hw: 4/23

hw: ws 11.1

notes 11.1

11.1 Ratio and Proportion
Proportion- 2 equal ratios or fractions
a/b = c/d a and d are the extremes and b and c are the means

• If 2 ratios are equal, then their reciprocals are equal too
• If you cross multiply, the products will also be equal
Try: 3/y = 5/8

x/3 = 12/x

Practice for Algebra 1 Test Ch 10!!!!!!!!

10.1 Adding and subtracting Polynomials

Find the sum or difference:

1) (-6x³+5x²-3)-(2x³+4x²-3x+1) 2) (6x²-x+3) + (-2x+x²-7)

3) (12x-8x²+6)-(-8x²-3x+4) 4) -(2x³+3x – x +5) – (x³+2x -1)

10.2 Multiplying Polynomials

Multiply:

4) (3t+5)(t-3) 5) (2x+10)( ½ x + 2 ) 6) (3x+4)²

7) (4x²-3x-1)(2x-5) 8) (2x+3)(8-x-3x²)

9) Write a polynomial expression for the area of a rectangle with a length of 2x-1 and a width of 3x+2.

10.4 Solving Polynomial Equations in Factored Form (Using Zero Product Property)

Solve:

10) y=(x-3)(x+2) 11) y=(x-4)(x+2)

12) (2x+1)(3x-2)(x-1)=0 13) (x+5)²=0

10.5 Factoring x²+bx+c

Solve by factoring:

14) x²+11x+10=0 15) x²-17x+60=0 16) x²+6x+9=0

17) x²-2x=24 18) x²-15x= -54 19) –x²-4x=3

10.6 Factoring ax²+bx+c

Solve by factoring :

20) 2x²+x-6=0 21) 9x²+24x=-16 22) 2x²+7x= -3

23) 20x²+23x+6=0 24) 4x²-5x= 6 25) 2x²+3x+9

10.8 Factoring Using the Distributive Property

Solve by factoring:

26) 2x³-10x²+8x=0 27) x⁴-4x³+x²-4x=0 28) -2x⁵-2x⁴+4x³=0

29) 4x²+40x+100 30) 4x²-16x-48 31) 2x²+28x+98

32) The width of a box is 1 cm less than its length. The height of the box is 9cm greater than the length. The box has a volume of 72 cm³. What are the dimensions of the box?

Chapter Wrap Up- Solve the following using any method you choose. Your choices are: Graphing by hand, “Square Rooting”, Quadratic formula, Factoring, **Factoring by Grouping, **Distributive Property + Factoring. You should then choose a SECOND method to check your answer. Lastly, check with the graphing calculator!!!!!!!!! The bold indicates methods that your test will be focusing on. **= you may only use these methods when applicable.

33) x²-60= -11 34) x²-16=0 35) x²-13x= -40

36) (x+9)² 37) 20x²+23x+6 = 0 38) 4x²+12x+9=0

39) 4x²+4x -5=0 40) -2x²+4x+6=0 41) 3x²+14x=5

notice: Ch 10 Test

notice: We will be having a test on Chapter 10 this Friday 4/13. The plan is to review tomorrow and Thursday, however if there is a delay or no school due to weather- WE WILL STILL HAVE THE TEST FRIDAY!!!!!!

hw: 4/10

hw: ws 10-8 DO THE PUZZLE ON THE BACK FOR EXTRA CREDIT!!!!!! You must show work to get extra credit points!

notes 10.7 and 10.8

10.7 Factoring Special Products
Difference of 2 squares: a2-b2=(a+b)(a-b)
Ex. 16x2-4 = (4x+2)(4x-2)

Perfect Square Trinomial:
a2+2ab+b2= (a+b)2 Ex: x2+8x+16=(x+4)2

a2-2ab+b2= (a-b)2 Ex: x2-12x+36=(x-6)2


10.8 Factoring Using the Distributive Property
Before you begin to factor a polynomial, it is useful to factor out any common factor among all the terms first.
9x2-15 From this, I can factor out a 3 to get 3(3x2-5)

Once you have factored a polynomial completely, it is called prime

5x2-10x-40 –Factor out a 5 first to get:
5(x2-2x-8) since this it equal to 0, divide both sides by 5 to “get rid” of it
Then factor like normal

Try: 45x4-20x2

5x3+30x2+40x

3x3-15x2-6m+30



ws 10-8 //// puzzle

notes 10.6

10.6 Factoring ax2+bx+c
1) Write the trinomial in standard form
4x2-21x+5=0
2) Multiply a by c
4•5=20
3) Find factors of ac that will add up to “b”
factors of 20: -1,- 20 -2,- 10 -4,- 5
4)Rewrite the quadratic replacing “bx” with the two new factors
4x2-1x-20x +5=0
4) Split this into two groups
4x2-1x -20x+5
5)”Pull out” common factors
x(4x-1) -5(4x-1)
6) You should now have both binomials in the parentheses identical. If you do not, check your work and adjust your negatives.
7)Whatever is inside the parentheses becomes one factor, the second factor is the terms outside the parentheses
(4x-1)(x-5)
8) FOIL to check

try: 7x2-4x-3

6x2-5x-21

10x2+25x-90

21n2+14n+7=6n+11

ws 10-6