 \boxed {\sf p \bigg( \frac{1}{2}  \bigg)} \\  \\

Now,

p(x) = 4x³-12x²+14x-3

 \\  \implies \sf p \bigg( \frac{1}{2}  \bigg) = 4 \bigg( \frac{1}{2}  \bigg) {}^{3}  - 12 \bigg( \frac{1}{2}  \bigg) {}^{2}  \\  \\  \sf + 14 \bigg( \frac{1}{2} \bigg) - 3 \\  \\  \\  \implies \sf  \frac{4}{8}  -  \frac{12}{4}  +  \frac{14}{2}  - 3 \\  \\  \\  \implies \sf \frac{1}{2}  - 3 + 7 - 3 \\  \\  \\  \implies \sf \blue{ \frac{3}{2} } \\  \\

Hence, the required remainder :

 \boxed{ \sf p \bigg( \frac{1}{2}  \bigg) =  \frac{3}{2} } \\  \\

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