4.4 day 1

4.4 FACTORING QUADRATIC EXPRESSIONSPart 1

FACTORS

Factors are the numbers you multiply together to get another number.

The factors of an expression are expressions that you multiply together to get another expression.

Factoring is rewriting an expression as a product of its factors.

FACTORING

To factor a polynomial means to transform it to a product of two or more factors (usually binomials)

Factoring is the reverse process of FOIL (Double Distribution)

FOIL can be used to check your work

TO FACTOR A POLYNOMIAL OF THE FORM

1. What are factors of c that add up to b?2. Set up factors

3. Plug in the numbers4. Check

2x bx c

x x

FACTOR EACH EXPRESSION2 9 20x x

REMEMBER

When the third term is positive in a quadratic trinomial, the binomial factors have the same sign

THIRD TERM IS NEGATIVE

When the third term is negative the binomial factors have opposite signs

2x bx c x x

GCF

The greatest common factor (GCF) of an expression is a factor that all the terms in an expression have in common.

Always factor out the GCF first! The GCF can be a number, a variable, or both

FIND THE GCF OF THE EXPRESSION. THE FACTOR THE EXPRESSION.

27 21n


26 9x x


24 20 56x x


29 9 18x x

LEADING COEFFICIENTS The leading coefficient of a polynomial is

the coefficient of the term with the highest degree

We know how to factor quadratic trinomials whose leading coefficient is 1

We will learn how to factor quadratic trinomials whose leading coefficients are not 1

THE ARC METHOD

Used to factor quadratic trinomials whose leading coefficients are not 1

STEPS OF THE ARC METHOD

1. “Arc” the leading coefficient2. Factor3. Divide both by the leading coefficient that

was arced4. Simplify if possible5. Undo the arc6. Check

FACTOR THE EXPRESSION

22 11 12x x


24 4 3x x


22 7 6x x

HOMEWORK

P221 #1 – 3, 15 – 45odd

4.4 day 1

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