Lect1 - Factoring Recall that factoring an expression means...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
92.131 Lecture 1 1 of 13 Ronald Brent © 2010 All rights reserved. Factoring Recall that factoring an expression means writing it as a product. 1) Common factors 2) Special formulas 3) Grouping Common Factors The easiest tool to use is to take out all factors that are common to all the terms of the expression. Factor 2 3 3 4 3 20 16 4 y x y x y x + . Notice that all three terms share a factor of 4, as well as x and 2 y . So, taking out this common factor of 2 4 y x , we get ) 5 4 ( 4 20 16 4 2 2 2 2 2 3 3 4 3 x y y x y x y x y x y x + = + .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
92.131 Lecture 1 2 of 13 Ronald Brent © 2010 All rights reserved. Special Formulas (i) ) ( ) ( 2 2 y x y x y x + = (ii) ) ( ) ( 2 2 3 3 y xy x y x y x + + = + (iii) ) ( ) ( 2 2 3 3 y xy x y x y x + + = (iv) ) ( ) ( ) ( 2 b x a x ab x b a x + + = + + + (v) ) ( ) ( ) ( 2 d x c b x a bd x ad bc acx + + = + + + (vi) 2 2 2 ) ( 2 y x y xy x + = + + and 2 2 2 ) ( 2 y x y xy x = +
Background image of page 2
92.131 Lecture 1 3 of 13 Ronald Brent © 2010 All rights reserved. Example: Using Difference of Squares a) ) 4 ( ) 4 ( 16 2 + = s s s (Here we are using (i) with x = s and y = 4.) b) ( ) ) 2 3 ( ) 2 3 ( ) 2 ( ) 3 ( 4 9 2 2 2 2 y x y x y x y x + = = c) ( ) ) 3 5 ( ) 3 5 ( ) 3 ( ) 5 ( 3 5 2 2 2 2 t s t s t s t s + = = d) ) )( )( ( ) ( ) ( 2 2 2 2 2 2 4 4 y x y x y x y x y x y x + + = + = e) ) 3 2 )( 3 2 )( 9 4 ( ) 9 4 ( ) 9 4 ( 81 16 2 2 2 2 2 2 4 4 t s t s t s t s t s t s + + = + = f) ) 3 2 )( 3 2 ( ) 3 2 ( ) 3 2 ( ) 3 2 ( 3 2 4 4 4 4 2 2 2 2 2 2 4 4 t s t s t s t s t s t s + + = + =
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
92.131 Lecture 1 4 of 13 Ronald Brent © 2010 All rights reserved. Example: Using ) ( ) ( 2 2 3 3 y xy x y x y x + + = + a ) ) 4 6 9 ( ) 2 3 ( ) 2 ( ) 3 ( 8 27 2 2 3 3 3 3 b ab a b a b a b a + + = + = + b ) 3 2 3 2 6 3 6 3 ) 2 ( ) 4 ( 8 64 z y t s z y t s + = + ) 4 8 16 ( ) 2 4 ( 4 2 2 2 4 2 2 2 z y z syt t s yz t s + + = c ) 3 3 2 b a +
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 13

Lect1 - Factoring Recall that factoring an expression means...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online