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

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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 .

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Similar questions

In each of the following, two polynomials, find the value of a, if x + a is a factor.

(i) $x^{3} + a x^{2}$ - 2x + a + 4

(ii) $x^{4} - a^{2} x^{2}$ + 3x - a

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

f(x) = $x^{5} + 3 x^{4} - x^{3} - 3 x^{2}$ + 5x + 15, g(x) = x + 3

x = 1

a = 2

3 x^{4} - a x^{3} + 5 x - 3

x + 2

x^{3} - 2 a x^{2} + 16

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