#### (i) What number must be subtracted from 2x^{2} – 5x so that the resulting polynomial leaves the remainder 2 when divided by 2x + 1?

(ii) What number must be added to 2x^{3} – 7x^{2} + 2x so that the resulting polynomial leaves the remainder -2 when divided by 2x – 3?

**Solution:**

#### (i) When divided by x – 3 the polynomials x^{2} – px^{2} + x + 6 and 2x^{3} – x^{2} – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’

(ii) Find ‘a’ if the two polynomials ax^{3} + 3x^{2} – 9 and 2x^{3} + 4x + a, leaves the same remainder when divided by x + 3.

**Solution:**

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