7-4 Factoring Polynomials (by grouping).notebook
7-4 Factoring Polynomials (by grouping)
January 21, 2016
1
Ex 1:
Can I combine like terms?
NO
Can I pull out a number?
NO
Can I pull out a letter (variable)?
NO
Step1: If four terms, split polynomial in two groups.
Step2: Factor first group.
5x2(
)
5x2 5x2
5x2( 2x - 5 )
Step3: Factor second group.
+3( 2x - 5 )
Step4: Place both factorizations side by side & check to
see if both parenthesis are identical.
5x2( 2x - 5 ) + 3( 2x - 5 )
Step5: Take outside terms & sign and place inside their own parenthesis.
5x2( 2x - 5 ) + 3( 2x - 5 )
( 5x2 + 3 )( 2x - 5 )
ANSWER
Step6: Check answer by using FOIL.
(5x2 +3)(2x -5)
10x3 -25x2 +6x -15
7-4 Factoring Polynomials (by grouping).notebook
7-4 Factoring Polynomials (by grouping)
Checks for Example 1
January 21, 2016
2
7-4 Factoring Polynomials (by grouping).notebook
7-4 Factoring Polynomials (by grouping)
Ex 2:
Can I combine like terms?
NO
Can I pull out a number?
NO
Can I pull out a letter (variable)?
NO
Step1: If four terms, split polynomial in two groups.
Step2: Factor first group.
2x2(
)
2x2 2x2
2x2( 7x - 3 )
Step3: Factor second group.
Rule: You must factor out negative if first term is negative.
-3(
)
-3 -3
-3( 7x -3 )
Step4: Place both factorizations side by side & check to
see if both parenthesis are identical.
2x2( 7x - 3 ) - 3( 7x -3 )
outside terms & sign and place inside their own parenthesis.
2x2( 7x - 3 ) - 3( 7x -3 )
( 2x2 - 3 )( 7x - 3 )
ANSWER
January 21, 2016
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7-4 Factoring Polynomials (by grouping).notebook
7-4 Factoring Polynomials (by grouping)
Checks for Example 2:
January 21, 2016
4
7-4 Factoring Polynomials (by grouping).notebook
January 21, 2016
7-4 Factoring Polynomials (by grouping)
5
Ex 3:
Can I combine like terms?
NO
Can I pull out a letter (variable)?
Can I pull out a number?
YES
NO
2( 2x3 - 3x2 - 6x + 9 )
Step1: Inside has four terms. Split polynomial in two groups.
2( 2x3 - 3x2 -6x + 9 )
Step2: Factor first group.
2x3 - 3x2
x2(
)
2x3 - 3x2
x2
x2
x2( 2x - 3 )
Step3: Factor second group.
-6x + 9
-3(
)
-6x + 9
-3 -3
-3( 2x -3 )
Step4: Place both factorizations side by side & check to
see if both parenthesis are identical
x2( 2x - 3 ) - 3( 2x -3 )
outside terms & sign and place inside their own parenthesis.
x2( 2x - 3 ) - 3( 2x -3 )
( x2 - 3 )( 2x - 3 )
Don't forget about factor outside...
2( x2 - 3 )( 2x - 3 )
ANSWER
2(2x3 - 3x2 -6x + 9)
7-4 Factoring Polynomials (by grouping).notebook
7-4 Factoring Polynomials (by grouping)
Checks for Example 3:
January 21, 2016
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