Q2 of 274 Page 91

Find the remainder when p (x) = 4x3 + 8x2 – 17x + 10 is divided by (2x – 1).

We have,

p (x) = 4x3 + 8x2 – 17x + 10


Also, 2x – 1 = 0


2x = 1


x =


∴ p () = 4 ()3 + 8 ()2 – 17 () + 10


= 4 × + 8 × - 17 × + 10


= + 2 – + 10


= + 12


= + 12


= - 8 + 12


= 4


Hence, remainder = 4


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Match the following columns:























Column I



Column II



(a) If p (x) = 81x4 + 54x3 - 9x2 – 3x + 2 is divided by (3x + 2), then remainder = ……



(p) 1



(b) p (x) = ax3 + 3x2 – 3 and q (x) = 2ax3 – 5x + a divided by (x – 4) leave the same remainder. Then, a = …..



(q) -7



(c) If p (x) = 7x2 - 4x + c is completely divisible by (x - ), then c = …..



(r) 0



(d) If q (x) = 2x3 + bx2 + 11x + b + 3 is divisible by (2x – 1), then b = …..



(s) – 6



The correct answer is:


(a)-……., (b)-……., (c)-……., (d)-…….,

 1

Let Find p(-2).

 3

If (x – 2) is a factor of 2x3 – 7x2 + 11x + 5a, find the value of a.

 4

For what value of m, p(x) = (x3 – 2mx2 + 16) is divisible by (x + 2)?