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Steps 1. Find the greatest common factor (GCF) 2. Divide the polynomial by the GCF. The quotient is the other factor. 3.Express the polynomial as the product of the quotient and the GCF. FACTORING USING GCF
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FACTORINGINTEGRATED
MATHEMATICS
• Students will calculate the GCF of 2 or 3 terms of a polynomial.
• Students will apply concepts of GCFs and Factoring to write the factored form of a polynomial.
FACTORING USING GCF
Steps1. Find the greatest common
factor (GCF)2. Divide the polynomial by
the GCF. The quotient is the other factor.
3.Express the polynomial as the product of the quotient and the GCF.
FACTORING USING GCF
𝑬𝒙 .𝟏¿𝟔 𝒙 ¿𝟐+𝟑 𝒙FACTOR
𝑬𝒙 .𝟐¿𝟓 𝒚 ¿𝟒−𝟐𝟎 𝒚 𝟑FACTOR
𝑬𝒙 .𝟑¿𝟏𝟔𝒂¿𝟐+𝟐𝟎𝒂FACTOR
𝑬𝒙 .𝟒¿𝟏𝟓𝒙 ¿𝟓−𝟏𝟐𝒙𝟒+𝟐𝟕𝒙𝟑−𝟑 𝒙𝟐FACTOR
𝑬𝒙 .𝟓¿−𝟒𝒏¿𝟑−𝟐𝒏𝟐−𝟔𝒏FACTOR
Students will apply concepts of Perfect Squares and Factoring to write the factored form of the Difference of Two Squares.
DIFFERENCE OF TWO SQUARES
There must be two terms that are both squares Examples of squares
There must be a minus sign between the two terms
DIFFERENCE OF TWO SQUARES
1² = 1 11²= 1212² = 4 12² = 1443² = 9 13² = 1694² = 16 14² = 1965² = 25 15² = 2256² = 36 16² = 2567² = 49 17² = 2898² = 64 18² = 3249² = 81 19² = 36110² = 100 20² = 400
PERFECT SQUARES
FACTORING DIFFERENCE OF TWO SQUARESFORMULA
A2 – B2 = (A + B)(A – B)
FACTOR
42 xEx. 6)
FACTOR
642 yEx. 7)
FACTOREx. 8) 254 2 x
FACTOR
Ex. 9)
26 16nm
FACTOR
Ex. 10)
22 2536 yx
FACTOR
Ex. 11)
499 2 a
FACTOR
Ex. 12)
21 x
FACTOR
Ex. 13)
22 81169 zy
FACTOR. LOOK FOR GCF FIRST!
6205 yEx. 14)
FACTOR. LOOK FOR GCF FIRST!
33 4abba Ex. 15)
FACTOR. LOOK FOR GCF FIRST!
622 5018 aba Ex. 16)
FACTORING COMPLETELY
Means to factor until factoring is no longer possible
FACTOR.
8416 nm
FACTOR.
125 4 x
FACTORING TRINOMIALS
FACTORING A TRINOMIAL:
1. Write two sets of parenthesis, ( )( ). These will be the factors of the trinomial.
2. Think of factors of c that add up to b.
FACTOR
652 xxExample 1
FACTOR
1282 xx
Example 2
FACTORExample 3 36132 xx
FACTORExample 4 21413 mm
FACTORExample 5 1582 xx
FACTORExample 6 2092 xx
FACTORExample 7 16102 xx
FACTORExample 8 2082 xx
FACTORExample 9 1242 xx
FACTORExample 10 1452 aa
FACTORExample 11 1452 xx
FACTORExample 12
202 xx
FACTORExample 13 12112 xx
