Using the remainder theorem, factorise each of the following completely :
3x³ + 2x² - 23x - 30

Question

Using the remainder theorem, factorise each of the following completely : 3x³ + 2x² - 23x - 30

KnowledgeBoat · Accepted Answer

For x = -2 the value of 3x³ + 2x² - 23x - 30, = 3(-2)³ + 2(-2)² - 23(-2) - 30 = 3(-8) + 2(4) + 46 - 30 = -24 + 8 + 46 - 30 = 54 - 54 = 0. Hence, (x + 2) is the factor of 3x³ + 2x² - 23x - 30. On dividing 3x³ + 2x² - 23x - 30 by x + 2, we get, quotient = 3x² - 4x - 15 Factorising, 3x² - 4x - 15 = 3x² - 9x + 5x - 15 = 3x(x- 3) + 5(x - 3) = (3x + 5)(x - 3). ∴ 3x² - 4x - 15 = (3x + 5)(x - 3). Hence, 3x³ + 2x² - 23x - 30 = (x + 2)(3x + 5)(x - 3).

Mathematics

Using the remainder theorem, factorise each of the following completely :
3x³ + 2x² - 23x - 30

Factorisation

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Mathematics

Using the remainder theorem, factorise each of the following completely :3x3 + 2x2 - 23x - 30

Factorisation

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