Review Commutative, Polynomials, algebra

Review Properties, Polynomials, Algebra

by Michael Martino

​Review Commutative, Associative, Identity

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​Review Commutative, Associative, Identity

​1.

5 + b = b + 5 is Commutative, because the terms switch

​Review Commutative, Associative, Identity

​2.

3 + (f + d) = (3 + f) + d is Associative, because:

​

​ 1. They stay in the same order, and

​ 2. The parenthesis grouping moves

​Review Commutative, Associative, Identity

​3.

5 + 0 = 5 is Identity Addition because when I add zero to something, I get the original term

​Review Commutative, Associative, Identity

​4.

5 * 1 = 5 is Identity Multiplication because when I multiply one to something, I get the original term

Fill in the Blank

1.   State the name of the property demonstrated:

a + 7 = 7 + a

(use the previous slides to help you. spelling matters!)

Fill in the Blank

2.   State the name of the property demonstrated:

8 + (t + 9) = (8 + t) + 9

(use the previous slides to help you. spelling matters!)

Fill in the Blank

3.   State the name of the property demonstrated:

r + 0 = r

(use the previous slides to help you. spelling matters!)

​When you multiply like bases

​

​x times x is x²

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​because you add the exponents 1 + 1 when multiplying like bases

Multiple Choice

4.  What is  (4x³)(3x⁴)

(write down the question on paper and show work)

• 7x⁷

• 12x¹²

• 12x⁷

• 12x^-1

Multiple Choice

5.  What is  4x²(x³ + 8x⁵)

(write down the question on paper and show work)

• 4x⁵ + 32x⁷

• 5x⁵ + 32x⁷

• 4x⁶ + 32x¹⁰

• 4x⁵ + 12x⁷

​To distribute binomials:

​(x + 6)(x + 2)

​

​use the box method:

​

​-multiply the outsides

​-combine (add or subt) the insides

​To distribute binomials:

​(x + 6)(x + 2)

​

​use the box method:

​

​-multiply the outsides

​-combine (a or s) the insides

​

​this gives us:

​ ​x² + 8x + 12

Fill in the Blank

6.   Simplify by multiplying:   (x + 4)(x + 2)

(hint, use the box method on the previous page!)

(to type in  $$x^2$$ , type in x^2 below

(write down the question on paper and show work)

​Adding or Subtracting

​

x + x = 2x

​Adding or Subtracting

​

x + x = 2x --> because you combined like terms

​Adding or Subtracting

​Adding or Subtracting

​When you add or subtract, do you add the exponents?

​

​When you add or subtract, do you add the exponents?

​

​

​

​NO!!

​When you add or subtract, do you add the exponents?

​

​

​

​NO!! --> only add the coefficients! exponents stay the same

Multiple Choice

7.   What is  $$7x^2\ +\ 9x^2$$  

(write down the question on paper and show work)

• $$16x^2$$  

• $$16x^4$$  

• $$63x^2$$  

• $$63x^4$$  

Multiple Choice

8. What is -x + 3x

• -3x

• $$-3x^2$$  

• $$2x^2$$  

• 2x

Multiple Choice

9.  Simplify:    $$\left(7x^2-1x\ +\ 7\right)\ +\ \left(9x^2\ +\ 3x\ +\ 4\right)$$  

(write down the question on paper and show work)

• $$16x^4+2x^2+11$$  

• $$63x^2-3x+28$$  

• $$16x^2+2x+11$$  

• $$16x^4+2x^2+28$$  

Multiple Choice

10. Solve for x:

6x - 8 = 4

Hint: do SA DM E P

• x = -0.6666

• x = 2

• x = 6

• x = -2

Multiple Choice

11. Solve for x:      $$\frac{1}{2}\left(x+4\right)=20$$  

Hint: distribute, then do SA DM E P

• x = 36

• x = 32

• x = 48

• x = 8

Multiple Choice

12. Solve for x:

2x = 3x -8

• x = -8

• x = 8

• x = -1.6

• x = 1.6

Multiple Choice

13.  Solve for x:     $$\frac{x-1}{3}=\frac{x+3}{5}$$  

• x = 7

• x = 2

• x = -1

• x = 1.75

Fill in the Blank

14. Filomena is 36 inches tall. She casts a shadow that is 8 inches long.

Vincenzo is 12 inches tall. How what is the length of his shadow?

Multiple Choice

15.  Solve for d: 

6d - r = 8

• $$d=\frac{8+r}{6}$$  

• $$d=\frac{6+r}{8}$$  

• d = 8+r-6

• $$d\ =\frac{8r}{6}$$