Textbook

10 Principles of Mathematics Nelson
Chapter

Chapter 4
Section

Quadratic Relations Practice Test

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Solutions
25 Videos

Determine the value for each symbol.

```
\displaystyle
x^2 - \diamond x - 56 = (x + 7)(x - \square)
```

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Q1a

Determine the value for each symbol.

```
\displaystyle
16x^2 - \diamond = ( \square x -3)(\square x + \circ)
```

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Q1b

Determine the value for each symbol.

```
\displaystyle
12x^2 + \circ x + 5 = (4x + \square)(\diamond x + 5)
```

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Q1c

Determine the value for each symbol.

```
\displaystyle
25x^2 + \circ x + 49 = (\square x + \diamond)^2
```

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Q1d

Identify each trinomial that is modelled below, and state its factors.

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Q2a

Identify each trinomial that is modelled below, and state its factors.

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Q2b

Factor fully.

```
\displaystyle
20x^5 -30x^3
```

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Q3a

Factor fully.

```
\displaystyle
-8yc^3 + 4y^2c - 6yc
```

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Q3b

Factor fully.

```
\displaystyle
2a(3b + 5) + 7(3b + 5)
```

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Q3c

Factor fully.

```
\displaystyle
2st + 6s + 5t + 15
```

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Q3d

Factor `25x^2 -30x + 9`

using two different strategies.

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Q4

Factor fully.

```
\displaystyle
x^2 + 4x - 77
```

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Q5a

Factor fully.

```
\displaystyle
a^2-3a -10
```

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Q5b

Factor fully.

```
\displaystyle
3x^2 -12x + 12
```

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Q5c

Factor fully.

```
\displaystyle
m^3 + 3m^2-4m
```

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Q5d

Factor fully.

```
\displaystyle
6x^2 -x -2
```

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Q6a

Factor fully.

```
\displaystyle
8n^2 + 8n - 6
```

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Q6b

Factor fully.

```
\displaystyle
9x^2 +12x +4
```

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Q6c

Factor fully.

```
\displaystyle
6ax^2+5ax-4a
```

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Q6d

A graphic arts company creates posters with areas that are given by the equation `A = 2x^2 + 11x+12`

a) Write expressions for possible dimensions of the posters.

b) Write expressions for the dimensions of a poster whose width is doubled and whose length is increased by 2. Write the new area as a simplified polynomial.

c) Write expressions for possible dimensions of a poster whose area is given by the expression `18x^2 + 99x + 108`

.

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Q7

Factor fully.

```
\displaystyle
225x^2 -4
```

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Q8a

Factor fully.

```
\displaystyle
9a^2 -48a + 64
```

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Q8b

Factor fully.

```
\displaystyle
x^6 -4y^2
```

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Q8c

Factor fully.

```
\displaystyle
(3 + n)^2 -10(3 + n) + 25
```

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Q8d

A parabola is defined by the equation `y = 2x^2 - 11x + 5`

. Find the location of the vertex.

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Q9