Algebra 3Lesson 2.1

Objective: SSBAT multiply polynomial expressions.

Standards: M11.D.2.2.1

Algebra 3Warm-Up 2.1

Multiply each.

1. 9x2 ∙ 3x4 ∙ 2x3

2. 10mn ∙ -12mn

3. -7x5y2 ∙ -2xy6

Examples: Multiply each.

1. 3x(x3 – 7x2 + 8x – 2)

= 3x4 – 21x3 + 24x2 – 6x

2. x3(5x2 – 12x + 8)

= 5x5 – 12x4 + 8x3

3. (x + 2)(x – 3)

= x2 – 3x + 2x – 6

= x2 – 1x – 6

FOIL

4. (2x + 9)(3x – 5)

= 6x2 – 10x + 27x – 45

= 6x2 + 17x – 45

5. (5x – 7)(5x + 7)

= 25x2 + 35x – 35x – 49

= 25x2 – 49

6. (3x2 – 5)(4x2 – 2)

7. (m2 – 5n2)(2m2 + 3n2)

8. 5(x – 1)(2x + 3)

Work with 2 at a time

5(x – 1) = 5x – 5

Then: (5x – 5)(2x + 3)

= 10x2 + 15x – 10x – 15

= 10x2 + 5x – 15

9. 3x(x – 5)(x – 4)

3x(x – 5) = 3x2 – 15x

Then: (3x2 – 15x)(x – 4)

= 3x3 – 12x2 – 15x2 + 60x

= 3x3 – 27x2 + 60x

10. (x + 2)(x2 – 5x + 8)

= x3 – 5x2 + 8x + 2x2 – 10x + 16

= x3 – 3x2 – 2x + 16

11. (x – 3)(2x2 + x – 9)

= 2x3 + x2 – 9x – 6x2 – 3x + 27

= 2x3 – 5x2 – 12x + 27

12. (x – 4)2

= (x – 4)(x – 4)

= x2 – 4x – 4x + 16

= x2 – 8x + 16

13. Find the Area of a Rectangle whose width is (x + 7) units and length is (x2 – 2x + 11) units.

A = lw

A = (x + 7)(x2 – 2x + 11)

A = x3 – 2x2 + 11x + 7x2 – 14x + 77

A = x3 + 5x2 – 3x + 77 units2

14. Which has a greater Area, a square with a side that is (x + 3) units long or a Rectangle with a width of x units and a length of (x + 6) units?

Area of Rectangle: A = lw

Find Area of Square A = (x + 3)(x + 3)

= x2 + 3x + 3x + 9

= x2 + 6x + 9

Find Area of Rectangle A = x(x + 6)

= x2 + 6x

The Area of the Square is Greater.

Quadratic Equation

An equation of the form, ax2 + bx + c = 0

There is an exponent of 2 and that is the highest exponent

Examples: 5x2 – 3x + 8 = 0

9x2 – 7 = 0

-5x2 = 0

Determine if each of the following is a Quadratic Equation or not. (you may need to simplify first)

1. 5x3 – 6x2 – 3x + 18 = 0

No

2. 8 – 7x + 12x2 = 0

Yes

3. (x – 2)(x + 8) = 0

x2 + 8x – 2x – 16 = 0

x2 + 6x – 16 = 0

Yes

4. -15x2 – 12 = 0

Yes

5. 7x – (15x + 6x2) + 6x2 = 0

7x – 15x – 6x2 + 6x2 = 0

-8x = 0

No

On Your Own. Multiply each.

1. (x – 7)(x – 9)

2. x(x + 5)(3x + 7)

Homework

Worksheet 2.1