Question

factorise using factor theorem
4x^3+12x^2+5x-6​

Answer 1

ANSWER.

• (x + 2)(2x + 1)(2x - 3)

SOLUTION.

Let,

→ f(x) = 4x³ + 12x² + 5x - 6

Put x = -2, we get,

→ f(-2) = 4 × (-2)³ + 12 × (-2)² + 5 × (-2) - 6

→ f(-2) = -32 + 48 - 10 - 6

→ f(-2) = 0

So,

→ x = -2

→ (x + 2) is a factor of f(x).

Divide f(x) by (x + 2) –

x + 2) 4x³ + 12x² + 5x - 6( 4x² + 4x - 3

         4x³ +  8x²

––––––––––––––––––––––

                    4x² + 5x - 6

                    4x² + 8x

––––––––––––––––––––––

                             -3x - 6

                             -3x - 6

––––––––––––––––––––––

                                  0

So,

→ f(x) = (x + 2)(4x² + 4x - 3)

= (x + 2)[(4x² - 6x + 2x - 3)]

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

= (x + 2)(2x + 1)(2x - 3) Which is our required answer.