Q1 of 31 Page 245

For each pair of polynomial is below, check whether the first is a factor of the second. If not a factor, find the remainder on dividing the second by the first.

x + 2, x3 + 3x2 – 4x – 12

Given, a pair of polynomial as x + 2, x3 + 3x2 – 4x – 12


Need to find out the first polynomial is factor of second and if not a factor need to find the remainder


⇒ To check x + 2 is a factor of x3 + 3x2 – 4x – 12 we must substitute x = – 2 in the second polynomial, we get as follows


⇒ (– 2)3 + 3(– 2)2 – 4(– 2) – 12 = – 8 + 12 + 8 – 12 = 0


∴ x + 2 is a factor


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