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

2 Answers
May 12, 2018

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)#

May 12, 2018

Answer:

#-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)#