Chapter 1: Algebra II Review

Topic 1: Simplifying Polynomials

Polynomial Operations:

Addition/Subtraction: Combine like-terms only

1. 2.

3. 4. Subtract from

Multiplication: Every term by every term

1. 2.

3. 4.

Homework: p. 56 #10-24, 32-36, 44, 48

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Chapter 1: Algebra II Review

Topic 2: Exponent Rules

Exponent Rules:

Remember: Exponents are always a little off from regular arithmetic rules.

Addition/Subtraction: Combine coefficients of

like-terms; exponents are unchanged

Multiplication: Multiply coefficients; add

exponents of like-bases

Division: Divide coefficients; subtract

exponents of like-bases

Negative Exponents: “I’m stuck on the wrong

side of the fraction line!” Hint: deal with these

first in complex questions!

1. 2. 3.

4. 5. 6.

7.

8. 9.

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Practice

Perform the indicated operation.

1. (9y2 - 12y + 5) - (12y2 + 6y - 11)

2. 8(7r + y) - 3(5r - 2)

3. 2(y2 + 4y) + 6y(y - 3) 4. (8r -1) - 3(10r - 8)

5. (3g3 - 2g2 + 1)(g - 4) 6. (9 - y2)(2y + 1)

7.

8.

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Use your knowledge of exponent rules to simplify the following expressions

9. 10.

11. 12.

13. 14.

15.

16.

17.

18.

Homework: p. 30 #24-64 Even

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Chapter 1: Algebra II Review

Topic 3: Simplifying Radical Expressions

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

Homework: p. 45 #13-20

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Chapter 1: Algebra II Review

Topic 4: Adding and Subtracting Radical Expressions

Adding & Subtracting Radicals:

Just like anything else, we can only _____________________________________________________________

When adding or subtracting radicals, both the ______________________ AND the

____________________________ must be exactly the same

Before we begin to combine, we must first _________________________________________________.

Example:

Add:

1. Simplify each of the terms

2. Combine the like terms (add/subtract the

coefficients of the like-radicands)

1. 2.

3. 4.

5. 6.

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7. 8.

9. 10.

11. 12.

Homework: p. 45 #37-44

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Chapter 1: Algebra II Review

Topic 5: Multiplying Radical Expressions

Multiplying Radicals: Multiply the numbers outside the radicals… the ________________________

Multiply the numbers inside the radicals… the _______________________

Simplify the radicals in your final answers. Do not simplify until __________________________!!!

Example:

Multiply:

1. Multiply coefficients; Multiply Radicands

2. Simplify at the end

*observe: if we simplified at the beginning,

we’d have to simplify again at the end!

1.

2.

3.

4.

5.

6.

7.

8.

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9.

10.

Definition: Conjugate Pairs -

_____________________________________________________________________________________

The result of multiplying conjugate pairs of radical expressions will ALWAYS be an INTEGER.

When multiplying conjugate pairs, we can skip FOIL and just multiple first & last terms. Be VERY sure you are

dealing with conjugate pairs before you take this shortcut!

Example:

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Homework:

Math 12 1-5 Multiplying Radical Expressions Worksheet

1) 2)

3) 4)

5) 6)

7) 8)

9) 10)

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Chapter 1: Algebra II Review

Topic 6: Rationalizing Expressions

Dividing Radicals: Divide the numbers outside the radicals, divide the numbers inside the radicals.

Simplify the radicals in your final answers. If necessary, _____________________ ________

____________________

Example: Rationalizing Monomial Denominators

Divide:

1. Divide as much as possible

2. Simplify at the end – Rationalize if necessary

Example: Rationalizing Binomial Denominators

Divide:

1. Divide as much as possible (usually nothing is possible with

binomial denominators)

2. Simplify at the end – Rationalize if necessary

1.

2.

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3.

4.

5.

6.

Homework: p.45 #45-54

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Chapter 1: Algebra II Review

Topic 7: Cube Roots

Finding the cube root of something is similar to finding the square root, but we must first become familiar with the

following list of perfect cubes:

This is the notation for a cube root, the 3 outside of the radical is known as the __________________

When simplifying a cube root expression, we follow the same procedure as simplifying a square root expression with

two differences:

1) For numbers, we are looking for the largest ________________________ that goes into the number.

2) For variable, we are looking for the largest __________________________ that goes into the exponent.

Simplify.

1. 2.

3.

4.

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5. 6.

7. 8.

9. 10.

11. 12.

Homework: p. 45 #55-58, 67-72

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Chapter 1: Algebra II Review

Topic 8: Fractional Exponents

Rational (Fractional) Exponents

The exponent is now a fraction. P = _____________

R = _____________

R = tells you what _________ to take

P = tells you what ____________ to _____________ it to

There are multiple ways of writing fractional

________________________ powers. We should be familiar with them all.

When you are dealing with a radical expression, you can convert it to an expression containing a rational (fractional)

power. This conversion may make the problem easier to solve.

1) Rewrite each of the following using roots instead of fractional exponents; then evaluate.

(a)

(b) 161/4

(c) 9-1/2 (d) 32-1/5

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2.) Rewrite the following as equivalent roots, then evaluate.

(a) 36-1/2 (b) 43/2 (c) 815/4

(d) 4-5/2 (e) 1283/7 (f) 625-3/4

3.) Which of the following is not equivalent to 163/2?

(1) (2) 83 (3) 64 (4)

4.) Which of the following is equivalent to x-1/2?

(1)

(2) (3)

(4)

5.) Which expression is equivalent to

?

(1)

(2) 3xy3 (3)

(5)

Homework: p. 46 #83-100