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

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

Question

(C) Let the polynomial be $p(x) = x^{3} - ax^{2} + 6x - a$.According to the Remainder Theorem,when a polynomial $p(x)$ is divided by $(x - a)$,the rem

Vedclass · Accepted Answer

$5a$

Vedclass · Answer

(C) Let the polynomial be $p(x) = x^{3} - ax^{2} + 6x - a$.According to the Remainder Theorem,when a polynomial $p(x)$ is divided by $(x - a)$,the remainder is $p(a)$.To find the zero of the divisor $(x - a)$,we set $x - a = 0$,which gives $x = a$.Now,substitute $x = a$ into the polynomial $p(x)$:$p(a) = (a)^{3} - a(a)^{2} + 6(a) - a$$p(a) = a^{3} - a^{3} + 6a - a$$p(a) = 0 + 5a$$p(a) = 5a$Therefore,the remainder is $5a$.

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

Similar Questions

Evaluate $105 \times 106$ without multiplying directly.

Determine which of the following polynomials has $(x + 1)$ as a factor: $x^{3} + x^{2} + x + 1$.

Verify whether the following is a zero of the polynomial indicated against it:
$p(x) = x^{2}, \, x = 0$

Factorise: $27x^3 + y^3 + z^3 - 9xyz$

Divide the polynomial $3x^{4} - 4x^{3} - 3x - 1$ by $x - 1$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module