How do you factor -7x^2+1757x2+175?

2 Answers
May 12, 2018

Prime factorize them
-7x^2=-1xx7xx x xx x7x2=1×7×x×x
175=5xx5xx7175=5×5×7
As you can see... both have 7 as common
7(-x^2+25)7(x2+25)
Leaving it like this will not complete the answer
Notice
7(25-x^2)=7(5^2-x^2)7(25x2)=7(52x2)

This is a law of exponents
a^2-b^2=(a+b)(a-b)a2b2=(a+b)(ab)

Here... 5=a, x=b5=a,x=b
7(5^2-x^2)=7(5+x)(5-x)7(52x2)=7(5+x)(5x)

May 12, 2018

-7(x-5)(x+5)7(x5)(x+5)

Explanation:

-7x^2+1757x2+175

Factor out the -77

=-7(x^2-25)7(x225)

Using the rule difference of two squares: (x-a)(x+a)=x^2-a^2(xa)(x+a)=x2a2

=-7(x-5)(x+5)7(x5)(x+5)