Factoring polynomials -by-Grouping for grade 8

Factoring-by-Grouping

1. FACTORING BY GROUPING

2. Review: Factor the polynomial. 10x 4 – 5x 2 (2 ∙ 5 ∙x∙x ∙x ∙x) – (5∙x∙x) 5∙x∙x [(2 ∙x ∙x)-1] 5x 2 (2x 2 -1)

3. Review: Factor the polynomial. 2x 2 (2x + 1) + x(2x+1) (2 ∙x∙x)(2x+1) – (x)(2x+1) ( 2x+1 )[( 2 ∙x∙x)-x] (2x+1)( x )(2x-1)

4. Lesson Proper Consider: 2x – 10 + xy – 5y What is the common monomial factor of the given polynomial? How can we factor the given polynomial? When a polynomial has no common factor, we group the terms in such a way that each group will have a common factor.

5. Example 1: Factor the polynomial. 2x – 10 + xy – 5y

6. Example 1: STEP 1 Group the terms into two binomial in such a way that each group will have a common factor. 2x – 10 + xy – 5y (2x – 10) + ( xy – 5y)

7. Example 1: STEP 2 Get the common monomial factor of each group. 2x – 10 + xy – 5y (2x – 10) + ( xy – 5y) 2 (x – 5) + y (x – 5)

8. Example 1: STEP 3 Take out the common binomial factor and get the other factor. 2x – 10 + xy – 5y (2x – 10) + ( xy – 5y) 2 (x – 5) + y (x – 5) (x – 5) ( 2 + y )

9. Example 2: Factor Step 1 4xz – 4yz – x + y Step 2 Step 3 (4xz – 4yz) – (x - y) 4z ( x – y ) – 1 ( x - y ) ( x – y ) ( 4z – 1 )

10. Example 3: Factor Step 1 3xy – zw + 3xw - yz Step 2 Step 3 (3xy + 3xw) – ( zw + yz ) 3 x ( y + w ) – z ( y + w ) ( y + w ) ( 3x – z ) 3xy + 3xw – zw - yz

11. Example 4: Factor Step 1 rq – 2rp + 5q – 10p Step 2 Step 3 ( rq + 5q) + (2rp – 10p) q ( r + 5 ) – 2p ( r + 5 ) ( r + 5 ) ( q – 2p ) rq + 5q – 2rp – 10p

12. Example 5 : Factor Step 1 6ab 2 – 3ab – 14b + 7 Step 2 Step 3 (6ab 2 – 3ab) – (14b + 7) 3ab ( 2b – 1 ) – 7 ( 2b - 1 ) ( 2b - 1 )( 3ab + 7 )

13. SUMMARY

14. Factoring by grouping method is applied when the polynomial has no common factor. Step 1: Group the terms into two binomials. Step 2: Get the common monomial factor of each group. Step 3: Take out the common binomial factor and get the other factor.

15. ANSWER: MODULE Activity #

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