Using factor theorem, show that (x − 3) is a factor of (x^3 − 7x^2 + 15x − 9). Hence, factorise the given expression completely

Question

KnowledgeBoat · Accepted Answer

Let f(x) = x3 - 7x2 + 15x - 9. We know that, (x - 3) will be the factor of f(x), if f(3) will be equal to 0. ⇒ f(3) = (3)3 - 7(3)2 + 15(3) - 9. = 27 - 63 + 45 - 9 = 72 - 72 = 0. Since, f(3) = 0, thus (x - 3) is a factor of f(x). Now, dividing f(x) by x - 3, ∴ x3 - 7x2 + 15x - 9 = (x - 3)(x2 - 4x + 3) = (x - 3)(x2 - 3x - x + 3) = (x - 3)[x(x - 3) - 1(x - 3)] = (x - 3)(x - 1)(x - 3) = (x - 3)2(x - 1). Hence, x3 - 7x2 + 15x - 9 = (x - 3)2(x - 1).

Mathematics

Using factor theorem, show that (x - 3) is a factor of (x³ - 7x² + 15x - 9). Hence, factorize the given expression completely.

Factorisation

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Mathematics

Using factor theorem, show that (x - 3) is a factor of (x3 - 7x2 + 15x - 9). Hence, factorize the given expression completely.

Factorisation

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