Mid Chapter Review
Chapter
Chapter 4
Section
Mid Chapter Review
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Solutions 44 Videos

State the GCF for the following pair of terms.

24 and 60

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Q1a

State the GCF for the following pair of terms.

x^3 and x^2

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Q1b

State the GCF for the following pair of terms.

10y and 5y^2

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Q1c

State the GCF for the following pair of terms.

-8a^2b and -12ab^2

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Q1d

State the GCF for the following pair of terms.

c^4 d^2 and c^3 d

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Q1e

State the GCF for the following pair of terms.

27 m^4 n^2 and 36 m^2 n^3

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Q1f

Determine the missing factor.

7x - 28y = (\blacksquare)(x - 4y)

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Q2a

Determine the missing factor.

6x - 9y = (3)(\blacksquare)

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Q2b

Determine the missing factor.

24a^2 + 12b^2 = (\blacksquare)(2a^2 + b^2)

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Q2c

Determine the missing factor.

x^2 - xy^3 = (x)(\blacksquare)

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Q2d

Determine the missing factor.

-15x^2 + 6y^2 = (\blacksquare)(5x^2 -2y^2)

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Q2e

Determine the missing factor.

a^4b^3 - a^3b^2 = (a^3b^2)(\blacksquare)

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Q2f

The tiles in the model represent an algebraic expression. Identify the expression and the greatest common factor of its terms.

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Q3a

The tiles in the model represent an algebraic expression. Identify the expression and the greatest common factor of its terms.

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Q3b

Factor the expression.

7z + 35

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Q4a

Factor the expression.

-28x^2 + 4x^3

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Q4b

Factor the expression.

5m^2 - 10mn + 5

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Q4c

Factor the expression.

x^2y^4 - xy^2 + x^3y

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Q4d

A parabola is defined by the equation y = 5x^2 -15x. Explain how you would determine the coordinates of the vertex of the parabola, without using a table of values or graphing technology.

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Q5

Factor the expression.

3x(5y - 2) + 5(5y - 2)

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Q6a

Factor the expression.

4a(b + 6) - 3(b + 6)

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Q6b

Factor the expression.

6xt - 2xy - 3t + y

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Q6c

Factor the expression.

4ab + 4ac - b^2 - bc

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Q6d

The model represents a quadratic expression. Identify the expression and its factors.

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Q7a

The model represents a quadratic expression. Identify the expression and its factors.

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Q7b

Determine the value of each symbol.

x^2 + \blacklozenge x + 12 = (x + 3)(x + \blacksquare)

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Q8a

Determine the value of each symbol.

x^2 + \blacksquare x + \blacklozenge = (x + 3)(x + 3)

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Q8b

Determine the value of each symbol.

x^2 - 12x + \blacksquare = (x - \blacklozenge)(x - \blacklozenge)

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Q8c

Determine the value of each symbol.

x^2 - 7x + \blacklozenge = (x - 3)(x - \blacksquare)

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Q8d

Factor.

x^2 + 8x - 33

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Q9a

Factor.

n^2 + 7n -18

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Q9b

Factor.

b^2 - 10b - 11

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Q9c

Factor.

x^2 - 14x + 45

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Q9d

Factor.

c^2 + 5c - 14

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Q9e

Factor.

y^2 - 17y + 72

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Q9f

Factor.

3a^2 - 3a - 36

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Q10a

Factor.

x^3 - 6x^2 - 16x

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Q10b

Factor.

2x^2 + 14x - 120

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Q10c

Factor.

4b^2 - 36b + 72

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Q10d

Factor.

-d^3 + d^2 + 30d

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Q10e

Factor.

xy^3 + 2xy^2 + xy

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Q10f

Deanna throws a rock from the top of a cliff into the air. The height of the rock above the base of the cliff is modeled by the equation h = -5t^2 + 10t + 75, where h is the height of the rock in metres and t is the time in seconds.

a) How high is the cliff?

b) When does the rock reach its maximum height?

c) What is the rock's maximum height?

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Q11

When factoring a quadratic expression of the form x^2 + bx + c, why does it make more sense to consider the value of c before the value of b? Explain.

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Q12

Use the quadratic relation determined by y = x^2 + 4x - 21.

a) Express the relation in factored form.

b) Determine the zeros and the vertex.

c) Sketch its graph.

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Q13