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Write the standard form of an equation of a line passing through (-4,3) with a slope of -2.
Write the equation in standard form with integer coefficientsy = -1/3x - 4
1) Factor GCF of 12a2 + 16a
12a2 = 16a =
2 2 3 a a
2 2 2 2
2 2 a = 4a212 16a a 4a (3 )a 4a (4)
Use distributive
property
4a (3 4)a
a
PRIME POLYNOMIALSA POLYNOMIAL IS PRIME IF IT IS NOT THE PRODUCT OF POLYNOMIALS HAVING INTEGER COEFFICIENTS.
TO FACTOR A PLYNOMIAL COMPLETLEY, WRITE IT AS THE PRODUCT OF •MONOMIALS• PRIME FACTORS WITH AT LEAST TWO TERMS
2X2 + 8 = 2(X2 + 4)
YES, BECAUSE X2 + 4 CANNOT BE FACTORED USING INTEGER COEFFICIENTS
2X2 – 8 = 2(X2 – 4)
NO, BECAUSE X2 – 4 CAN BE FACTORED AS (X+2)(X-2)
TELL WHETHER THE POLYNOMIAL IS FACTORED COMPLETELY
Using GCF and Grouping to Factor a Polynomial
First, use parentheses to group terms with common factors.
Next, factor the GCF from each grouping. Now, Distributive Property…. Group both GCF’s.
and bring down one of the other ( ) since they’re both the same.
2) Factor 4 8 3 6ab b a ( ) ( )4b ( 2)a 3 ( 2)a
(4 3)b ( 2)a
Using GCF and Grouping to Factor a Polynomial
First, use parentheses to group terms with common factors.
Next, factor the GCF from each grouping. Now, Distributive Property…. Group both GCF’s.
and bring down one of the other ( ) since they’re both the same.
23) Factor 6 15 8 20x x x ( ) ( )3x (2 5)x 4 (2 5)x
(3 4)x (2 5)x
Using GCF and Grouping to Factor a Polynomial
First, use parentheses to group terms with common factors.Next, factor the GCF from each grouping.Now, Distributive Property…. Group both GCF’s. and bring down one of the other ( ) since they’re both the same.
24) Factor 2 6 3 9a a a ( ) ( )2a ( 3)a 3 ( 3)a
(2 3)a ( 3)a
Using the Additive Inverse Property to Factor Polynomials.
When factor by grouping, it is often helpful to be able to recognize binomials that are additive inverses. 7 – y is
y – 7 By rewriting 7 – y as -1(y – 7)
8 – x is x – 8 By rewriting 8 – x as -1(x – 8)
5) Factor 35 5 3 21x xy y ( )( )5x (7 )y 3 ( 7)y
( 5 3)x ( 7)y
Factor using the Additive Inverse Property.
5x( 1) ( 7)y 3 ( 7)y
5x ( 7)y 3 ( 7)y
6) Factor 2 8 4c cd d ( ) ( )c (1 2 )d 4 (2 1)d
( 4)c (2 1)d
Factor using the Additive Inverse Property.
c ( 1) (2 1)d 4 (2 1)d
c (2 1)d 4 (2 1)d
27) Factor 10 14 15 21x xy x y
There needs to be a + here so change the minus to a
+(-15x)
210 14 ( 15 ) 21x xy x y •Now group your common terms.
•Factor out each sets GCF.
•Since the first term is negative, factor out a negative number.
•Now, fix your double sign and put your answer together.
( ) ( )2x(5 7 )x y 3( ) (5 7 )x y
(2 3)x (5 7 )x y
8) Factor 8 6 12 9ax x a
There needs to be a + here so change the minus to a
+(-12a)
8 6 ( 12 ) 9ax x a •Now group your common terms.
•Factor out each sets GCF.
•Since the first term is negative, factor out a negative number.
•Now, fix your double sign and put your answer together.
( ) ( )2x (4 3)a 3( ) (4 3)a
(2 3)x (4 3)a