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Question

Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x)

f(x) = x36x2 + 11x - 6, g(x) = x2 -3x + 2

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Solution

g(x) = x2 -3x + 2

=x2-x-2x+2

=x(x-1)-2(x-1)

=(x-1)(x-2)

If x -1 = 0, then x = 1

f(1)=(1)36(1)2+11(1)6

=1-6+11-6=12-12=0

Remainder is zero

x - 1 is a factor of f(x)

and if x - 2 = 0, then x = 2

f(2)=(2)36(2)2+11(2)6

=8-24+22-6=30-30=0

Remainder k= 0

x - 2 is also a factor of f(x)


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