Pre-CalculusSec 1.3 Algebraic ExpressionObjectives:•To use special product formulas to factor expressions by finding common factors & recognizing special cases.•To factor quadratics.

Class Work

Simplify.1. (x3 – 6x2 + 2x + 4) + (x3 + 5x2 – 7x) 2x3 – x2 – 5x + 42. (x3 – 6x2 + 2x + 4) - (x3 + 5x2 – 7x) –11x2 + 9x + 43. (x2 – 3)(x3 + 2x + 1)

Special Product Formulas

If A and B are real numbers or algebraic expressions then,

1) 2)3)4)5)

2 2A B A B A B

2 2 22A B A AB B

2 2 22A B A AB B

3 3 2 2 33 3A B A A B AB B

3 3 2 2 33 3A B A A B AB B

Ex 1. Use special product formulas to find each product.

(a) (3x + 5)2

(b) (x2 – 2)3

(c) (2x – )(2x + )y y

Class Work

Use special product formulas to find the products.

4.

5.

22 7x

35 2x

Factoring.

Factoring an expression - writing that expression as a product of simpler ones.

2 4 ( 2)( 2)

Factoring

Expanding

x x x

Factoring out a GCF

Ex 2. Factor each expression.(a)3x2 – 6x

(b)8x4y2 + 6x3y3 – 2xy4

(c)(2x + 4)(x – 3) – 5(x – 3)

Factoring x2 + bx + c.

Ex 3. Factor each expression.a)x2 + 7x + 12

b) x2 + x – 6

c) x2 – 2x – 3

Class Work

Factor.6.

7. x2 + 4x – 21

8. x2 - 4x – 45

3 5 2 36 12a b a b

Factor ax2 + bx + c .

Ex. 4 Factor.a)6x2 + 7x – 5

b)8x2 + 11x +3

c) 6x2 + 13x – 5

Special Factoring Formulas

1) Difference of Squares:2) Perfect Square:

3) Difference of Cubes: 4) Sum of Cubes:

2 2A B A B A B

22 22A AB B A B

22 22A AB B A B

3 3 2 2A B A B A AB B

3 3 2 2A B A B A AB B

Ex 5 Factor each expression.

a) 4x2 – 25

b) x3 + 8

Class Work

Factor.9. 5x2 – 9x – 2

10. 4x2 – 25x + 6

11. 27x3 – 1

12. 49x2 – 64

Factoring by Grouping

Ex 6. Factor by grouping.(a)x3 + x2 +4x + 4

(b) x3 – 2x2 – 3x + 6

HW #3 p 31 7-15 odd, 33-96 mult of 3, omit 69