ICSE Class 10th Mathematics Chapter 8 - Remainder and Factor Theorem Important Questions with Answers

Find the values of constants a and b when x – 2 and x + 3 both are the factors of expression x³ + ax² + bx – 12.

Find the value of k, if 2x + 1 is a factor of (3k + 2)x³ + (k ? 1).

Find the value of a, if x – 2 is a factor of 2x⁵ – 6x⁴ – 2ax³ + 6ax² + 4ax + 8. 

Find the values of m and n so that x – 1 and x + 2 both are factors of x³ + (3m + 1)x² + nx – 18.

When x³ + 2x² – kx + 4 is divided by x – 2, the remainder is k. Find the value of constant k.

Find the value of a, if the division of ax³ + 9x² + 4x – 10 by x + 3 leaves a remainder 5.

If x³ + ax² + bx + 6 has x – 2 as a factor and leaves a remainder 3 when divided by x – 3, find the values of a and b.

The expression 2x³ + ax² + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b.

What number should be added to 3x³ – 5x² + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?

What number should be subtracted from x³ + 3x² – 8x + 14 so that on dividing it by x – 2, the remainder is 10?