Question

Use the remainder theorem to factorise the following expression :

2x³ + x² - 13x + 6 ​

Answer 1

Heya!!

Here's your answer!!

Let f(x) = 2x³ + x² - 13x + 6

Put x = 2,

f(2) = 2(2)³ + 2² - 13(2) + 6 = 0, satisfied.

Hence (x-2) is a factor of f(x) x-3

2x² + 5x -3

__________________

x - 2 ) 2x³ + x² - 13x + 6

2x³ - 4x²

- +

________________

5x² - 13x

5x² - 10x

- +

________________

- 3x + 6

- 3x + 6

+ -

____________

0

____________

Thus,. f(x) = (x-2) (2x² + 5x - 3)

= (x - 2) (2x² + 6x - x - 3)

= (x -2) [2x ( x+3) - 1(x+3)]

= (x-2) (x +3) (2x-1).

Glad help you,

it helps you,

thanks.