Using the remainder theorem, factorise each of the following completely :
2x³ + x² - 13x + 6

Question

Using the remainder theorem, factorise each of the following completely : 2x³ + x² - 13x + 6

KnowledgeBoat · Accepted Answer

For x = 2, the value of 2x³ + x² - 13x + 6 = 2(2)³ + (2)² - 13(2) + 6 = 2(8) + 4 - 26 + 6 = 26 - 26 = 0. On dividing 2x³ + x² - 13x + 6 by (x - 2), we get, quotient = 2x² + 5x - 3 Factorising, 2x² + 5x - 3 = 2x² + 6x - x - 3 = 2x(x + 3) - 1(x + 3) = (2x - 1)(x + 3) ∴ 2x² + 5x - 3 = (2x - 1)(x + 3) Hence, 2x³ + x² - 13x + 6 = (x - 2)(2x - 1)(x + 3).

Mathematics

Using the remainder theorem, factorise each of the following completely :
2x³ + x² - 13x + 6

Factorisation

Related Questions

Using Factor Theorem, show that :
(x + 5) is a factor of 2x³ + 5x² - 28x - 15. Hence, factorise the expression 2x³ + 5x² - 28x - 15 completely.

Using the remainder theorem, factorise each of the following completely :
3x³ + 2x² - 19x + 6

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

Using the remainder theorem, factorise each of the following completely :
4x³ + 7x² - 36x - 63

Mathematics

Using the remainder theorem, factorise each of the following completely :2x3 + x2 - 13x + 6

Factorisation

Related Questions

Using Factor Theorem, show that :(x + 5) is a factor of 2x3 + 5x2 - 28x - 15. Hence, factorise the expression 2x3 + 5x2 - 28x - 15 completely.

Using the remainder theorem, factorise each of the following completely :3x3 + 2x2 - 19x + 6

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

Using the remainder theorem, factorise each of the following completely :4x3 + 7x2 - 36x - 63

Using the remainder theorem, factorise each of the following completely :
2x³ + x² - 13x + 6

Using Factor Theorem, show that :
(x + 5) is a factor of 2x³ + 5x² - 28x - 15. Hence, factorise the expression 2x³ + 5x² - 28x - 15 completely.

Using the remainder theorem, factorise each of the following completely :
3x³ + 2x² - 19x + 6

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

Using the remainder theorem, factorise each of the following completely :
4x³ + 7x² - 36x - 63