Question

How do you factor the expression `2x^2-9x-5`?

Answer 1

`(2x+1)(x-5)`

Explanation:

`"using the a-c method to factorise the quadratic"`

`"the factors of the product "2xx-5=-10`

`"which sum to - 9 are - 10 and + 1"`

`"split the middle term using these factors"`

`2x^2-10x+x-5larrcolor(blue)"factor by grouping"`

`=color(red)(2x)(x-5)color(red)(+1)(x-5)`

`"take out the "color(blue)"common factor "(x-5)`

`=(x-5)(color(red)(2x+1))`

`rArr2x^2-9x-5=(x-5)(2x+1)`