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Question

Question 16
Show that:
(i) x + 3 is a factor of 69+11xx2+x3.

(ii) 2x – 3 is a factor of x+2x39x2+12.

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Solution

(i) Let p(x)=x3x2+11x+69
We have to show that, x + 3 is a factor of p(x).
i.e. p(-3) = 0 [Using Remainder Theorem]
Now, p(3)=(3)3(3)2+11(3)+69
=27933+69=69+69=0.
Therefore, x +3 is a factor.

(ii) p(x)=2x39x2+x+12
We have to show that, 2x - 3 is a factor of p(x).
i.e. p(32)=0 [Using Remainder Theorem]
p(32)=2(32)39(32)2+32+12
=274814+32+12
=81814=0
Hence, (2x-3) is a factor of p(x).

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