A.3 ObjectivesA. Polynomials and Factoring

1. Understand the vocabulary of polynomials

2. Add and subtract polynomials

3. Write polynomials in standard form.

4. Multiply polynomials

5. Special Products

6. GCF

7. Factor Polynomials with 2 or 3 terms.

8. Factor Polynomials with more than 3 terms.

9. Find the GCF of any polynomial expression

9. Special cases: Simple case, when

cbxx 2

124 6) 2 xx

1a

Warning: is Prime

9. Special Binomial Products

BABA 22 BA

22 BABABA

22 BABABA

33 BA

33 BA

22 BA

10. Practice

Factor each. If it does not factor, state that it is PRIME.1.

2.

3.

4.

Study Tip: No middle term = special product!

14 x

162 x

57 xx

18 3 x

Factoring PolynomialsSummary

1. Factor out GCF

2. Binomial? is it “special” ?

3. Trinomial? Use factoring algorithm

4. 4 terms? Use grouping

333322 or or BABABA

11. Polynomial with 4 terms

3x 3 2x 2 12x 8

Use Grouping (double bubble)

1)

2)

4x 3 20x 2 9x 45

Example: Factor the expression:

1)

2)

Where t is algebraic expression is called quadratic in form.

12. An expression Quadratic in Form

cbtat 2

6)13(4)13(2 2 xx

12 36 xx

324 29)2(6 xxxx 1.

13. Finding the GCF of an expression13. Finding the GCF of an expression

2. 433243 2 xxx