A square has the given sides: x-1, x, x+6, x+1, Given an expression in terms of x for the area that equals to x^2+2x-3.
Formula for area of a square is:
A = s^2.
So, we can try to factor the given expression for area to get the
expression for the each side.
Factor x^2 + 2x - 3.
Use ac method to factor.
Here, a = 1, b = 2, and c = -3.
So, ac = -3. We will find two numbers which has a product of -3 (value of ac), and a sum of 2 ( value of b).
List the pair factors of -3, and their sum.
-3 and 1: -3 + 1 = -2
3 and -1: 3 + (-1) = 2
Hence, the two numbers we are looking for are 3 and -1.
We use it to rewrite the middle term.
x^2 + 2x - 3 = x^2 - 1x + 3x - 3
Split the terms into two groups, where each group has a gcf.
(x^2 - 1x) + (3x - 3)
Factor out the gcf from each group.
x(x - 1) + 3(x - 1)
Factor out the common factor.
(x - 1)(x + 3).
Hence, each side has a measure x - 1.