Question

How do you factor `-7x^2+175`?

Answer 1

Prime factorize them
`-7x^2=-1xx7xx x xx x`
`175=5xx5xx7`
As you can see... both have 7 as common
`7(-x^2+25)`
Leaving it like this will not complete the answer
Notice
`7(25-x^2)=7(5^2-x^2)`

This is a law of exponents
`a^2-b^2=(a+b)(a-b)`

Here... `5=a, x=b`
`7(5^2-x^2)=7(5+x)(5-x)`

Answer 2

`-7(x-5)(x+5)`

Explanation:

`-7x^2+175`

Factor out the `-7`

=`-7(x^2-25)`

Using the rule difference of two squares: `(x-a)(x+a)=x^2-a^2`

=`-7(x-5)(x+5)`