Factoring Polynomials Undoing FOIL

Basic Factoring Take out what is common in all terms Look for GCF this can be numbers, variables or both 10x+35 GCF=5 5(2x+7)

Trinomials with a=1 Find factors of c that add to b (x factor of c)(x factor of c) The sign of the factors will be the operation in the binomial Factors are not just positive and negative numbers

Examples

Perfect Square (short cut) If first terms is a perfect square If last term is a perfect square If you add the last term If middle terms is square root of first times square root of last times 2 (square root of first sign of second square root of third)square

Difference of two squares Only two terms First term is perfect square Second term is perfect square Minus between (square root of first + square root of second)(square root of first – square root of second)

Examples Factor the Special Cases

Factoring A trinomial when a is not 1 a times c (include sign of c) Factors of ac that add to b (factors can be positive and negative) Rewrite polynomial with factors instead of b values, keep the x Group first two terms, group last 2 terms, if third term has a minus sign in front include it in the ( ) and put a plus sign between Factor our GCF of each group, what is left inside the parenthesis is exactly the same Write GCFs as a group multiplied to what is inside parenthesis

Example

Examples

Homework Wkst 1 Factoring when a=1 (4,6,8, 10) Wkst 2 Determining special case (first 6 in each column), if special case then factor Wkst 3 Factoring when a >1 Set 1, show all steps