Quiz about A2: Unit 2 Practice Test

Question 1

The following polynomial is written in standard form:
7x³ - 11x² + 8x - 5

Accepted Answer

True

Answer

False

Question 2

If f(x) = 6x + 4x⁴ - 3x² and g(x) = 7x⁴ + 5x² + 8x

Find f(x) + g(x).

Accepted Answer

11x⁴ + 2x² + 14x

Answer

16x⁴ + x² + 14x

Answer

11x⁴ + x² + 14x

Answer

11x⁴ + 2x² + 10x

Question 3

If f(x) = 4x⁴ - 8x + 4 and g(x) = 8x² + 4x⁴ + 1

Find f(x) - g(x)

Accepted Answer

-8x² - 8x + 3

Answer

-7x² - 8x + 3

Answer

-6x²- 8x + 3

Answer

-7x² - 4x + 3

Question 4

Multiply the monomial by the polynomial:

7x²y³ (2x⁴y⁵+6xy³)

Accepted Answer

14x⁶y⁸+ 42x³y⁶

Answer

14x⁸y¹⁵+ 42x²y⁹

Answer

9x⁶y⁸+ 13x³y⁶

Answer

14x⁶y⁸+ 42x²y⁶

Question 5

Multiply the binomial and the trinomial:

(5x + 2)(x²- 3x + 6)

Accepted Answer

5x³ - 13x² + 24x +12

Answer

5x³- 17x²+24x +12

Answer

5x³+ 17x² - 24x +12

Answer

5x³ +13x² - 24x - 12

Question 6

Expand the binomial:

(x + 2)³

Accepted Answer

x³+ 6x²+ 12x + 8

Answer

x³+ 6x²- 12x + 8

Answer

x³- 6x²+ 12x - 8

Answer

x³+ 4x²+ 12x + 6

Question 7

Divide the following polynomials:

$$\left(x^2+2x-63\right)\div\left(x+9\right)$$

Accepted Answer

x - 7

Answer

x2 - 7

Answer

x + 7

Answer

x²+ 3x - 54

Question 8

Divide the polynomials:

$$\left(x^3+12x^2+20x-96\right)\div\left(x-2\right)$$

Accepted Answer

$$x^2+14x+48$$

Answer

$$x^2+14x+8-\frac{4}{x+2}$$

Answer

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

Answer

$$x^2+8x+48$$

Question 9

Divide the following polynomials:

$$\left(2x^2+6x-20\right)\div\left(2x-4\right)$$

Accepted Answer

x + 5

Answer

$$x+5+\frac{2}{2x-4}$$

Answer

x - 8

Answer

$$x-5+\frac{3}{2x-4}$$

Question 10

Evaluate P(x) = $$3x^3-2x^2+10$$ for P(-5) using synthetic division.

Accepted Answer

-415

Answer

-89

Answer

11

Answer

335

Question 11

Factor the polynomial completely:
x³ + 3x² - 4x - 12

Accepted Answer

(x + 3) (x + 2)(x - 2)

Answer

(x + 3)(x² - 4)

Answer

(x² + 4) (x - 3)

Answer

(x² + 3)(x - 4)

Question 12

Factor the polynomial:
x² - 100

Accepted Answer

(x - 10)(x +10)

Answer

(x - 2)(x + 50)

Answer

(x - 4)(x + 25)

Answer

(x - 1)(x + 100)

Question 13

Factor the polynomial completely:
x³ - 4x² - 4x + 16

Accepted Answer

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

Answer

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

Answer

(x-4)(x² - 4)

Answer

(x+4)(x² - 4)

Question 14

If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent

Accepted Answer

True

Answer

False

Question 15

Determine if (x + 4) is a factor of $$g\left(x\right)=x^3-13x+12$$

Accepted Answer

Yes, because the remainder is 0.

Answer

Yes, because the remainder is 80.

Answer

No, because the remainder is 0.

Answer

No, because the remainder is 80.

