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Algebra – TOOL KIT

Chapter 5 Test Review

5.1 ExponentsSimplify. Express using only positive exponents.

1) a4 ( a7

2) (3x2y3)(-2x4y)

3)

4) 5a-4

5.2 More with ExponentsSimplify. Express using only positive exponents.

1) (n5)3

2) (2c3d)4

3)

5.3 Multiplying and Dividing MonomialsMultiply:

1) (-4a3b)(2a2b5)

2) (3m4)(-m3)(7m)

Divide

3)

4)

Simplify:

5) (x4y)3(x2y-3)2

6)

5.5 Scientific NotationWrite in standard notation.

1) 3.14 ( 105

2) 2.05 ( 10-3

Write in scientific notation.

3) 0.0000417

4) 8,640,000,000,000

Multiply or divide. Write your answer in scientific notation.

5) (3.6 ( 104)(1.5 ( 108)

6)

5.5 PolynomialsIdentify as a monomial, binomial, trinomial or polynomial. Give the coefficient of each term.

1) –x3 + 5x4 – 3

2) 12x2y3z5

Collect like terms.

3) –4x2y + 5xy2 – x2y + 3

4) 5a3 + a4 – 2a + 6a4

5.6 More about PolynomialsWrite in descending order for the variable x.

1) 7x3 – 4x5 + x + 5x2 – 4x4y

Write in ascending order for the variable x.

2) 2x3 – 4x5 + x + 4x2 – 9

Evaluate the polynomial for the given value.

3) 2x3 – 5x2 + 4x – 8 for x = -2

5.7 Addition of PolynomialsAdd:

1) 5m3 – 2m4 + m and 2m – 5m3

2) (5x3 – 7x2 + 4) + (-2x3 + 5x2 +6x)

3)

5.8 Subtraction of PolynomialsSubtract:

1) (4n2 – 3n + 8) – (n2 + 5n – 3)

2) (x3 – 2x2 + 5) – (4x3 + 5x2 – x)

3)

5.9 Multiplication of Monomials and BinomialsMultiply:

1) 3x2(4x3 – 2x + 5)

2) (3x – 5)(2x + 1)

3) (4x2 – 3)(x + 5)

5.10 Multiplying Binomials: Special ProductsMultiply:

1) (x – 5)(x + 5)

2) (3x – 2)(3x + 2)

3) (2x + 3)2

4) (x – 4)2

5.11 Multiplying PolynomialsMultiply:

1) (5x2 – 2x + 4)(x + 6)

2) (2x – 1)(x3 – 2x2 + 5x)

3) (x – 9)(3x + 4)

4) 4x2y(3x2 – 4x + 7)

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