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The polynomials $p (x) = a x^{2} + 3 x - 1$ and $q (x) = x^{2} + 2 x + a$ leave the same remainder when each is divided by $(x - 2)$ .
Find the value of a.

Class 9Remainder TheoremPolynomials

A1
B3
C0
D2

Step-by-Step Solution

p (2) = 4 a + 6 - 1 = 4 a + 5. q (2) = 4 + 4 + a = a + 8

. Set equal:

4 a + 5 = a + 8

, so

3 a = 3, a = 1

.

Answer: A) 1

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