Using factor theorem, factorize the following: 2x^3 − x^2 − 13x − 6

Question

KnowledgeBoat · Accepted Answer

Let, f(x) = 2x3 − x2 − 13x − 6. Substituting, x = 3 in f(x) we get : f(3) = 2(3)3 − (3)2 − 13(3) − 6 = 2(27) − 9 − 39 − 6 = 54 − 9 − 39 − 6 = 0. Since, f(3) = 0, thus (x − 3) is factor of f(x). Dividing, f(x) by (x − 3), we get : ∴ 2x3 − x2 − 13x − 6 = (x − 3)(2x2 + 5x + 2) = (x − 3)(2x2 + 4x + x + 2) = (x − 3)[2(x + 2) + 1(x + 2)] = (x − 3)(2x + 1)(x + 2). Hence, 2x3 − x2 − 13x − 6 = (x − 3)(2x + 1)(x + 2).

Mathematics

Using factor theorem, factorize the following:
2x³ − x² − 13x − 6

Factorisation

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Mathematics

Using factor theorem, factorize the following:2x3 − x2 − 13x − 6

Factorisation

Related Questions

Using factor theorem, factorize the following:3x3 + 2x2 - 19x + 6

Using factor theorem, factorize the following:2x3 + x2 - 13x + 6

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Using factor theorem, factorize the following:
2x³ − x² − 13x − 6

Using factor theorem, factorize the following:
3x³ + 2x² - 19x + 6

Using factor theorem, factorize the following:
2x³ + x² - 13x + 6

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.

Using the remainder and factor theorems, factorize the polynomial.
x³ + 10x² - 37x + 26