FACTORING INTEGRATED MATHEMATICS. Students will calculate the GCF of 2 or 3 terms of a polynomial....

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