Warm-up: Pick up a calculator Find the greatest common factor. 12x2 + 6x 2. 28m2 – 35m + 14 3. 4v3 + 36v2 + 10 12x2 + 6x 12x2 = 2 • 2 • 3 • x • x; 6x = 2 • 3 • x; GCF = 2 • 3 • x = 6x 28m2 – 35m + 14 28m2 = 2 • 2 • 7 • m • m; 35m = 5 • 7 • m; 14 = 2 • 7; GCF = 7 4v3 + 36v2+10 4v2 = 2 • 2 • v • v; 36v2 = 2 • 2 • 3 • 3 • v • v; 10 = 2 • 5 GCF = 2

Remind ALL Make Up WORK due next Friday, May 25th!!! HW Check: Collect Worksheet Collect Q4 W7 Warmups Remind ALL Make Up WORK due next Friday, May 25th!!!

HW Check

HW Check 7. 8. 9. 10. 11. 12. 13. 14. 15.

HW Check 16. 17. 18. 19. 20. 21.

HW Check 22. 23. 24.

7.15 Factoring with X-Box Objective: To explore factoring.

X-box Factoring

X- Box ax2 + bx + c Trinomial (Quadratic Equation) Product of a & c ax2 + bx + c Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’. b

X- Box x2 + 9x + 20 Trinomial (Quadratic Equation) Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’. 5 4 9

X- Box 2x2 -x - 21 Trinomial (Quadratic Equation) -42 Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’. 6 -7 -1

X-box Factoring This is a guaranteed method for factoring quadratic equations—no guessing necessary! We will learn how to factor quadratic equations using the x-box method

LET’S TRY IT! Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. Objective: I can use the x-box method to factor non-prime trinomials.

Factor the x-box way x2 -5x -10 2x Example: Factor x2 -3x -10 -5 (1)(-10)= -10 x x2 -5x x GCF -5 2 -3 2x -10 +2 GCF GCF GCF x2 -3x -10 = (x-5)(x+2)

First and Last Coefficients Factor the x-box way y = ax2 + bx + c GCF GCF Product ac=mn First and Last Coefficients 1st Term Factor n GCF n m Middle Last term Factor m b=m+n Sum GCF

Factor the x-box way Example: Factor 3x2 -13x -10 x -5 -30 3x 3x2 -15x +2 3x2 -13x -10 = (x-5)(3x+2)

Examples Factor using the x-box method. 1. x2 + 4x – 12 x +6 x2 6x x -12 4 x2 6x -2x -12 x 6 -2 -2 Solution: x2 + 4x – 12 = (x + 6)(x - 2)

Examples continued x -4 x x2 -4x -5x 20 -4 -5 20 -9 x x2 -4x -5x 20 -5 Solution: x2 - 9x + 20 = (x - 4)(x - 5)

Examples continued 2x -7 x 2x2 -7x 2x -7 -14 -5 -7 2 x 2x2 -7x 2x -7 +1 Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1)

Examples continued 3x +2 5x 15x2 10x -3x -2 a) b) 3x +2 -30 7 5x 15x2 10x -3x -2 10 -3 -1 Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1)

You Try… #1 By Hand (x+8)(x-4) x2 +4x -32

#2 By Hand 4x2 +4x -3 (2x+3)(2x-1)

#3 By Hand 3x2 + 11x – 20 (3x-4)(x+5)

(x + 1)(x+5) (3x-2)(3x+1) (3a-2)(2a+1) Not Factorable (x-4)(x+4)

Don’t forget to check your answer by multiplying! Reminder!! Don’t forget to check your answer by multiplying!

The Grouping Method!!

backwards Demonstrate 3(8) = 24 add to equal 10 standard First two Last two GCF GCF

(x + 3)(x+4) (x - 1)(7x+2) Not Factorable (x + 5)(x-5) (2y + 1)(y - 7)

Classwork: 7.15 Factoring a=1 WS Homework: 7.15 p. 42-43 RSG