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Question
If x − 2 is a factor of each of the following two polynomials, find the values of a in each case
(i) x3 − 2ax2 + ax − 1
(ii) x5 − 3x4 − ax3 + 3ax2 + 2ax + 4
(i) x3 − 2ax2 + ax − 1
(ii) x5 − 3x4 − ax3 + 3ax2 + 2ax + 4
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Solution
(i) Let 
be the given polynomial.
By factor theorem, if (x − 2) is a factor of f(x), then f (2) = 0
Therefore,
Thus the value of a is 7/6.
(ii) Let f(x) = x5 − 3x4 − ax3 + 3ax2 + 2ax + 4 be the given polynomial.
By the factor theorem, (x − 2) is a factor of f(x), if f (2) = 0
Therefore,
Thus, the value of a is 
.
(i) Let be the given polynomial.
By factor theorem, if (x − 2) is a factor of f(x), then f (2) = 0
Therefore,
Thus the value of a is 7/6.
(ii) Let f(x) = x5 − 3x4 − ax3 + 3ax2 + 2ax + 4 be the given polynomial.
By the factor theorem, (x − 2) is a factor of f(x), if f (2) = 0
Therefore,
Thus, the value of a is .
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