Objective : To factor trinomials of the form Ax 2 + Bx + C.

Lesson 9.4: FACTORING TRINOMIALS: Ax² + Bx + C Page 495 Objective: To factor trinomials of the form Ax2 + Bx + C. To solve equations of the form Ax2 + Bx + C = 0

Reminder… FACTORING REVERSES MULTIPLICATION. For example: What can you multiply to get 4? x2? 6x2? Answer: 1 times 4 or 2 times 2; x times x 2x(3x) or 6x(x)

INTRODUCTION • When factoring Ax2 + Bx + C, we must find factors of AC that combine to give us B. • Note: There will only be one correct way to factor these, but there are numerous ways (different methods) we can use to arrive at that answer.

Steps for Factoring ax2 + bx + c with the “ac” Method • Find factors of “ac” that combine to give you “b”. • When “c” is positive, the sign in each binomial is the same as “b”. (add to find “b”) • If “c” is negative, the sign in each binomial is different. (subtract to find “b”) • Write as the product of 2 binomials. ( )( ) • Use FOIL or the Distributive Prop. to check.

A) 2y2 + 5y + 2 B) 6n2 – 23n + 7 Ex. 1: Factor each trinomial (c > 0)

C) 5d2 – 14d – 3 D) 2n2 + n - 3 Examples (c < 0)

E) 12x2 + 11x – 5 F) 2x2 + 9x + 10 More Examples

G) 20a2 -21a – 5 H) 6t2 + 25t + 14 More Examples

3x² + 7x - 5 5x² + 27x + 10 Your turn…

GCF? • Some polynomials will have a GCF that needs to be factored out first. • RULE: You should never have a binomial with a common factor in your final answer. • For example, look at (4x + 2)(3x – 7). The first binomial has a common factor of 2. So this is not completely factored.

I) 18k2 – 12k – 6 J) 18x2 + 33x - 30 Examples

Your turn…. • K) 6x² + 15x - 9

1) 3x² + 11x + 6 = 0 2)10p² - 19p = - 7 Ex. 2: Solve each equation.

Your turn….. • 6n² + 7n = 20

NBA #4, page 499, problems 14-44 even omit 32 & 34

Objective : To factor trinomials of the form Ax 2 + Bx + C.