This week in Math 10 we learned how to factor ugly polynomials (polynomials that aren’t able to be factored with other patterns). There is a simple process to follow and finding the factors of ugly polynomials.

Expression: 12x^2 + 17x + 6

Step 1- Go through the list of patterns and choose which one relates to your expression

Common – any common factors within the expression

Difference of Squares – a squared number subtracted from another squared number

Pattern – does it follow the pattern of polynomial that can be factored (x^2 + x + #)

Easy- no leading coefficients

Ugly- don’t follow any of the patterns

Step 2- Take the leading coefficient and the constant of the expression, multiply them together, and find all the possible ways it can be the product of different numbers.

Step 3- Make a box with 4 squares and put the first term in the top left square and the constant in the bottom right square. 

Step 4- Go through the list of the numbers you created and find the one that equals the middle term. If the sign before the constant is a negative then the pairs are different signs. If the the sign before the middle term is a negative, the bigger number of the pair is a negative and if it is a positive then the bigger number is positive. If the sign before the constant is a positive that indicates that both numbers are the same sign.

Step 5- Put the bigger number and its sign in the top right square and the smaller number in the bottom left. With the box completed, go around the box and take out the Greatest Common Factor (The highest number that divides exactly into two or more numbers) with each row and column. The length and width of the box is the factored form of that expression.