Algebra 2 Unit 1: Polynomial Functions

End behavior, zeros and multiplicity, polynomial division, the remainder and factor theorems, and complex zeros. 12 questions. Have a go at each one on paper before you tap "Show me how".

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Question 1

End behaviorNo calculator

Which describes the end behavior of $f(x)=-2x^5+3x^2-1$?

1. Falls to the right and rises to the left
2. Falls on both sides
3. Rises to the right and falls to the left
4. Rises on both sides

Question 2

Zeros and multiplicityNo calculator

At which zero does the graph of $f(x)=(x-2)^3(x+1)^2$ touch the $x$-axis without crossing it?

1. $x=1$
2. $x=-2$
3. $x=-1$
4. $x=2$

Question 3

Remainder theoremNo calculator

Without dividing, find the remainder when $x^3-4x^2+2x-5$ is divided by $x-3$.

1. $4$
2. $-8$
3. $-26$
4. $8$

Question 4

Polynomial divisionNo calculator

What is the quotient when $2x^3+3x^2-8x+3$ is divided by $x+3$?

1. $2x^{2}+3x-1$
2. $2x^{2}-3x-1$
3. $2x^{2}+9x+19$
4. $2x^{2}-3x+1$

Question 5

Factor theoremNo calculator

For what value of $k$ is $x-1$ a factor of $x^3+kx^2-5x+2$?

1. $4$
2. $3$
3. $2$
4. $-2$

Question 6

Real zerosNo calculator

What are the real zeros of $x^3-7x-6$?

1. $x=-2 \text{ or } x=3$
2. $x=1 \text{ or } x=2 \text{ or } x=-3$
3. $x=-1 \text{ or } x=6$
4. $x=-1 \text{ or } x=-2 \text{ or } x=3$

Question 7

Sum and difference of cubesNo calculator

Factor $x^3+27$.

1. $(x+3)(x^{2}-3x+9)$
2. $(x+3)^{3}$
3. $(x+3)(x^{2}+3x+9)$
4. $(x-3)(x^{2}+3x+9)$

Question 8

Writing polynomialsNo calculator

Which polynomial has zeros 2, $-1$ and 3 and leading coefficient 1?

1. $x^{3}-2x^{2}-5x+6$
2. $x^{3}-4x^{2}+x+6$
3. $x^{3}-4x^{2}-x+6$
4. $x^{3}+4x^{2}+x-6$

Question 9

Complex zerosNo calculator

A polynomial with real coefficients has zeros 3 and $2+i$. What is the least possible degree of the polynomial?

1. $1$
2. $2$
3. $3$
4. $4$

Question 10

Relative extremaCalculator

What is the relative maximum value of $f(x)=x^3-6x+1$, to the nearest tenth?

1. $-4.7$
2. $6.7$
3. $-1.4$
4. $6.6$

Question 11

Real zerosNo calculator

How many real zeros does $x^4-5x^2+4$ have?

1. $2$
2. $0$
3. $3$
4. $4$

Question 12

Evaluating polynomialsNo calculator

If $p(x)=x^4-3x^3+2x-7$, what is $p(-2)$?

1. $-19$
2. $45$
3. $29$
4. $13$