Question

If P(x) = 4x power 3 - 12x power 2 + 14 x -3,find the remainder when p (x) is divided by 2x-1 . Also verify that result by actual division​

Answer 1

Step-by-step explanation:

$Here, p(x) = 4 {x}^{3} - 12 {x}^{2} + 14x - 3 \: (given) \\ and \: g(x) \: = 2x - 1$

Now, zero of g(x) = 1/2

So, Putting the value of x in the p(x), we get

$p( \frac{1}{2} ) = 4{( \frac{1}{2} )}^{3} - 12{( \frac{1}{2})}^{2} + 14( \frac{1}{2} ) - 3 \\ = \frac{4}{8} - \frac{12}{4} + \frac{14}{2} - 3 \\ = \frac{1}{2} - 3 + 7 - 3 \\ = \frac{1}{2} + 1 \\ = \frac{3}{2}$

For long division refer to the image attached

Both show that remainder is same.

Hence, it is verified.

OM NAMAH SHIVAYA

Debasish Biswal