Question

How do you factor `50 + 5a - a^2`?

Answer 1

`(5+a)(10-a)`

Explanation:

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

`"the factors of the product "50xx-1=-50`

`"which sum to "+5" are "+10" and "-5`

`"split the middle term using these factors"`

`50+10a-5a-a^2larrcolor(blue)"factor by grouping"`

`=color(red)(10)(5+a)color(red)(-a)(5+a)`

`"take out the "color(blue)"common factor "(5+a)`

`=(5+a)(color(red)(10-a))`

`50+5a-a^2=(5+a)(10-a)`