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Question

Using factor theorem, show that x2+5x+6 is a factor of x4+5x3+9x2+15x+18.

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Solution

To show that x2+5x+6 is a factor of x4+5x3+9x2+15x+18

When we multiply x2+5x+6 with some other factors, we should get x4+5x3+9x2+15x+18

So, when we multiply x2+5x+6 with (x2+3) we get,

(x2+5x+6)×(x2+3)

=x4+5x3+6x2+3x2+15x+18

=x4+5x3+9x2+15x+18

Hence proved.

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