Using factor theorem, factorize the following: 2x^3 + 19x^2 + 38x + 21

Question

KnowledgeBoat · Accepted Answer

Let, f(x) = 2x3 + 19x2 + 38x + 21. Substituting, x = −1 in f(x), we get : f(-1) = 2(-1)3 + 19(-1)2 + 38(-1) + 21 = 2(-1) + 19(1) - 38 + 21 = -2 + 19 - 38 + 21 = 0. Since, f(−1) = 0, (x + 1) is a factor of f(x). Dividing f(x) by (x + 1), we get : ∴ 2x3 + 19x2 + 38x + 21 = (x + 1)(2x2 + 17x + 21) = (x + 1)(2x2 + 14x + 3x + 21) = (x + 1)[2x(x + 7) + 3(x + 7)] = (x + 1)(x + 7)(2x + 3) Hence, 2x3 + 19x2 + 38x + 21 = (x + 1)(x + 7)(2x + 3).

Mathematics

Using factor theorem, factorize the following:
2x³ + 19x² + 38x + 21

Factorisation

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Mathematics

Using factor theorem, factorize the following:2x3 + 19x2 + 38x + 21

Factorisation

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