Question

factories x cube + 6x square +11x + 6​

Answer 1

Answer.

• Factorised form – (x + 1)(x + 2)(x + 3)

Steps.

Given:

→ f(x) = x³ + 6x² + 11x + 6

Put x = -1, we get,

→ f(-1) = (-1)³ + 6 × (-1)² + 11 × (-1) + 6

        = -1 + 6 - 11 + 6

        = 12 - 12

        = 0

So, by factor theorem,

→ (x + 1) is a factor of f(x).

Divide f(x) by (x + 1):

x + 1 ) x³ + 6x² + 11x + 6 ( x² + 5x + 6

         x³ +   x²

–––––––––––––––––––––

                5x² + 11x + 6

                5x² +  5x

–––––––––––––––––––––

                          6x + 6

                          6x + 6

–––––––––––––––––––––

                               0

Therefore:

→ f(x) = (x + 1)(x² + 5x + 6)

        = (x + 1){x² + 2x + 3x + 6}

        = (x + 1){x(x + 2) + 3(x + 2)}

        = (x + 1)(x + 2)(x + 3)

Which is our required answer.