Textbook

Advanced Functions Nelson
Chapter

Chapter 3
Section

Chapter Practice Test on Polynomial Functions

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Solutions
9 Videos

Determine the equation of the polynomial function y=f(x) shown.

Express your answer in factored form.

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Q2

Factor fully.

```
\displaystyle
2x^3 -x^2 -145x - 72
```

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Q3a

Factor fully.

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

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Q3b

If you have `g(x) = x^3 -4x^2`

and then vertically translate it by `1`

unit, does the resulting graph have fewer zeros, the same number of zeros, or more zeros than `g(x)`

?

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Q4

During which intervals of x is the graph of the function

```
\displaystyle
f(x) = -(x+ 3)(x + 5)(x - 1)
```

below the x-axis?

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Q5

Divide `6x^3 + x^2 -12x + 5`

by `2x -1`

. Is `2x -1`

a factor?

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Q6

The function `y =x^3`

has been vertidcally stretched by a factor of 5, horizontally compressed by a factor of `\frac{1}{2}`

, horizontally translated 21 units to the right, and vertically translated 4 units up.

a) Write the equation of the transformed function.

b) The point `(1, 1)`

is on the parent function. Determine the new coordinates of the transformed function.

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Q7

Ellie divided `x^4+3x^3 -9x^2 +6`

by a polynomial. Her answer was `x^3 -2x^2 +x - 5`

, with a remainder of `31`

. What polynomial did Ellie divide by?

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Q8

The function `f(x) = ax^4 + 8x^2`

has three turning points, an absolute maximum of `8`

, and one of its zeros at `x =2`

. Determine the value of `a`

and the location of the other zeros. Then sketch the graph of `f(x)`

.

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Q9