Question 16

Determine if (x - 3) is a factor of g(x) = 3x³+ 10x²- x - 12

Accepted Answer

No, because the remainder is 156.

Answer

Yes, because the remainder is 0.

Answer

Yes, because the remainder is 156.

Answer

No, because the remainder is 0.

Question 17

Assume (x + 4) is a factor of $$f\left(x\right)=x^3+x^2-16x-16$$ , what is another factor?

Accepted Answer

(x + 1)

Answer

(x + 2)

Answer

(x - 1)

Answer

(x + 3)

Question 18

One root of the polynomial equation is P(1) = 0. Find the other roots.

$$x^3+8x^2-x-8=0$$

Accepted Answer

x = -1 or x = -8

Answer

x = -1

Answer

x = 8

Answer

x = 1 or x = -8

Question 19

Which of the following statements about the graph are TRUE?

I. f(x) has exactly 3 real zeros

II. Two of the zeros have an even multiplicity

III. The minimum degree of f(x) is 3.

Accepted Answer

I and III only

Answer

I only

Answer

I and II only

Answer

III only

Question 20

Which of the following statements about the graph are TRUE?

I. f(x) has exactly 3 real zeros

II. One of the zeros has an even multiplicity

III. The minimum degree of f(x) is 3.

Accepted Answer

I and II only

Answer

I only

Answer

III only

Answer

II and II only

Question 21

Is this function even or odd?

Accepted Answer

even

Answer

odd

Question 22

Identify the end behavior of the function:

f(x) = 3x² + 5x - 9

Accepted Answer

$$+\infty,+\infty$$

Answer

$$-\infty,+\infty$$

Answer

$$+\infty,-\infty$$

Answer

$$-\infty,-\infty$$

Question 23

Is the leading coefficient positive or negative

Accepted Answer

positive

Answer

negative

Question 24

Identify the end behavior of the function:

f(x) = -3x⁵ + 5x⁴ - 7x³ + 2x - 12

Accepted Answer

$$+\infty,-\infty$$

Answer

$$-\infty,+\infty$$

Answer

$$+\infty,+\infty$$

Answer

$$-\infty,-\infty$$

Question 25

Which function has this end behavior?

Accepted Answer

-2x⁷+2x⁴+4

Answer

-1x⁴-3x³+3

Answer

3x⁸+3x⁵-4x+7

Answer

4x⁵-4x⁴+2x³-9

Question 26

Which function has this end behavior?

Accepted Answer

-x2-3x+1

Answer

-x³+2x²+3

Answer

x⁴+3x³-4x+1

Answer

x⁵-4x⁴+2x²-1

Question 27

What are the zeros of the function?

Accepted Answer

-3, -1, 2, 5

Answer

4,1

Answer

3,1,-2,-5

Answer

-2,4

Question 28

Even Multiplicities have which of the following effects on the x-axis?

Accepted Answer

bounce on the x-axis

Answer

Cross the x-axis

Answer

wiggle on the x-axis

Answer

don't touch the x-axis

Question 29

Describe the transformation that occurred
p(x) = f(x + 3)

Accepted Answer

Left three units

Answer

Right 3 units

Answer

Less Steep

Answer

Steeper

Question 30

Which equation describes the transformation of shifting f(x)=x³ seven units up?

Accepted Answer

f(x) = x³+ 7

Answer

f(x) = x³- 7

Answer

f(x) = (x - 7)³

Answer

f(x) = (x + 7)³

Question 31

Which equation describes the transformation of shifting f(x)=x³ three units left?

Accepted Answer

f(x) = (x + 3)³

Answer

f(x) = x³ + 3

Answer

f(x) = x³ - 3

Answer

f(x) = (x - 3)³

Question 32

Match the equation to its description.

f(x) = (x - 2)² + 2

Accepted Answer

Right 2 and up 2

Answer

Left 2 and up 2

Answer

Right 2 and down 2

Answer

Left 2 and down 2

A2: Unit 2 Practice Test

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