Question

Find the remainder when p(x)=4x3-12x3+14x-3 is divided by (2x-1)

Answer 1

$\sf\huge\underline{Answer}$

The remainder is 3 respectively.

Solution :-

p(x) = 4x³ - 12x³ + 14x - 3 when divided by the linear polynomial (2x - 1)

At first, we will find out the zero of the linear polynomial (2x - 1),

=> 2x - 1 = 0

=> 2x = 1

=> x = 1/2

From the remainder theoreom, we know that p(x) when divided by (2x - 1) gives the remainder p(1/2)

Putting the value of x in p(x) :-

$= 4 {x}^{3} - 12 {x}^{3} + 14x - 3$

$= 4 \times ({ \frac{1}{2}) }^{3} - 12 \times { (\frac{1}{2}) }^{3} + 14 \times \frac{1}{2} - 3$

$= 4 \times \dfrac{1}{8} - 12 \times \dfrac{1}{8} + 7 - 3$

$= \dfrac{1}{2} - \dfrac{3}{2} + 7 - 3$

$= \dfrac{1}{2} + 7 - \dfrac{3}{2} - 3$

$= \dfrac{1 + 14 - 3 - 6}{2}$

$= \dfrac{15 - 9}{2}$

$= \dfrac{6}{2}$

$= 3$

Hence, the remainder is 3