Practice30 Create account

Find the values of a and b so that $x^{4} + x^{3} + 8 x^{2}$ + ax + b is exactly divisible by $x^{2} + 1$ .
What is the value of a?

Class 10Division AlgorithmAlgebra — Polynomials

A2
B0
C3
D1

Step-by-Step Solution

Dividing

x^{4} + x^{3} + 8 x^{2}

+ ax +

b

by

x^{2} + 1

gives quotient

x^{2} + x + 7

and remainder

(a - 1) x + (b - 7)

. For exact division,

a - 1 = 0

so

a = 1

.

Answer: D) 1

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Division Algorithm practice questions

More Class 10 Division Algorithm practice

Find the values of a and b so that x^4 + x^3 + 8x^2 + ax + b is exactly divisible by x^2…Two of the zeroes of x^4 - 6x^3 - 26x^2 + 138x - 35 are 2 + √3 and 2 - √3. The product…Continuing: x^4 - 6x^3 - 26x^2 + 138x - 35 is divided by x^2 - 4x + 1. What is the…On dividing p(x) by g(x) = x^2 - 3, a student gets quotient (x + 1) and remainder (2x -…In the Division Algorithm for polynomials, p(x) = g(x) x q(x) + r(x). What does p(x)…