Textbook

10 Principles of Mathematics Nelson
Chapter

Chapter 4
Section

Quadratic Relations Chapter Review

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Solutions
51 Videos

The model represents an algebraic expression. Identify the expression and its factors.

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Q1a

The model represents an algebraic expression. Identify the expression and its factors.

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Q1b

Factor

```
\displaystyle
20x^2 -4x
```

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Q2a

Factor

```
\displaystyle
3n^2 -6n + 15
```

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Q2b

Factor

```
\displaystyle
-2x^3 + 6x^2 + 4x
```

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Q2c

Factor

```
\displaystyle
6a(3- 7a) -5(3 - 7a)
```

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Q2d

The area of a rectangle is given by the relation
```
\displaystyle
A = 16x^2 -24
```

.

Determine the possible dimensions of this rectangle.

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0.50mins

Q3

a) Write three polynomials whose terms have a greatest common factor of `4x^3 y`

.

b) Factor each polynomial you wrote in part a)

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Q4

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

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Q5a

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

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Q5b

Factor fully

```
\displaystyle
x^2 + 16x + 63
```

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Q6a

Factor fully

```
\displaystyle
x^2 - 7x - 60
```

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Q6b

Factor fully

```
\displaystyle
x^2 + 6x - 27
```

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Q6c

Factor fully

```
\displaystyle
5x^2 - 5x - 100
```

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Q6d

Examine the relation `y = x^2+7x +12`

.

a) Write the relation in factored form.

b) Determine the coordinates of the xâ€”intercepts.

c) Determine the coordinates of the vertex.

d) State the minimum value of the relation and where the minimum value occurs.

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Q7

Identify the expression that is modelled below, and state its factors.

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Q8a

Identify the expression that is modelled below, and state its factors.

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Q8b

Factor fully.

```
\displaystyle
15x^2 -4x -4
```

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Q9a

Factor fully.

```
\displaystyle
20x^2+3x-2
```

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Q9b

Factor fully.

```
\displaystyle
7x^2-19x -6
```

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2.04mins

Q10a

Factor fully.

```
\displaystyle
5a^2+23a+15
```

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Q10b

Factor fully.

```
\displaystyle
12x^2-16x+5
```

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1.28mins

Q10c

Factor fully.

```
\displaystyle
6n^2 -11ny-10y^2
```

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1.59mins

Q10d

The profit on the watches they sell is determined by the relation `P = -2n^2 + 120n -1000`

, where `n`

is the number of watches sold and `P`

is the profit in dollars.

a) What are the break-even points?

b) What is the maximum profit?

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Q11

Identify the expression that is modelled below, and state its factors.

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Q12a

Identify the expression that is modelled below, and state its factors.

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0.52mins

Q12b

Factor fully.

```
\displaystyle
144x^2 -25
```

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Q13a

Factor fully.

```
\displaystyle
36a^2+12a + 1
```

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1.39mins

Q13b

Factor ```
\displaystyle
18x^5 - 512xy^2
```

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Q13c

Factor fully.

```
\displaystyle
4(x-2)^2-20(x -2) + 25
```

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Q13d

Factor fully.

```
\displaystyle
(x + 5)^2-y^2
```

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0.43mins

Q13e

Factor fully.

```
\displaystyle
x^2-6x+9-4y^2
```

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Q13f

Factor fully

```
\displaystyle
7x^2-26x -8
```

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Q16a

Factor fully

```
\displaystyle
64x^6 -25
```

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Q16b

Factor fully

```
\displaystyle
18ac - 12a - 15c + 10
```

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Q16c

Factor fully

```
\displaystyle
4x^2y - 44xy + 72y
```

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Q16d

Factor fully

```
\displaystyle
20x^2+61x + 45
```

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Q16e

Factor fully

```
\displaystyle
z^4-13z^2+40
```

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Q16f

Factor fully

```
\displaystyle
2s^2+3s-5
```

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Q17a

Factor fully

```
\displaystyle
15-2x -x^2
```

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Q17b

Factor fully

```
\displaystyle
x^4-4x^2-32
```

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Q17c

Factor fully

```
\displaystyle
16x^2-121y^2
```

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Q17d

Factor fully

```
\displaystyle
9 - 30a + 25a^2
```

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Q17e

Factor fully

```
\displaystyle
x^2 + 16x + 64-25y^2
```

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Q17f

A box has dimension defined by `V =18x^3 -2x + 45x^2 -5`

.

a) Determine expressions for the possible dimensions of these boxes.

b) Determine the dimensions and volume of a box if `x = 2`

cm

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Q18

Determine the coordinates of the vertex of each relation.

```
\displaystyle
y = x^2 -10x + 24
```

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Q19a

Determine the coordinates of the vertex of each relation.

```
\displaystyle
y = 2x^2 -24x + 72
```

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Q19b

Determine the coordinates of the vertex of each relation.

```
\displaystyle
y = -5x^2 + 500
```

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Q19c

Determine the coordinates of the vertex of each relation.

```
\displaystyle
y = 2x^2-7x -4
```

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Q19d

Determine the coordinates of the vertex of each relation.

```
\displaystyle
y = 4x^2 + 16x
```

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0.35mins

Q19e

Determine the coordinates of the vertex of each relation.

```
\displaystyle
y = x^2 + 10x + 25
```

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Q19f