Use factor theorem to show that (x + 2) and (2x - 3) are factors of (2x² + x - 6).
Factorisation
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Question

Use factor theorem to show that (x + 2) and (2x − 3) are factors of (2x^3 + 2x^2 − 4x − 6)

KnowledgeBoat · Accepted Answer

Let f(x) = 2x2 + x - 6 Given, Factors : (x + 2) and (2x - 3) ⇒ x + 2 = 0 and 2x - 3 = 0 ⇒ x = -2 and 2x = 3 ⇒ x = -2 and x = By factor theorem, (x - a) is a factor of f(x), if f(a) = 0. Thus, (x + 2) and (2x - 3) are factors of f(x), if f(-2) = 0 and f = 0. On dividing 2x2 + x - 6 by (x + 2), we get : ⇒ f(-2) = 2(-2)2 + (-2) - 6 = 2(4) - 2 - 6 = 8 - 2 - 6 = 8 - 8 = 0. On dividing 2x2 + x - 6 by (2x - 3), we get : Since, f(-2) = = 0. Hence, proved that x + 2 and 2x - 3 are factors of 2x2 + x - 6.

Mathematics

Use factor theorem to show that (x + 2) and (2x - 3) are factors of (2x² + x - 6).

Factorisation

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Mathematics

Use factor theorem to show that (x + 2) and (2x - 3) are factors of (2x2 + x - 6).

Factorisation

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Using factor theorem, show that:
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