Chapter

Chapter 5
Section

Practice Test on Quadratic Expressions

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Solutions
44 Videos

What binomial product does each diagram illustrate?

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Q1a

What binomial product does each diagram illustrate?

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Q1b

Simplify.

```
\displaystyle
4x^2(3x -5y + 8z)
```

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Q2a

Simplify.

```
\displaystyle
3m(6m^205m + 4) -(4m^3 - 8m^2 + 9)
```

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Q2b

Expand and simplify.

```
\displaystyle
(y + 5)(y+ 9)
```

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Q3a

Expand and simplify.

```
\displaystyle
(4x -7)(3x + 2)
```

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Q3b

Expand and simplify.

```
\displaystyle
(6k + 1)(6k -1)
```

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Q3c

Expand and simplify.

```
\displaystyle
(w -8)^2
```

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Q3d

Expand and simplify.

```
\displaystyle
(4c + 5d)^2
```

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Q3e

Expand and simplify.

```
\displaystyle
2(x -4)(x - 7)-5(8x -9)(8x + 9)
```

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Q3f

The minimum stopping distance, after a delay of 1 s, for a particular car is
modelled by the formula `d = 0.006(s + 1)^2`

, , where `d`

represents the stopping distance, in metres, and s represents the initial speed, in kilometres per hour.

a) Expand and simplify the formula.

b) Compare the results in both versions of the formula for an initial speed of 60 km/h.

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Q4

Factor.

```
\displaystyle
9d^2e^2 +6d^3e
```

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Q5a

Factor.

```
\displaystyle
15p^2qr^3-25p^3q^2r + 5pqr
```

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Q5b

Factor.

```
\displaystyle
5(x + 6)-2(x + 6)
```

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Q5c

Factor.

```
\displaystyle
16x^2 + 8x -6x -3
```

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Q5d

a) Find an algebraic expression for the surface area of the squareâ€”based prism.

b) Expand and simplify your expression from part a).

c) Factor the resulting expression from part b).

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Q6

Factor.

```
\displaystyle
x^2 + 11x + 24
```

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Q7a

Factor.

```
\displaystyle
y^2 -15y + 56
```

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Q7b

Factor.

```
\displaystyle
n^2 - n - 90
```

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Q7c

Factor.

```
\displaystyle
x^2 -14x + 49
```

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Q7d

Factor.

```
\displaystyle
h^2 -100
```

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Q7e

Factor.

```
\displaystyle
d^3 + 16d + 64
```

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Q7f

Factor fully.

```
\displaystyle
3k^2 + 12km -36 m^2
```

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Q8a

Factor fully.

```
\displaystyle
8y^2 + 19y + 6
```

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Q8b

Factor fully.

```
\displaystyle
9w^2-24w + 7
```

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Q8c

Factor fully.

```
\displaystyle
25a^2 + 60a + 36
```

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Q8d

Factor fully.

```
\displaystyle
121w^2 - 144
```

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Q8e

Factor fully.

```
\displaystyle
10x^2 -7xy - 6y^2
```

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Q8f

Explain how to determine whether or not you can factor `9x^2 - 10x + 18`

over the integers.

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Q9

The area of a rectangle is given as `x^2 + 13x - 30`

.

a) Determine polynomials that represent the length and width of the rectangle.

b) What is the smallest integer value of `x`

for which this area expression makes sense?

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Q10

Determine all values of `k`

so that each trinomial is a perfect square.

```
\displaystyle
36x^2 + kx + 121
```

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Q11a

Determine all values of `k`

so that each trinomial is a perfect square.

```
\displaystyle
49k^2 -56d + k
```

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Q11b

Determine all values of `k`

so that each trinomial is a perfect square.

```
\displaystyle
25x^2 -60xy + ky^2
```

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Q11c

Determine all values of `k`

so that each trinomial is a perfect square.

```
\displaystyle
ka^2 +30ab + 9b^2
```

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Q11d

a) Write an algebraic expression for the area of the shaded region.

b) Write the area expression in factored form.

c) Substitute `x = 7`

into both forms. Are the results the same? Why?

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Q12

A parabola has equation ```
\displaystyle
y = 2(x + 6)^2 -2
```

a) Expand and simplify to write the equation in the form `y =ax^2 + bx + c`

.

b) Factor your equation from part a).

c) Do the three equations represent the same parabola? Justify your response.

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Q13

The volume of a rectangular prism is given as `9x3 - 30x^2 + 25x`

.

a) Determine algebraic expressions for the dimensions.

b) Describe the faces of the prism.

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Q14

Determine two values of `k`

so that the trinomial can be factored as a difference of squares.

```
\displaystyle
km^2 -25
```

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Q15a

Determine two values of `k`

so that the trinomial can be factored as a difference of squares.

```
\displaystyle
16d^2 -k
```

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Q15b

Determine two values of `k`

so that the trinomial can be factored as a difference of squares.

```
\displaystyle
a^2 -kb^2
```

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Q15c

Factor to evaluate the difference.

```
\displaystyle
34^2-31^2
```

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Q16a

Factor to evaluate the difference.

```
\displaystyle
127^2-126^2
```

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Q16b

The first three diagrams in a pattern are shown.

a) Write a formula for the total number of small squares in the nth diagram.

b) Write a formula for the number of shaded small squares in the nth diagram.

c) Write a formula for the number of unshaded small squares in the nth diagram.

d) Write your formula from part c) in factored form.

e) Show that both forms of the formula give the same results for the 15th diagram.

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Q17

a) Find all values of b so that `x^2 + bx + 10`

can be factored over the integers.

b) Find all values of b so that `4y^2 + by + 5`

can be factored over the integers.

c) Write an algebraic expression for the shaded area. Then, write the expression in factored form.

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Q18