Download presentation

Presentation is loading. Please wait.

Published byPaula Arrasmith Modified over 3 years ago

1
Warm up Factor: 1. p2 + 13p – 30 2. a2 – 12a – 45 3. x2 – 9x – 8

2
**Lesson 5-9 Factoring Pattern for ax2 + bx + c**

Objective: To factor general quadratic trinomials with integral coefficients.

3
**Trial & Error Method Example: 3x2 + 2x - 8**

List the factors of the a term and the c term. a = 3 factors: 1 and 3 c = -8 factors: 2 and 4 or 1 and 8 Write down two sets of parentheses with empty spaces like this: ( x )( x )

4
**Trial & Error Method 3x2 + 2x - 8**

Fill the spaces in front of the x's with a pair of possible factors of the a value. There is only one possibility for our example: (3x )(1x ) Fill in the two spaces after the x's with a pair of factors for the constant. Let's say we choose (3x 8)(x 1).

5
**Trial & Error Method 3x2 + 2x - 8**

Decide what signs should be between the x's and the numbers. Here's a guide: If ax2 + bx + c then (x + h)(x + k) If ax2 - bx - c or ax2 + bx - c then (x - h)(x + k) If ax2 - bx + c then (x - h)(x – k) For our example 3x2 + 2x - 8 so (x - h)(x + k) (3x + 8)(x - 1)

6
**Trial & Error Method 3x2 + 2x - 8**

Test your choice by multiplying (use FOIL) the two parentheses together. Swap out your choices if necessary. In our example, let's try 2 and 4 instead of 1 and 8: (3x + 2)(x - 4) Reverse the order if necessary. Let's try moving the 2 and 4 around: (3x + 4)(x - 2)

7
**Trial & Error Method 3x2 + 2x - 8**

Double-check your signs if necessary. We're going to stick with the same order, but swap which one has the subtraction: (3x - 4)(x + 2) This finally foils to the correct trinomial.

8
**Triple Play or “Magic” Method**

Example: 4x2 + 5x + 1 Multiply the a term (4 in the example) by the c term (1 in this example). 4•1 = 4 Find the two numbers whose product is this number (4) and whose sum is equal to the b term (5). 1•4 = 4 1 + 4 = 5

9
**Triple Play or “Magic” Method**

Take these two numbers (which we will call h and k) and substitute them into this expression: (ax + h)(ax + k) a (4x + 4)(4x + 1) 4

10
**Triple Play or “Magic” Method**

Look to see which one of the two parenthesis terms in the numerator is evenly divisible by a {in this example it is (4x + 4)}. Divide this term by a and leave the other one as is. (4x + 4)(4x + 1) 8 Answer:(x + 1)(4x + 1)

11
**Triple Play or “Magic” Method**

Take the GCF (if any) out of either or both parentheses. (x + 1)(4x + 1)

12
Try 2b2 + 13b – 24 5y2 – 17y + 6 3k2 – 8k – 35

Similar presentations

Presentation is loading. Please wait....

OK

AC Method of factoring ax2 + bx +c

AC Method of factoring ax2 + bx +c

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on charge coupled device patent Ppt on solar power generation Ppt on indian industrial revolution Ppt on question tags test Ppt on voice based web browser Download ppt on famous indian mathematicians Ppt on ip address classes history Ppt on computer graphics and multimedia Ppt on indian army weapons and equipment Ppt on andhra pradesh history