Question

Factorise 2xcube-5 xsquare- 23 x -10​

Answer 1

Question :

$\sf \small 2 {x}^{3} - 5 {x}^{2} - 23x - 10$

Solution :

$\sf \small 2 {x}^{3} + {x}^{2} - 6 {x}^{2} - 3x - 20x - 10$

$\sf \small {x}^{2} (2x + 1) - 3x(2x + 1 ) - 10(2x + 1)$

Taking (2x + 1) as common we get :

$\sf \small (2x + 1)[ {x}^{2} - 3x - 10]$

Again we need to factorise the x² - 3x - 10 to get the result by middle term factorisation

$\sf \small(2x + 1)[x + (5 - 2)x - 10]$

The process for getting it clear are that how 5 and 2 came and why we subtracted it are given below :

Conditions :

• When the third term has a negative sign it means that factors to be subtracted in middle term factorisation

• When the third term is positive it means that factors to be added in the middle term factorisation

Here 10 is negative so factors of 10 i.e. 5 and 2 are subtracted to get 3

$\sf \small(2x + 1)[x + 5x - 2x - 10]$

Now we need to factorise

$\sf \small(2x + 1)[x(x + 5) - 2(x + 5)]$

$\sf \small(2x + 1)(x + 5)(x - 2)$

$\boxed{ \sf \small \: \therefore \: the \: answer \: is \: \pink{(2x + 1)(x + 5)(x - 2)}}$

More Information :

• In Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to last term.

• To Factor the form :ax2 + bx + c. Factor : 6x2 + 19x + 10.

1. Find the product of 1st and last term( a x c).