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.  

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violy | High School Teacher | (Level 1) Associate Educator

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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.

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