Question

Factorize using factor theorem: 2x³ - x² - 11x + 10.​

Answer 1

ANSWER :-

$p(x) = 2 {x}^{3} - {x}^{2} - 11x + 10 \\ p(1) = 2(1) - 1 - 11 + 10 \\ p(1)= 12 - 12 = 0$

Answer is (x-1)

HOPE THIS HELPS YOU!!!!!!!!!

Answer 2

Answer:

Given to Factorise:-

2x³ - x² - 11x + 10

Using factor theoram:-

x-2 is a factor of 2x³ - x² - 11x + 10

f(-x)

x=2

Checking whether it is a factor:-

$= 2 \times { 2}^{3} - { (2)}^{2} - 11( 2) + 10 = 0$

$= 16 - 4 - 22 + 10 = 0$

$= 12 - 12 = 0$

0=0

Hence ,x-2 is a factor of 2x³ - x² - 11x + 10

Dividing 2x³ - x² - 11x + 10 by x-2

• Refer to the attachment for working.

Factorising the remaining part:-

$(x - 2)( {2x}^{2} + 3x - 5)$

Product= -10

Sum= 3

Numbers= 5,-2

$Factorising \: \: {2x}^{2} + 3x - 5$

$(x - 2)(2 {x}^{2} + 5x - 2x - 5)$

$= (x - 2) \: \: x(2x + 5) - 1(2x + 5)$

$= (x - 2)(x - 1)(2x + 5)$