Show that (x − 3) is a factor of (2x^3 − 3x^2 − 11x + 6) and hence factorise (2x^3 − 3x^2 − 11x + 6)

Question

KnowledgeBoat · Accepted Answer

Let f(x) = 2x3 - 3x2 - 11x + 6 Substituting x = 3 in f(x), we get : f(3) = 2(3)3 - 3(3)2 - 11(3) + 6 = 54 - 27 - 33 + 6 = 60 - 60 = 0. Since f(3) = 0, thus (x − 3) is a factor of 2x3 - 3x2 - 11x + 6. Now, dividing f(x) by x - 3, ∴ 2x3 - 3x2 - 11x + 6 = (x - 3)(2x2 + 3x - 2) = (x - 3)(2x2 + 4x - x - 2) = (x - 3)[2x(x + 2) - 1(x + 2)] = (x - 3)(2x - 1)(x + 2). Hence, 2x3 - 3x2 - 11x + 6 = (x - 3)(2x - 1)(x + 2).

Mathematics

Show that (x - 3) is a factor of (2x³ - 3x² - 11x + 6) and hence factorize (2x³ - 3x² - 11x + 6).

Factorisation

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If 2x³ - 3x² - 3x + 2 = (2x - 1)(x² + ax + b)
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Mathematics

Show that (x - 3) is a factor of (2x3 - 3x2 - 11x + 6) and hence factorize (2x3 - 3x2 - 11x + 6).

Factorisation

Related Questions

Using factor theorem, show that (x - 3) is a factor of (x3 - 7x2 + 15x - 9). Hence, factorize the given expression completely.

Using factor theorem, show that (x - 4) is a factor of (2x3 + x2 - 26x - 40) and hence factorize (2x3 + x2 - 26x - 40).

Show that (3x + 2) is a factor of (6x3 + 13x2 - 4) and hence factorize (6x3 + 13x2 - 4).

If 2x3 - 3x2 - 3x + 2 = (2x - 1)(x2 + ax + b)(a) using Remainder and Factor theorem, find the value of ‘a’ and ‘b’.(b) hence, factorise the polynomial 2x3 - 3x2 - 3x + 2 completely.

Show that (x - 3) is a factor of (2x³ - 3x² - 11x + 6) and hence factorize (2x³ - 3x² - 11x + 6).

Using factor theorem, show that (x - 3) is a factor of (x³ - 7x² + 15x - 9). Hence, factorize the given expression completely.

Using factor theorem, show that (x - 4) is a factor of (2x³ + x² - 26x - 40) and hence factorize (2x³ + x² - 26x - 40).

Show that (3x + 2) is a factor of (6x³ + 13x² - 4) and hence factorize (6x³ + 13x² - 4).

If 2x³ - 3x² - 3x + 2 = (2x - 1)(x² + ax + b)
(a) using Remainder and Factor theorem, find the value of ‘a’ and ‘b’.
(b) hence, factorise the polynomial 2x³ - 3x² - 3x + 2 completely.