Download presentation

Presentation is loading. Please wait.

Published byAnya Minnie Modified over 3 years ago

1
**8-4A Factoring Trinomials when the Leading Coefficient isn’t 1.**

X-Factor method Algebra Glencoe McGraw-Hill Linda Stamper

2
Factoring quadratic trinomials means finding the binomial factors when given a product. The factors represent the length and width of the rectangle. You need to find the factors! You need to find the factors! x + 2 You are given the product – quadratic trinomial!

3
**Multiply a times c to find the product. –3**

All of the previous problems involving quadratic trinomials had a leading coefficient of 1. Multiply a times c to find the product. –3 –3 1 –2 b in the bottom represents the sum Check by doing FOIL in your head! You know there will be an x in each factor! You know there will be an x in each factor!

4
Today’s problems involve factoring quadratic trinomials when the leading coefficient isn’t 1 - this includes negative 1. To factor quadratic trinomials when the leading coefficient isn’t 1, you will use the X figure and then factor out the greatest monomial factor (aka greatest common factor).

5
**Step 1 Use the X figure as you did when the leading coefficient was 1.**

–10 Multiply a times c to find the product. – 5 –5 + 2 2 –3 b in the bottom represents the sum Step 2 Take the coefficient “a” and the x from the ax2 term and the numbers from the sides of your X figure and place them into two parentheses in the following manner. ( )( ) Step 3 Factor out the greatest monomial factor from each parentheses if you can. Step 4 Discard the factor/s you pull out after X figure. Step 5 Check using FOIL.

6
**–3 –10 2 – 5 –5 + 2 ( )( ) Check using FOIL.**

You must discard (X out) the GMF that is pulled out after using the X figure! ( )( ) Check using FOIL.

7
**DO NOT DISCARD THIS FACTOR!**

Before you use the X figure, you must factor out any greatest monomial factor, if possible! You must keep the GMF that is pulled out before using the X figure! DO NOT DISCARD THIS FACTOR!

8
Factor. -10 - 5 -5 + 2 2 -3 ( )( ) If you factor out a GMF: before using the X figure, keep it, after using the X figure, discard it. Check using FOIL.

9
**Factor out a GMF before the X figure – you must keep it! **

Factor out a GMF after the X figure – discard it (X it out)!

10
Try this problems... 5 –4 A polynomial that cannot be written as a product of two polynomials with integral coefficients is called a prime polynomial!

11
**Copy all of the above problems before you start to factor!**

Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Example 7 Copy all of the above problems before you start to factor!

12
**Can you factor out a greatest monomial factor?**

Example 1 Factor. 6 + 3 3 + 2 2 5 Can you factor out a greatest monomial factor? ( )( ) Check using FOIL.

13
**before using the X figure, keep it, **

Factor. Example 2 Example 3 -22 -18 + 22 22 - 1 -1 Can you factor out a greatest monomial factor? Can you factor out a greatest monomial factor? + 6 6 - 3 -3 21 3 ( )( ) ( )( ) Check using FOIL. If you factor out a GMF: before using the X figure, keep it, after using the X figure, discard it.

14
**Factor. Example 4 Example 5 36 + 9 9 + 4 4 13 ( )( ) Check using FOIL.**

Can you factor out a greatest monomial factor? Can you factor out a greatest monomial factor? 13 ( )( ) Check using FOIL.

15
**Factor. Example 6 Example 7 280 -12 - 6 -6 + 2 2 -8 -35 -4 -43**

Make an organized list of factors. 1•280 2•140 4 •70 5 •56 7 •40 8 •35 280 -12 - 6 -6 + 2 2 -8 -35 Can you factor out a greatest monomial factor? Can you factor out a greatest monomial factor? -4 -43 (10x - 8)(10x - 35) ( )( ) Check using FOIL. Check using FOIL.

16
Factor. Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Example 7

17
Homework 8-A9 Page # 11–22,44,46-51.

Similar presentations

Presentation is loading. Please wait....

OK

Polynomials and Factoring

Polynomials and Factoring

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on presidents of india Ppt on data collection methods examples Ppt on contributor personality development Ppt on law against child marriage in yemen Ppt on model view controller jsp Ppt on statistics in maths games Ppt on success and failure of reconstruction Ppt on depth first search algorithms Ppt on secret of success Ppt on water our lifeline