B. deTreville HSHS FACTORING

To check your answer to a factoring problem you simplify it by multiplying out the factors. The expression can be factored as You can check that this is correct by foiling. The expression can be factored as You can check this by distributing. You need to recognize when an expression is in factored form and when it is in simplified or polynomial form. Factored form means there are things being multiplied together. Simplified or polynomial form means there are no parentheses and all like terms are combined. Simplified/Polynomial Factored Factored Simplified/Polynomial Furthermore, you need to recognize when an expression is not completely factored. If an expression is not completely factored that means there is more factoring that can be done. Factoring means to write an expression as a product of primes.

AFTER YOU FACTOR L K AT THE FACTORS TO SEE IF THEY CAN STILL BE FACTORED!!!

Whenever you do factoring problems you should ask a series of questions. Use the following slides to walk you through the factoring process. Use these slides for each problem until you can work through them on your own.

Question 1: Is there a GCF? The first thing you must do when factoring any expression is pull out the GCF if there is one.

GCF Don’t forget…… if you pull Don’t forget…… if you pull out a GCF it must be part out a GCF it must be part of the final answer. It IS one of the final answer. It IS one of the factors in the answer. of the factors in the answer.

Question 2: How many terms does the expression have? 2 3 4

Are both terms perfect squares with subtraction between them? Yes Yes Are both terms perfect squares with addition between them? Yes Yes Are both terms perfect cubes with subtraction between them? Yes Yes Are both terms perfect cubes with addition between them? Yes Yes Start New Problem

DIFFERENCE OF SQUARES The difference of squares is easy to factor. The factors are as follows: Ex: Start New Problem

Sum of Squares A sum of squares cannot be factored. The binomial is prime. Start New Problem

Difference of Cubes Remember: CSC SOPAS The difference of cubes factors as: C S C S O P A S C S C S O P A S u a u q p r d q u a u q p r d q b m b u p o d u b m b u p o d u e e e a o d a e e e a o d a R S R r s u r R S R r s u r o i o e i c e o i o e i c e o g o t t o g o t t t n t e t n t e S i g n

Difference of Cubes cube root square product

Difference of Cubes Same sign Opposite sign Addition Start New Problem

Sum of Cubes Remember: CSC SOPAS The sum of cubes factors as: C S C S O P A S C S C S O P A S u a u q p r d q u a u q p r d q b m b u p o d u b m b u p o d u e e e a o d a e e e a o d a R S R r s u r R S R r s u r o i o e i c e o i o e i c e o g o t t o g o t t t n t e t n t e S i g n

Sum of Cubes cube root square product

Sum of Cubes Same sign Opposite sign Addition Start New Problem

Trinomials Is the leading coefficient 1? Yes No YesNoYesNo

Trinomials If the leading coefficient is 1 you can factor the trinomial quick and easy. factors as sum = b product = c Start New Problem

Trinomials If the trinomial has a leading coefficient other than 1 you will use the multiply divide method. Start New Problem 1. Multiply a and c to make a trinomial with a leading coefficient of Factor the new trinomial using the quick and easy method. 3. Divide each constant in both factors by a. 4. Reduce any fractions and make any denominator a coefficient on the variable.

Factor by Grouping Group the first two and last two terms using parentheses. Pull the GCF out of each group. Pull out the new GCF. Ex. Start New Problem

L K Are you sure you are finished? Can any of the factors still be factored? If so, factor them. If not then you are ready to start a new problem. Start New Problem