This week in Precalc 11 I learned how to factor polynomials by grouping them. This is a good skill to have as polynomials can look scary sometimes and factoring them isn’t easy.

Example: x^{2}+2x+6x+12

Step 1: Start by drawing a square and dividing it into 4 equal boxes inside. Then, place numbers in each box. It’s crucial to arrange these numbers in a specific order so that when you examine them diagonally, the products of the diagonals are equal. Additionally, ensure that similar variables are positioned diagonally opposite each other. For example, if you have 2x in one box, place 6x in the box diagonally opposite to it.

Step 2: Take out the greatest common factor (GCF) or common variable from each row.  This process will result in having two numbers at the top of the box and two numbers at the left of the box. If there’s no apparent GCF or common variable in a row, simply write 1, as 1 is divisible by everything. This step helps simplify the expressions within each row, making further calculations easier.

Step 3: Next, let’s group the numbers together. The two expressions at the top of the box should be grouped together, as well as the two expressions on the left. Ultimately, you should have two binomials formed, where the product of these binomials equals the polynomial we began with.

(x+2)(x+3)