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


⇒ 23 + 3(2)2 – 4(2) – 12 = 8 + 12 – 8 – 12 = 0


∴ x – 2 is a factor


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