9 24 16 32 −7 15 Bell-Ringer: Simplify each fraction (Complete on form I sent to you via Remind, or complete on separate sheet of paper and turn that in) 9 24 16 32 −7 15

Factoring

FACTORING TRINOMIAL BINOMIAL Product/Sum Factor by Grouping GCF GCF 4-TERM POLYNOMIAL GCF GCF GCF Difference of Squares Product/Sum Factor by Grouping

Greatest Common Factor What You Should Know: The Greatest Common Factor of a Set of Monomials is the largest factor that can be divided into all monomials in the set. For example: The greatest common factor of 8xy and 6x is .

Greatest Common Factor State the GCF for each. A. 6xy2 and 39xy B. 15x3y, 45x2y, and 30xy

When you factor, you MUST REMEMBER!?! When you factor, you MUST be able to take something that is the same out of EVERY term.

GCF( binomial ) OR GCF( trinomial ) To factor the GCF out of a bi- or tri-nomial: 1. Find the GCF 2. Divide it out 3. Express your answer as… GCF( binomial ) OR GCF( trinomial )

Factor our the GCF from each binomial. Ex.1 7x2 + 42x Ex.2 15m2n – 27mn2 Ex.3 36k5 + 24k3 Ex.4 16g + 14gh2

Factor the GCF from each Trinomial. Ex.5 a + a2b3 + a3b3 Ex.6 3p3q - 9pq2 + 36pq

Factoring by Grouping

Factor by Grouping What you should know: Factoring by Grouping: use when you have 4 or more terms. You may have to rearrange the terms to find something in common. ay–bx +ax – by

Factor by Grouping Steps to factor by Grouping: 1. Check for GCF and factor it out if one exists. 2. Group the first two terms and the last two terms together. 3. Factor the GCF out of each group. 4. Factor out the common binomial GCF. 5. Express your answer as the product of two binomials.

Factor by Grouping Examples: Factor completely. 1. 10xy + 12x + 15y + 18 2. 5ab + 25a – b – 5 Steps: 1. Check for GCF 2. Group 3. Factor GCF out of groups 4. Express answer as… (binomial)(remainder)

Factor by Grouping Examples: Factor completely. 3. 63xy + 21x + 45y + 15 4. 10xy – 20y + 14x – 28

binomial additive inverse: Factor by Grouping When you factor by grouping, you may encounter a ___________________ binomial additive inverse: 3 - a and a - 3 Factor out a -1 to change -1(3 – a) -3 + a a – 3

Factor by Grouping Examples: Factor completely. 4xy – 10y – 14x + 35

Factor by Grouping Examples: Factor completely. 4xy – 10y – 14x + 35

Factoring Trinomials Steps to factor trinomials: ax2 + bx + c 1. Factor out any GCF if it exists. 2. Multiply ac. 3. Complete the product/sum X. 4. Use the two numbers you found and substitute in for b. 5. Factor by grouping.

Factoring Trinomials Examples: Factor the following. 10. x2 + 10x + 24

Factoring Trinomials Examples: Factor the following. 11. 3x2 + 22x + 7

Factoring Trinomials Examples: Factor the following. 12. x2 + 5x – 14

Factoring Trinomials Examples: Factor the following. 13. 8x2 – 14x + 3

Factoring Trinomials Examples: Factor the following. 14. 3y2 + 30y - 72

Factoring Trinomials Examples: Factor the following. 15. 3y2 – 11y + 6

Bell Ringer: Solve each quadratic equation by factoring Bell Ringer: Solve each quadratic equation by factoring. Check your solutions using the graphing calculator. (Calc) 1. d2+2d+80 = 0 2. b2-10b = -24 3. 3x2-25 = -10x 4. -9x+1 = -14x2 5. a2-5a-24 = 0

Difference of Squares Difference of Squares is exactly what it sounds like – the difference (minus) of two perfect squares. Perfect Squares are numbers that are the product of a number and itself. Difference of Squares looks like this: 4x2 – 25

Difference of Squares x2 - 16 To factor difference of squares: Square root each term. Place each square root into the ( )’s accordingly. Inside the parentheses, alternate a plus and a minus. The square root of x2 is x. The square root of 16 is 4. (x 4)(x 4) (x + 4)(x – 4 )

Difference of Squares Examples: Factor completely. 16. 4x2 – 25