Ch 6. Exponents and Polynomials

Simplify the expression below.

1. 5m

2. m⁵

3. m¹³

4. m²⁴

5. m⁵/ m

m⁵

Which of the following is equivalent to the expression below?

1. 

2. 

3. 

4. 

5. 

Which of the following is equivalent to the expression below?

1. 

2. 

3. 

4. 

5. 

r³/t³

Which of the following is equivalent to the expression below?

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2. 

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4. 

5. 

Simplify using ONLY positive exponents.

1. 1/x⁷

2. 0

3. 1

4. x⁷

5. x^-7

1

Simplify using ONLY positive exponents.

1. 

2. 

3. 

4. 

5. 

What is the formula for zero exponents if the base is nonzero?

1. Any nonzero number or letter raised to the zero exponent is always -1.

2. Any nonzero number or letter raised to the zero exponent is always a fraction.

3. Any non zero number or letter raised to the zero exponent is always 1.

4. Any nonzero number or letter raised to the zero exponent is always 0.

Any non zero number or letter raised to the zero exponent is always 1.

Which of the following is true regarding negative exponents?

1. To convert a negative exponent in the denominator to a positive exponent, move it to the numerator

2. A negative exponent requires subtracting the exponent from the base number.

3. A negative exponent requires subtracting the base number from the exponent.

4. Any number to any negative exponent is equal to 0.

To convert a negative exponent in the denominator to a positive exponent, move it to the numerator

Simplify the following expression.

1. 94

2. 1

3. 0

4. 93

5. -93

1

Which of the following is equivalent to the expression below?

1. 

2. 

3. 

4. mn

5. 1

1

Simplify the expression below using positive exponents only.

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5. 

Simplify the following expression using positive exponents.

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5. 

Simplify the following expression using positive exponents only.

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4. 

Simplify the expression below using only positive exponents.

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4. 

Which of the following radical expressions is equal to this exponential expression?

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Which of the following is equivalent to the following expression?

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5. 

Which of the following is equivalent to the following expression?

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Which of the following exponential expressions is equal to this radical expression?

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Simplify the following expression:

1. 1/(4x)

2. 1/4

3. 1/2

4. x/2

1/2

Simplify the following expression:

1. (5x)/81

2. (5x)/9

3. (25x)/81

4. (5/9)x

(5x)/9

Simplify the following expression:

2xy^2

Which of the following is NOT a part of a radical expression?

1. radicand

2. radical symbol

3. axis

4. index

axis

A simplified expression may contain _.

1. a radical in the numerator

2. a radical in the denominator

3. a radicand that is a fraction

4. a radicand with a perfect root factor

a radical in the numerator

Simplify the following expression so that all the exponents are positive.

Simplify the expression:

1. 

2. 

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4. 

5. 

Simplify this expression.

Simplify this expression so that all the exponents are positive.

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5. 

Simplify the expression and make sure all the exponents are positive in the answer.

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2. 

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4. 

5. 

Which of the following shows the graph of the equation below?

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Which of the following shows the graph of the equation below?

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5. 

Which of the following shows the graph of the equation below?

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5. 

Which of the following shows the graph of the equation below?

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Which of the following shows the graph of the equation below?

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5. 

Add: (x² + 5x + 2) + (x² - 2x + 7).

1. 2x² - 7x - 9

2. 2x² - 3x - 9

3. 2x² + 7x + 9

4. 2x² + 3x + 9

2x² + 3x + 9

Subtract: (x³ + x³ + 6) - (x³ - 2x + 1).

1. x³ + 2x - 5

2. x³ + 2x + 5

3. x² + 2x - 5

4. 3x³ + 2x - 5

x³ + 2x + 5

Multiply: (x + 1)(x + 6)

1. 2x + 7

2. x² + 7x + 6

3. 2x + 6

4. x² + 6x + 5

x² + 7x + 6

Subtract: (x² + 3x + 4) - (7x² - 5x + 2)

1. -6x² - 8x - 2

2. -6x² - 8x + 2

3. -6x² + 8x + 2

4. 6x² + 8x + 2

-6x² + 8x + 2

What is the procedure for subtracting polynomials:

1. Multiply the second expression by -1 and add the two expressions together.

2. Multiply the second expression by +1 and subtract the two expressions.

3. Multiply the second expression by +1 and add the two expressions together.

4. Multiply the second expression by -1 and subtract the two expressions.

Multiply the second expression by -1 and add the two expressions together.

Divide using long division.

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5. 

Divide using long division.

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5. 

Divide using long division.

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5. 

Divide using long division.

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5. 

Divide using long division.

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5. 

Divide using synthetic division.

(x³ + 9) / (x + 2)

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5. 

Divide using synthetic division.

(x⁴ + 5x³ - 15x² - 12x - 60) / (x - 3)

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Divide using synthetic division.

(x³ - 3x² + 5) / (x - 1)

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Divide using synthetic division.

(x² + x - 20) / (x + 5)

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Divide using synthetic division.

(2x³ + 5x² - 9) / (x + 1)

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Use the Remainder Theorem to find the remainder when f(x) = x^4 + 4x^3 - x^2 - 16x -12 is divided by x - 4.

1. 548

2. 36

3. 420

4. -92

420

Which of the following should be evaluated in order to determine if x - 2 is a factor of x^3 + 3x - 4?

1. f(-2)

2. f(x - 2)

3. f(4)

4. f(2)

f(2)

Use the Factor Theorem to determine which expression is a factor of the following polynomial:

f(x) = x³ - 2x² - 31x - 28.

1. (x + 3)

2. (x - 7)

3. (x + 7)

4. (x - 3)

(x - 7)

Which example correctly illustrates the Remainder Theorem?

1. f(x) = x^5 - 5; if x - 1 is a factor of f(x), then f(1) equals 0

2. f(x) = x^5 - 5; if f(x) is divided by x - 1, then the remainder equals f(-1)

3. f(x) = x^5 - 5; if f(1) equals 0, then x - 1 is a factor of f(x)

4. f(x) = x^5 - 5; if f(x) is divided by x - 1, then the remainder equals f(1)

f(x) = x^5 - 5; if f(x) is divided by x - 1, then the remainder equals f(1)

Which example correctly illustrates the Factor Theorem?

1. f(x) = x^3 - x^2 + x - 1; f(2) = 5, so x - 2 is a factor of f(x)

2. f(x) = x^3 - x^2 + x - 1; f(1) = 0, so x - 1 is a factor of f(x)

3. f(x) = x^3 - x^2 + x - 1; x - 1 is a factor of f(x), so f(-1) = 0

4. f(x) = x^3 - x^2 + x - 1; f(1) = 0, so x + 1 is a factor of f(x)

f(x) = x^3 - x^2 + x - 1; f(1) = 0, so x - 1 is a factor of f(x)

Divide the following polynomials:

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Divide the following polynomials:

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Divide the following polynomials:

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Divide the following polynomials:

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Divide the following polynomials:

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4.