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Question

Question 17
Determine which of the following polynomial has x – 2 a factor:
(i) 3x2+6x24
(ii) 4x2+x2

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Solution

(i) Let p(x)=3x2+6x24 ….(i)
On putting x = 2 in Eq. (i) we get,
P(2)=3(2)2+6(2)24
=3×4+1224=1212=0
Therefore, x - 2 is a factor.

(ii) Let p(x)=4x2+x2 ….(ii)
On putting x = 2 in Eq. (ii) we get,
P(2)=4(2)2+22=4×4+0
=160
Hence, x – 2 is not a factor of p(x).

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