Number must be subtracted from 2×2 – 5x

(i) What number must be subtracted from 2x² – 5x so that the resulting polynomial leaves the remainder 2 when divided by 2x + 1?
(ii) What number must be added to 2x³ – 7x² + 2x so that the resulting polynomial leaves the remainder -2 when divided by 2x – 3?

Solution:

(i) When divided by x – 3 the polynomials x² – px² + x + 6 and 2x³ – x² – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’
(ii) Find ‘a’ if the two polynomials ax³ + 3x² – 9 and 2x³ + 4x + a, leaves the same remainder when divided by x + 3.

Solution:

More Solutions:

• If (x + 2) and (x – 3) are factors of x3 + ax + b.
• If (x – 2) is a factor of the expression 2×3 + ax2 + bx – 14
• If ax3 + 3×2 + bx – 3 has a factor (2x + 3) and leaves remainder – 3
• When x3 – 3×2 + 5x – 7 is divided by x – 2.
• If on dividing 4×2 – 3kx + 5 by x + 2.