Find the remainder when x^{3}-a x^{2}+6 x-a i | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

We have $p ( x )= x ^{3}- ax ^{2}+6 x - a$

$\because $   Zero of $x - a$ is $a$.                &

Vedclass · Accepted Answer

$5a$

Vedclass · Answer

We have $p ( x )= x ^{3}- ax ^{2}+6 x - a$

$\because $   Zero of $x - a$ is $a$.                                  $[\because x-a=0 \Rightarrow x=a]$

$	herefore $ $p ( a )=( a )^{3}- a ( a )^{2}+6( a )- a = a ^{3}- a ^{3}+6 a - a =0+5 a =5 a$

Thus, the required remainder $=5 a$

Find the remainder when $x^{3}-a x^{2}+6 x-a$ is divided by $x-a$.

Similar Questions

Verify whether the following are zeroes of the polynomial, indicated against them.

$p(x) = (x + 1) (x -2)$, $x = -\,1, \,2$

Find the zero of the polynomial : $p(x) = 3x$

Write the degree of each of the following polynomials :

$(i)$ $5 x^{3}+4 x^{2}+7 x$

$(ii)$ $4-y^{2}$

Without actually calculating the cubes, find the value of each of the following : $(-12)^{3}+(7)^{3}+(5)^{3}$

Classify the following as linear, quadratic and cubic polynomials :

$(i)$ $1+x$

$(ii)$ $3 t$

$(iii)$ $r^{2}$

$(iv)$ $7 x^{3}$