Using factor theorem, factorize the following: 3x^3 + 2x^2 − 19x + 6

Question

KnowledgeBoat · Accepted Answer

Let, f(x) = 3x3 + 2x2 - 19x + 6. Substituting, x = 2 in f(x), we get : f(2) = 3(2)3 + 2(2)2 - 19(2) + 6 = 3(8) + 2(4) - 38 + 6 = 24 + 8 - 38 + 6 = 0. Since, f(2) = 0, thus (x - 2) is a factor of f(x). Dividing f(x) by (x - 2), we get : ∴ 3x3 + 2x2 - 19x + 6 = (x - 2)(3x2 + 8x - 3) = (x - 2)(3x2 + 9x - x - 3) = (x - 2)[3x(x + 3) - 1(x + 3)] = (x - 2)(3x - 1)(x + 3). Hence, 3x3 + 2x2 − 19x + 6 = (x − 2)(3x − 1)(x + 3).

Mathematics

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

Factorisation

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Mathematics

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

Factorisation

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