Question

The polynomials ax³ - 7x² + 7x - 2 and x³ - 2ax² + 8x - 8 when divided by x - 2 leave the remainder. Find the value of a.​

Answer 1

❍ Let f(x) = ax³ - 7x² + 7x - 2 and g(x) = x³ - 2ax² + 8x - 8.

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☆ By remainder theorem, when f(x) is divided by (x - 2), remainder = f(2), and when g(x) is divided by (x - 2), the remainder = g(2).

♩ Since the polynomials f(x) and g(x) when divided by (x - 2) leave the same remainder,

• f(2) = g(2)

≽ a.2³ - 7.2² + 7.2 - 2 = 2³ - 2a.2² + 8.2 - 8

≽ 8a - 28 + 14 - 2 = 8 - 8a + 16 - 8

≽ 16a = 32

≽ a = 32 / 16

≽ a = 2

⊛ Therefore,

• Hence, the value of a is 2.

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