Question

1. If the area of a square is (4x^ + 12x + 9) sq. units,
find the side of the square.​

Answer 1

4x2+12x+9= 4x2+12x+9

We find two numbers that multiply to get 36, but add to get 12.

These terms are, 6 and 6

6 × 6 =36

6 + 6 =12

So, we use these terms and replace them with 12x

4x2+6x+6x+9

We factor out the first two terms

4x2 =2 ×2 × x ×x

6x=2 ×3 ×x

We can see that they both share a factor of 2x

So, we write it as 2x(2x+3)

Now, we factor out the next two terms.

6x=2 ×3 ×x

9=3 ×3

We can see that these two have a common factor of 3

So, we write it as 3(2x+3)

We put the two together 2x(2x+3)+3(2x+3)

We add them, and get (2x+3)(2x+3)

In other words, the length is 2x+3

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