Question

Factor completely: x2 - 10x + 25

Answer 1

Since the first term is x², you know that each group will begin with x. To find the second part of the groups, you need to find two numbers that add up to 10 and multiply to 25. You can do this by listing all the factors of 25 until you find a set that adds to 10.

25 x 1
5 x 5
-5 x -5

The second terms in your groups will be -5 and -5.

(x - 5) (x - 5)   This can be simplified to (x - 5)².

Answer 2

x2 + -10x + 25 = 0
25 + -10x + x2 = 0
(5 + -1x)(5 + -1x) = 0
5 + -1x = 0
0 + -1x = 0 + -5 -1x = 0 + -5

x = 5