Question

Is it possible to factor `y=x^2 + 7x – 6`? If so, what are the factors?

Answer 1

`(x+7/2-1/2sqrt73)(x+7/2+1/2sqrt73)`

Explanation:

`"there are no whole number factors of - 6 which sum"`
`"+ 7"`

`"obtain the factors by finding the solution using the "`
`color(blue)"quadratic formula"`

`•color(white)(x)x=(-b+-sqrt(b^2-4ac))/(2a)`

`"with "a=1,b=7" and "c=-6`

`x=(-7+-sqrt(49+24))/2=(-7+-sqrt73)/2`

`x=-7/2+1/2sqrt73" or "x=-7/2-1/2sqrt73`

`"thus the factors are"`

`(x-(-7/2+1/2sqrt73))(x-(-7/2-1/2sqrt73))`

`=(x+7/2-1/2sqrt73)(x+7/2+1/2sqrt73)`