Question

How do you factor `10x^2 + 5 + 27x`?

Answer 1

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

Explanation:

let's first solve the equation:
`10x^2+27x+5=0`

and find the zeroes

`x=(-27+-sqrt(27^2-4*10*5))/(2*10)`
then
`x=(-27+-sqrt(729-200))/(20)`
`x=(-27+-23)/(20)`
`x=-5/2 and x=-1/5`

let's factor
`10x^2+27x+5=10(x+5/2)(x+1/5)`

let's eliminate fractions by multiplying :
`2(x+5/2)5(x+1/5)`
`(2x+5)(5x+1)`