If (x − 2) is a factor of (x^3 + 2x^2 − kx + 10), find the value of k. Hence, determine whether(x + 5) is also a factor of the given expression.

Question

KnowledgeBoat · Accepted Answer

Let, f(x) = x3 + 2x2 - kx + 10. Since, x - 2 is factor of f(x), thus f(2) = 0. ∴ (2)3 + 2(2)2 - k(2) + 10 = 0 ⇒ 8 + 2(4) - 2k + 10 = 0 ⇒ 8 + 8 - 2k + 10 = 0 ⇒ 26 - 2k = 0 ⇒ 2k = 26 ⇒ k = ⇒ k = 13. f(x) = x3 + 2x2 - 13x + 10 ⇒ x + 5 = 0 ⇒ x = -5. f(-5) = (-5)3 + 2(-5)2 - 13(-5) + 10 = -125 + 2(25) + 65 + 10 = -125 + 50 + 65 + 10 = 125 - 125 = 0. Since f(−5) = 0, thus (x + 5) is a factor of f(x). Hence, value of k = 13 and x - 5 is factor of x3 + 2x2 - 13x + 10.

Mathematics

If (x - 2) is a factor of (x³ + 2x² - kx + 10), find the value of k. Hence, determine whether (x + 5) is also a factor of the given expression.

Factorisation

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Mathematics

If (x - 2) is a factor of (x3 + 2x2 - kx + 10), find the value of k. Hence, determine whether (x + 5) is also a factor of the given expression.

Factorisation

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