FACTORINGMarch 25-26, 2014

OBJECTIVES The student will find the GCF of numbers and terms.

The student will use basic addition and multiplication to identify the factors of a number.

The student will demonstrate how multiplying polynomials relates to factoring polynomials.

The student will factor trinomials with one and two variables when the “a” value is 1.

COMMON CORE STANDARDS CCSS.Math.Content.A-SSE.2 Use the structure of an

expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).

CCSS.Math.Content.A-SSE.3a Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

CCSS.Math.Content.A-APR.4 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples.

CCSS.Math.Content.F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

WHAT IS A TRINOMIAL? Polynomial with three

terms.

cbxx 2

DEFINITIONSGCF: largest quantity that is a factor of all the integers or polynomials involved.

Factors: either numbers or polynomials.Factoring: writing a polynomial as a product of polynomials.

Prime Factors: A factor that is a prime number. One of the prime numbers that, when multiplied, give the original number.

FIND THE GCF OF THE NUMBERS12 and 8 7 and 20

4 1

FIND THE GCF OF THE NUMBERS6, 8 and 46 10, 25, and 100

2 5

FIND THE GCF OF THE TERMSx3 and x7

x3 = x · x · xx7 = x · x · x · x · x · x · xSo the GCF is x · x · x = x3

6x5 and 4x3

6x5 = 2 · 3 · x · x · x · x · x4x3 = 2 · 2 · x · x · x So the GCF is 2 · x · x · x = 2x3

FIND THE GCF OF THE TERMSa3b2, a2b5 and a4b7

a2b2

Notice that the GCF of terms containing variables will use the smallest exponent found amongst the individual terms for each variable.

STEPS IN FACTORING1. Find the GCF of all the terms.2. Write the polynomial as a

product by factoring out the GCF from all of the terms.

3. Remaining factors, in each term, will form a polynomial.

GREATEST COMMON FACTOR:

xx 105 2

)2(5 xxx5

GREATEST COMMON FACTOR:

pp 1421 2

)23(7 ppp7

GREATEST COMMON FACTOR:

xxx 1296 23

)432(3 2 xxxx3

GREATEST COMMON FACTOR:

xxx 321624 24

)423(8 3 xxxx8

FACTOR:

)2()2(6 xyx

)6)(2( yx )2( x

FACTOR:

)1()1( yyxy

)1)(1( xyy)1( y

FACTORING TRINOMIALS

When a = 1, we are looking for 2 numbers whose sum is “b” and

product is “c”

cbxax 2

X METHOD:

10

21Multiply

Add

3 7

FACTOR:

13

303 10

)10)(3( xx

30132 xx

FACTOR:

6

10

1062 xx

Not FactorablePrime Polynomial

FACTOR:

11

243 8

)8)(3( xx

24112 xx

FACTOR:

2

153 5

)5)(3( xx

1522 xx

APPLICATIONThe area of a rectangle is given by the trinomial x2 - 2x - 35. What are the possible dimensions of the rectangle? Use factoring.

x2-2x-35

)7)(5( xx

FACTORTWO VARIABLES:

6

555 11

)11)(5( yxyx

22 556 yxyx

PRACTICE ON YOUR OWN!

1272 xx

)3)(4( xx

PRACTICE ON YOUR OWN!

42132 ww

)6)(7( ww

PRACTICE ON YOUR OWN!

1032 nn

)5)(2( nn

COMPLETE.

5052 kk

)10)(5( kk 10

FACTORING WITH TWO VARIABLES - PRACTICE

22 183 baba

)3)(6( baba

HOW TO CHECK WORKDistribute answer out and you

should get the same answer.