Free Printable Alg 2 Chapter 3 Test Review

1.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

2.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

3.

Multiply using the 'FOIL' method.

( 3x + 5 ) ( 2x + 3 )

a)

6x² + 19x

b)

6x² + 15

c)

6x² + 19x + 8

d)

6x² + 19x + 15

4.

Find the product.

( 2x - 5y ) ( 3x + 4y )

a)

6x² - 7xy - 20y²

b)

6x² + 7xy - 20y²

c)

6x² - 7xy + 20y²

d)

6x² - 20y²

5.

Find the product:
(2x+3)²

a)

2x+3+2x+3

b)

4x²+12x+9

c)

4x²+9

d)

16x²+9

6.

Multiply.
(b+3)(b²+2b+1)

a)

b³+6b²+6b+3

b)

b³+5b²+7b+3

c)

4b³+8b²+3b

d)

3b³+6b²+3b

7.

What is the perimeter of the rectangle?

a)

$25x^{2\ }-\ 20x$

b)

$10x-4$

c)

$20x\ -\ 8$

d)

44

8.

What is the area of the rectangle?

a)

$25x^{2\ }-\ 20x$

b)

$20x\ -\ 8$

c)

$10x\ -\ 4$

d)

44

9.

a)

Degree 1

b)

Degree 2

c)

Degree 3

d)

Degree 4

10.

What is the leading coefficient of this polynomial?

a)

8

b)

-4

c)

-1

d)

1

11.

What is the value of the constant?
2x² + 4x − 5

a)

2

b)

4

c)

5

d)

−5

12.

What is the standard form of the polynomial,
9x² + 5x + 27 + 2x³

a)

27 + 5x + 9x² + 2x³

b)

9x² + 5x + 2x³ + 27

c)

9x² + 5x + 27 + 2x³

d)

2x³ + 9x² + 5x + 27

13.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

14.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

15.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

16.

Find the product:
(2x+3)²

a)

2x+3+2x+3

b)

4x²+12x+9

c)

4x²+9

d)

16x²+9

17.

Multiply.
(b+3)(b²+2b+1)

a)

b³+6b²+6b+3

b)

b³+5b²+7b+3

c)

4b³+8b²+3b

d)

3b³+6b²+3b

18.

(5x⁴- 4x³- 2x² + x - 19) - (x⁴+ 5x³ + 8x² + x + 5)

a)

4x⁴- 9x³- 10x²- 24

b)

4x⁴- 9x³ - 10x²- 2x - 24

c)

4x⁴ - 9x³ - 10x² + 2x - 24

d)

-4x⁴ - 9x³ - 10x² - 24

19.

What is the perimeter of the rectangle?

a)

$25x^{2\ }-\ 20x$

b)

$10x-4$

c)

$20x\ -\ 8$

d)

44

20.

What is the area of the ractangle?

a)

$25x^{2\ }-\ 20x$

b)

$20x\ -\ 8$

c)

$10x\ -\ 4$

d)

44

21.

Which is an example of a linear polynomial?

a)

x²-5

b)

6x+4

c)

5x⁵

d)

2x³-9x²

22.

Add the following polynomials
(x³-6x²+3)+(3x³+4x-1)

a)

4x³-2x²+2

b)

4x³-6x²+4x+2

c)

-2x³+2x+2

d)

4x³-2x²-2

23.

The largest exponent which is shown in a polynomial.

a)

exponent

b)

cubic

c)

degree

d)

linear

24.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

25.

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

a)

0

b)

2

c)

4

d)

6

26.

(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

27.

Divide: $\frac{x^4+2x^3+2x+4}{x+2}$

a)

$x^3+2x^2$

b)

$x^3+2$

c)

$x^3+4x^2+8x+18+\frac{42}{x+2}$

d)

$x^3+4x^2+10x+24$

28.

Divide: $\frac{5x^3-x^2+6}{x-4}$

a)

$5x^2-21x+84-\frac{330}{x-4}$

b)

$5x^2+19x+82$

c)

$5x^2+19x+76+\frac{310}{x-4}$

d)

$5x^2+19x+\frac{82}{x-4}$

29.

Divide: $\frac{x^3-12x^2+47x-60}{x-3}$

a)

$x^2-9x+20$

b)

$x^3-9x^2+20x$

c)

$x^2-15x+92+\frac{216}{x-3}$

d)

$x^2+9x+20$

30.

