Factoring A Factoring A Quadratic ExpressionQuadratic ExpressionFactoring A Factoring A Quadratic ExpressionQuadratic ExpressionFeb. 25, 2014Feb. 25, 2014

SWBAT Factor a Quadratic Expression

WARM – UP

6x6 – 4x2 + 2x12x2y + 24xy2 – 28xy

SWBAT Factor a Quadratic Expression

Greatest Common Factor (GCF)The Greatest Common Factor (GCF) is the largest numeric value and variable power that can be divided out of a polynomial. Always start by factoring out any GCF!

Example 1: Factor 8x4 – 12x3 – 16x2

GCF: 4x2

You can treat the coefficients separately from each variable. First, look for the largest value that is a factor of 8, 12, and 16. 4 is the largest valueThen, for each variable, find the greatest power of that variable that can be divided out of that variable. The greatest power of x that can be divided out of x4, x3, and x2 is x2.SWBAT Factor a Quadratic Expression

SWBAT Factor a Quadratic Expression

Think of what will remain when you divide each term by the GCF. Writing the problem this way may help you see what the remaining factor is. **Recall that when you divide powers of a variable, you subtract the exponents.Write the GCF on the left, and the remaining factor in parentheses on the right.4x2(2x2 – 3x – 4)

SWBAT Factor a Quadratic Expression

Example 2: 16x4 – 12x3 – 4x2 Be Careful of This!!! GCF: 4x2

4x2(4x2 – 3x – 1)

SWBAT Factor a Quadratic Expression

Practice 1: Factor each of these by determining the GCF1. 12ab + 30ac 2. p + prt3. 12x2y3 – 18xy4 4. 6b2 – 36b3

5. x3 – 3x2 + x 6. 2x4 – 6x2 + 12x6

SWBAT Factor a Quadratic Expression

Example 2: Factor by GroupingWhen a polynomial has four terms, make two groups and factor out the GCF from each group.Factor 8x3 + 6x2 + 20x + 15 Step 1: Group terms that have common factors8x3 + 6x2 + 20x + 15 Step 2: Identify and factor the GCF out of each group 2x2(4x + 3) + 5 (4x + 3)

SWBAT Factor a Quadratic Expression

Step 3: Factor out the common binomial factor & Regroup:(4x + 3)(2x2 + 5) Step 4: CHECK (4x + 3)(2x2 + 5) = 8x3 + 6x2 + 20x + 15

SWBAT Factor a Quadratic Expression

Factor each polynomial filling in the blanks.1. 2.

3x2

3x2

4

4

3x2 + 4

5a2 6

5a2 6

5a2 + 6

SWBAT Factor a Quadratic Expression

Factor each polynomial by grouping3.

4.

3x2(7x + 4) + 2(7x + 4)(3x2 + 2)(7x + 4)

10x2(4x – 5) + 3(4x – 5)(10x2 + 3)(4x – 5)

SWBAT Factor a Quadratic Expression

SUMMARY

HW P 14/ 1-20

SWBAT Factor a Quadratic Expression

A2T Apps: Greatest Common Factor Factoring EXIT TICKET QUIZ: Factor each of the following by GCF.