Q1 of 47 Page 80

Determine whether (x + 1) is a factor of the following polynomials:

2x4 + 9x3 + 2x2 + 10x + 15

Let f(x) = 2x4 + 9x3 + 2x2 + 10x + 15


By factor theorem,


x + 1 = 0 ;x = – 1


If f(– 1) = 0 then (x + 1) is a factor of f(x)


∴f(– 1) = 2(– 1)4 + 9(– 1)3 + 2(– 1)2 + 10(– 1) + 15


= 2 – 9 + 2 – 10 + 15 = 19 – 19 = 0


∴(x + 1) is a factor of f(x) = 2x4 + 9x3 + 2x2 + 10x + 15


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