Divide: $\frac{3x^3-4x^2-9x+10}{x-2}$

a)

$3x^2+2x-5$

b)

$3x^3+2x^2-5x$

c)

$3x^2-10x^{ }-29-\frac{48}{x-2}$

d)

$3x^2-10x-29+\frac{48}{x-2}$

31.

Divide: $\frac{x^2-2x-8}{x+2}$

a)

$x-4$

b)

$x^2-4$

c)

$x-\frac{8}{x+2}$

d)

$2x-4$

32.

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

33.

How many zeros does the polynomial function
P(x) = 3x⁴+4x-8 have?

a)

1

b)

2

c)

3

d)

4

34.

Identify the zeros:

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

35.

The polynomial
f(x) = 5x⁴ + 2x³ + 2x − 7 can have, at most, how many solutions?

a)

5

b)

4

c)

3

d)

2

36.

a)

The function has an Even degree

b)

The function has a Negative coefficient

c)

The function has an Odd degree

d)

The function has 3 real zeros

37.

a)

Positive Odd

b)

Positive Even

c)

Negative Odd

d)

Negative Even

38.

a)

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

b)

y=(x+1)²(x-3)(x-1)³

c)

y = 3x³ – 2x + 1

d)

y=(x+1)³(x-3)(x-1)²

39.

a)

A

b)

B

c)

C

d)

D

40.

Over the interval (−1, 2), the graph of the polynomial shown could be described as

a)

decreasing

b)

increasing

c)

quadratic

d)

complex

41.

Determine the y-intercept
f(x) = x³ - 5x² - 25x + 125

a)

(0,0)

b)

(0,25)

c)

(0,125)

d)

(0,5)

42.

Express the END BEHAVIOR of the function: $f\left(x\right)=-12x^7-19x^3+22$

a)

x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\

x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty

b)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

d)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

43.

Express the END BEHAVIOR of the function: $f\left(x\right)=7x^4+9x^3-21$

a)

x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\

x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty

b)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

d)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

44.

$\$ Which graph depicts the function $f\left(x\right)=\left(x-6\right)\left(x-3\right)\left(x+8\right)?$

a)

b)

c)

d)

45.

$\$ Which could be the graph of $\ f\left(x\right)=-4x^5-19x^4+22x^2-x\ ?$

a)

b)

c)

d)

46.

Which graphs have a POSITIVE leading coefficient? (Check all that apply)

a)

b)

c)

d)

e)

47.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

48.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

49.

Factor: 27x³ + 8

a)

(3x + 2)(9x² - 6x + 4)

b)

(9x + 2)(3x² + 18x + 4)

c)

(3x²+4)(9x + 2)

d)

(27x + 8)(x² - 216x + 64)

50.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

51.

Factor:
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

52.

Factor:
x²- 16

a)

Prime

b)

( x - 4) ( x + 4)

c)

( x - 8) ( x + 8)

d)

( x - 4) ( x - 4)

53.

Factor:
x²- 400

a)

( x - 200) ( x + 200)

b)

( x + 20) ( x + 20)

c)

Prime

d)

( x - 20) ( x + 20)

54.

Factor:
25x²- 100y²

a)

( 5x - 10y) (5xy + 10y)

b)

( 5x - 10y)²

c)

Prime

d)

( 5x - 50y) (5x + 50y)

55.

Factor:
3x²- 75

a)

3( x + 5 ) ( x - 5 )

b)

Prime

c)

( x + 5 ) ( x - 5 )

d)

3( x - 5 ) ( x - 5 )

56.

Factor:
x²+ 81

a)

Prime (not factorable)

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

57.

Factor:
x² - 30x + 225

a)

(x + 15)²

b)

(x - 15)²

c)

(x + 25)²

d)

(x - 25)²

58.

Factor, if possible: 4x²+36x+81

a)

(4x+81)²

b)

(2x+9)²

c)

Prime /
Not factorable.

d)

(2x-9)²

59.

Factor, if possible:
64x²-16x+1

a)

Not factorable.

b)

(32x-1)²

c)

(8x+1)²

d)

(8x-1)²

Alg 2 Chapter 3 Test Review

Total questions: 59

Worksheet time: 3hrs 16mins

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