Free Printable Polynomials (division and graphing)

1.

Looking at the end behavior of this graph is it.....

a)

Positive

b)

Negative

2.

Identify the zeros: (x-intercepts)

a)

x=-2, x=-1, x=0

b)

x=-2, x=0

c)

x=-1, x=0, x=2

d)

x=-2, x=0, x=1

3.

Match the equation to the graph.

a)

y=-(x+1)(x-2)(x-4)

b)

y=(x+1)(x-3)(x-1)

c)

y = 3x³ – 2x + 1

d)

y=(x+1)(x-3)(x-1)

4.

Identify the x-intercepts

a)

x=2, x=6, x=-4

b)

(x+2)(x+6)(x-4)

c)

(x-2)(x-6)(x+4)

d)

x=-2, x=-6, x=4

5.

Divide: (use synthetic division!)

\frac{x^2\ +\ 4x\ -\ 45}{x\ +\ 9}

a)

x+5

b)

-x+5

c)

-x-5

d)

x-5

6.

Divide: (using long or synthetic division)

\frac{2x^3\ -\ 5x^2\ +\ 3x\ +\ 7}{x\ -\ 2}

a)

$2x^2-x+1+\frac{9}{x-2}$

b)

$2x^3-x^2+x^2+9$

c)

$2x^2-x-10$

d)

$x^2-2x+1$

7.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x-12

b)

2x⁴-x³-25x²-12x+0

8.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

9.

How could you determine if x-2 is a factor of 2x³-5x²+x-2?

a)

Use synthetic division and see if the quotient is even

b)

Ask the person sitting next to me

c)

Use synthetic division and see if the remainder is zero

d)

Flip a coin

10.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

11.

For synthetic division, what would be the number in the left hand box?

(a)

12.

If you were dividing x⁶ + 4x³ - 3x + 2, how many 0's would you need when setting up the top row of your synthetic division?

(a)

13.

f(x)=(x+4)(x-3)(x-2)

List the zeros for this function.

a)

x= -4, x=3, x= -2

b)

x= -4, x=3, x=2

c)

x= -4, x=-3, x=2

d)

x=4, x= -3, x= -2

14.

$p\left(x\right)=9x^3+3x^2-8x-4$

Using synthetic division and the factor (x-1), find the zeros of the function.

a)

$x=\left\{-1,\ \frac{2}{3}\right\}$

b)

$x=\left\{-6,\ 1\right\}$

c)

$x=\left\{-\frac{2}{3},\ 1\right\}$

d)

$x=\left\{1,\ 6\right\}$

15.

When is this function increasing?

a)

−2.5 < x < 2.5

b)

0 < x < 5

c)

0 < x < 55

d)

−5 < x < 0

16.

When is the velocity decreasing?

a)

0 < t < 60

b)

40 < t < 60

c)

15 < t < 40

d)

−40 < t < 0

17.

Where is the function increasing?

a)

x ≤ 1

b)

x ≥ 1

c)

y ≤ −4

d)

y ≥ −4

18.

Identify where the function is positive.

a)

$x<-5\ \ ,\ \ \ x>0$

b)

$-5<x<0\ \ ,\ \ \ x>6$

c)

$x<-5\ \ ,\ 0<x<6$

d)

$x>-5\ \ ,\ \ \ x<6$

19.

Identify the interval(s) where the function is positive.

a)

$\left(-\infty,-3\right)$

b)

$\left(-3\ ,\ 3\right)$

c)

$\left(3\ ,\ \infty\right)$

20.

Identify all intervals where the function is negative.

a)

$\left(-\infty\ ,\ -7\right)$

b)

$\left(-7,\ -3\right)$

c)

$\left(-3\ ,\ 5\right)$

d)

$\left(5\ ,\ \infty\right)$

21.

Identify where the function is negative.

a)

$x\ >-3$

b)

All Real Numbers

c)

$-3<x<3$

d)

$x<-3,\ x>3$

22.

Identify where the function is negative.

a)

$-5<x<0,\ x\ >6$

b)

$x<-5,\ x\ >6$

c)

$-5<x<6$

d)

$x<-5,\ 0<x<6$

23.

Identify where the function is positive.

a)

$-3<x<3$

b)

All Real Numbers

c)

$x<-3,\ \ x>3$

24.

Identify where the function is increasing.

a)

$x\ <-4\ \ \ \ \ ,\ \ \ \ x\ >1$

b)

$-\ 4<x<1$

c)

$-6<x<-2$

d)

$x<-6\ \ \ \ ,\ \ \ x\ >-2$

25.

(2x³ + 7x² - 6x - 8) ÷ (x + 4)

a)

2x² - x - 2

b)

2x³ - x² - 2x

c)

2x² + 15x + 54 + 208/x+4

d)

2x³ + 15x² + 54x + 208

26.

Lukas divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

a)

Lukas wrote the remainder incorrectly.

b)

Lukas did not use a zero place holder for the x³ term.

c)

Lukas added instead of subtracting the rows.

d)

Lukas should have used -2 as his division since the factor was x-2.

27.

What is the remainder when a³ - 4 is divided by a+2?

(a)

28.

If 𝒙²+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?

(a)

29.

Find all the real zeros of the function

f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

a)

$x=\frac{1}{2},\ -6$

b)

$x=-\frac{1}{2},\ 6$

c)

$x\ =\ 4,\ -\frac{1}{2},\ 6$

d)

$x\ =\ -4,\ \frac{1}{2},\ -6$

30.

Simplify this expression.

a)

-5x¹⁰

b)

4x⁴+ 18x⁶

c)

-6x⁴+ 16x²

d)

4x⁴- 9x²

31.

Divide (6x²+12x) by 3x

a)

$2x+4$

b)

$2+\frac{6}{3x}$

c)

$2+\frac{4}{x}$

d)

$3+\frac{6}{2x}$

32.

Divide the polynomial by the monomial.

a)

2x⁸-8x²-28x

b)

2x⁸-2x²-7x

c)

8x⁷-8x-28x

d)

2x⁷-2x -7

33.

Divide 8x² -4x + 12 by 2x

a)

$4x+2$

b)

$4x-2+\frac{6}{x}$

c)

$4x-2$

d)

$4x-2+\frac{1}{6x}$

34.

What is the remainder R when the polynomial p(x) is divided by (x-5)?

p(x) = x³- 5x²+ 2x - 10

a)

0

b)

2x-10

c)

-2x-10

d)

2x+10

35.

$P\left(x\right)\ =3x^4-2x^3-7x^2\ +\ kx\ +\ 4$

where k is an unknown integer. P(x) is divided by (x - 2) and has a remainder of -6. Solve for the value of k.

(a)

Polynomials (division and graphing)

Total questions: 35

Worksheet time: 2hrs 13mins

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