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 = 2 in f(x) we get : f(2) = 2(2)3 + (2)2 - 13(2) + 6 = 2(8) + 4 - 26 + 6 = 16 + 4 - 26 + 6 = 0. Since, f(2) = 0, thus (x - 2) is factor of f(x). Dividing, f(x) by (x - 2), we get : ∴ 2x3 + x2 - 13x + 6 = (x - 2)(2x2 + 5x - 3) = (x - 2)(2x2 + 6x - x - 3) = (x - 2)[2x(x + 3) - 1(x + 3)] = (x - 2)(2x - 1)(x + 3). Hence, 2x3 + x2 − 13x + 6 = (x − 2)(2x − 1)(x + 3).

Mathematics

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

Factorisation

Related Questions

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

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.

Mathematics

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

Factorisation

Related Questions

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

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

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

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.