Using factor theorem, factorize the following: 6x^3 − 7x^2 − 11x + 12

Question

KnowledgeBoat · Accepted Answer

Let, f(x) = 6x3 - 7x2 - 11x + 12. Substituting, x = 1 in f(x), we get : f(1) = 6(1)3 - 7(1)2 - 11(1) + 12 = 6 - 7 - 11 + 12 = 0 Since, f(1) = 0, (x - 1) is a factor of f(x). Dividing f(x) by (x - 1), we get : ∴ 6x3 − 7x2 − 11x + 12 = (x − 1)(6x2 − x − 12) = (x − 1)(6x2 − 9x + 8x − 12) = (x − 1)[3x(2x − 3) + 4(2x − 3)] = (x − 1)(2x − 3)(3x + 4) Hence, 6x3 − 7x2 − 11x + 12 = (x − 1)(2x − 3)(3x + 4).

Mathematics

Using factor theorem, factorize the following:
6x³ - 7x² - 11x + 12

Factorisation

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Mathematics

Using factor theorem, factorize the following:6x3 - 7x2 - 11x + 12

Factorisation

Related Questions

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Using factor theorem, factorize the following:2x3 + 3x2 − 9x − 10

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

Using factor theorem, factorize the following:
6x³ - 7x² - 11x + 12

If (x³ + ax² + bx + 6) has (x - 2) as a factor and leaves a remainder 3 when divided by (x - 3), find the values of a and b.

Using factor theorem, factorize the following:
x³ + 7x² + 7x - 15

Using factor theorem, factorize the following:
2x³ + 3x² − 9x − 10

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