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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

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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