Factorize completely using factor theorem : 2x3 - x2 - 13x - 6.

Question

KnowledgeBoat · Accepted Answer

Substituting x = -2 in 2x3 - x2 - 13x - 6, we get : ⇒ 2(-2)3 - (-2)2 - 13(-2) - 6 ⇒ 2(-8) - 4 + 26 - 6 ⇒ -16 - 4 + 20 ⇒ -20 + 20 ⇒ 0. ∴ x + 2 is a factor of the polynomial 2x3 - x2 - 13x - 6. Dividing, 2x3 - x2 - 13x - 6 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).

Weight (in kg)	Number of students
28-30	2
30-32	4
32-34	10
34-36	13
36-38	15
38-40	9
40-42	5
42-44	2

Mathematics

Factorize completely using factor theorem : 2x³ - x² - 13x - 6.

Factorisation

ICSE 2023

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