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Question

If (x1) is a factor of (2x4+9x3+6x211xa), find a.

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Solution

Given that, (x1) is a factor of 2x4+9x3+6x211x9
To find out: The value of a.

Let the given polynomial be p(x).
According to the factor theorem, if (xa) is a factor of f(x), then f(a)=0.
p(1)=0
2(1)4+9(1)3+6(1)211(1)a=0
2+9+611a=0
a=6

Hence, the value of a is 6.

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