2.3 Factor and Solve 2.3 Factor and Solve Polynomial ExpressionsPolynomial Expressions

2.3 Factor and Solve 2.3 Factor and Solve Polynomial ExpressionsPolynomial Expressions

Pg. Pg. 7676

Factoring:• When Factoring expressions, there is an order

to follow when solving:– GCF

• Greatest Common Factor• This is for any polynomial

– Difference of Perfect Squares• Each term must be a perfect square• Coefficients must be perfect squares and even

exponents on the variables• This is for only BINOMIALS

– Reverse Foil• Finding the factors of the “C” term that when added

together make the “B” term with the correct sign

23 6 3 ( 2)a a a a

Remember to Completely Factor

2 16 4 4x x x

GCF (Greatest Common Factor)

23 6a a 2 3 3 2x y x y

3 23 12 12x x x

Difference of Perfect Squares

• Must be a Binomial• Must have subtraction between the terms

92 x 364 2 x

42 4925 yx

Reverse Foil Factoring x2 + bx + c

))((2 sxrxcbxx

Example:

1110

307

209

65

2

2

2

2

xx

xx

xx

xx

Factor by Grouping• Used when there is four terms in the

polynomial to factor• The object is to see if there is a common

GCF between the two groups

• Be careful when grouping monomials with a subtraction

3 22 4 3 6x x x

6397 23 yyy

Factoring Perfect-Square Trinomials

• If the first term and the last term of a trinomial are perfect squares but there is a center term

• It can not be the difference of perfect squares but it may be a perfect square trinomial

• a2 + 2ab + b2

• a2 – 2ab + b2

Example:

• x4 – 16

• 4x2 – 24x + 36

• 9x2 – 49

• 3x2 + 6x + 3

Sum and Difference of Cubes

• Just like with the Difference of Perfect Squares…….this must be a binomial.

• But now the 1st and 2nd terms are perfect cubes• These are formulas, answer is completely factored

3 3 2 2

3

3 3 2 2

3 3

( )( )

8

( )( )

27

a b a b a ab b

a

a b a b a ab b

a b

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