Question

factorise : 3x^3+5x^2+16x-2​

Answer 1

Step-by-step explanation:

bhai qution pura kr factorise ke okay bhai

Answer 2

factorise : 3x^3 - 5x^2 - 16x + 12​ = ( x - 3 ) ( 3x - 2 ) ( x + 2)

factorize P(x) = 3x^3 - 5x^2 - 16x + 12​ = 0 is the correct question.

Here Consider grouping the first 2 terms and the remaining 2 terms for factorization.

x^2( 3x - 5 )  - 4 ( 4x - 3 ) = 0

This cannot be factorised directly.

Lets try to find a solution by trial and error.

X = 0 is clearly not a solution.

X = 1 , P ( 1 ) = 3 - 5 -16 + 12 = -6

x= 2 , p (2 ) = 3x8 - 5x 4 - 32 + 12 is not equal to 0.

X = 3  P( 3 ) = 3 .27 - 5 .9 - 48 + 12 = 81 - 45 - 48 -+ 12 = 0

Therfore x = 3 is a solution.

x - 3 is a factor.

Divide the P ( X ) by x -3 .

3x^3 - 5x^2 - 16x + 12 / x -3 = 3x^2 + 4x -4

factorising 3x^2 + 4x -4 = 3x^2 +6x - 2x -4 = 3x(x + 2) -2 ( x + 2)

==> ( 3x -2 ) ( x + 2 )

Therefore P (x) can be factorised as ( x -3 ) ( 3x - 2 ) ( x + 2 ) = 0

Therefore solutions are x = 3 , x = 2/3 , x = -2