Question

factorise: 2x^3 + 9x^2 + 10x + 3

Answer 1

2x^3 + 9x^2 + 10x + 3

= 2x^3 + 6x^2 + 3x^2 + 9x + x + 3

= 2x^2 ( x + 3 ) + 3x ( x + 3 ) + 1 ( x + 3 )

= ( x + 3 ) ( 2x^2 + 3x + 1 )

= ( x + 3 ) ( 2x^2 + 2x + x + 1 )

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

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

Answer 2

Answer:

The factored form is

$2x^3 + 9x^2 + 10x + 3=(x + 3)(x + 1)(2x + 1)$

Step-by-step explanation:

$\text{Given the polynomial }2x^3 + 9x^2 + 10x + 3$

we have to factorise the above polynomial.

$2x^3 + 9x^2 + 10x + 3$

$\text{Split }9x^2\text{ to }6x^2\text{ and }3x^2$

$=2x^3 + 6x^2 + 3x^2 + 9x + x + 3$

$=2x^2(x + 3) + 3x(x + 3) + 1(x + 3)$

Taking (x+3) common both sides

$=(x + 3)(2x^2 + 3x + 1)$

$=(x + 3)(2x^2 + 2x + x + 1)$

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

Taking (x+1) common from both sides

$=(x + 3)(x + 1)(2x + 1)$

which is required factorization.