Question

Question #f21a9

Answer 1

`(7a-2)(3a-5)`

Explanation:

re-arrange the expression to have the first term positive:
In this case in descending order of powers of `a`

`21a^2-41a+10`

"Find factors of `21 and 10` whose products ADD to give 41."

Note that 41 is odd, which is the sum of an odd and an even.

The largest combination of `21 and 10` is `210`
A sum of `41` is likely to be made of combinations of `7 and 3` with `5 and 2`

`color(white)(........)7" "2" "rarr3xx2= 6`
`color(white)(........)3" "5" "rarr7xx5= ul35`
`color(white)(.............................................)41`

The signs in the brackets will both be negative:

`(7a-2)(3a-5)`