Using Remainder Theorem, find the value of k if on dividing 2x³ + 3x² - kx + 5 by (x - 2), leaves a remainder 7.
Factorisation
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Using Remainder Theorem, find the value of k if on dividing 2x^3 + 3x^2 − kx + 5 by (x − 2), leaves a remainder 7.

KnowledgeBoat · Accepted Answer

By remainder theorem, If f(x) is divided by (x - a), then remainder = f(a). Let f(x) = 2x3 + 3x2 - kx + 5 Given, Remainder = 7 Divisor : ⇒ x - 2 = 0 ⇒ x = 2 Substituting x = 2 in f(x), gives remainder 7. ⇒ f(2) = 7 ⇒ 2(2)3 + 3(2)2 - k(2) + 5 = 7 ⇒ 2(8) + 3(4) - 2k + 5 = 7 ⇒ 16 + 12 - 2k + 5 = 7 ⇒ -2k + 33 = 7 ⇒ 2k = 33 - 7 ⇒ 2k = 26 ⇒ k = ⇒ k = 13. Hence, the value of k is 13.

Mathematics

Using Remainder Theorem, find the value of k if on dividing 2x³ + 3x² - kx + 5 by (x - 2), leaves a remainder 7.

Factorisation

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Mathematics

Using Remainder Theorem, find the value of k if on dividing 2x3 + 3x2 - kx + 5 by (x - 2), leaves a remainder 7.

Factorisation

Related Questions

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Using remainder theorem, find the remainder when:
f(x) = 8x² - 2x - 15 is divided by (2x + 3).

On dividing (ax³ + 9x² + 4x - 10) by (x + 3), we get 5 as remainder. Find the value of a.

If the polynomials 2x³ + ax² + 3x - 5 and x³ + x² - 2x + a leave the same remainder when divided by (x - 2), find the value of a. Also, find the remainder in each case.

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