### About The Fundamental Theorem of Algebra:

The fundamental theorem of algebra tells us that a polynomial of degree n, will have n complex solutions, although some of these solutions may be repeated.

Test Objectives
• Demonstrate the ability to write a polynomial function given certain conditions
Fundamental Theorem of Algebra Practice Test:

#1:

Instructions: Write a polynomial function of degree 3 that satisifies the given conditions.

$$a)\hspace{.2em}f(2)=-30$$ $$\text{Zeros}: 5, 4, -3$$

#2:

Instructions: Write a polynomial function of degree 3 that satisifies the given conditions.

$$a)\hspace{.2em}f(1)=-8$$ $$\text{Zeros}: 2 \hspace{.25em}\text{multiplicity}\hspace{.25em}2, 5$$

#3:

Instructions: Write a polynomial function of degree 3 that satisifies the given conditions.

$$a)\hspace{.2em}f(2)=135$$ $$\text{Zeros}: -1 \hspace{.25em}\text{multiplicity}\hspace{.25em}3$$

#4:

Instructions: Write a polynomial function of degree 3 that satisifies the given conditions.

$$a)\hspace{.2em}f(3)=20$$ $$\text{Zeros}: -7, -1, 2$$

#5:

Instructions: Write a polynomial function of degree 3 that satisifies the given conditions.

$$a)\hspace{.2em}f(-1)=-16$$ $$\text{Zeros}: 3 \hspace{.25em}\text{multiplicity}\hspace{.25em}2, -\frac{1}{2}$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}f(x)=-x^3 + 6x^2 + 7x - 60$$

#2:

Solutions:

$$a)\hspace{.2em}f(x)=2x^3 - 18x^2 + 48x - 40$$

#3:

Solutions:

$$a)\hspace{.2em}f(x)=5x^3 + 15x^2 + 15x + 5$$

#4:

Solutions:

$$a)\hspace{.2em}f(x)=\frac{1}{2}x^3 + 3x^2 - \frac{9}{2}x - 7$$

#5:

Solutions:

$$a)\hspace{.2em}f(x)=2x^3 - 11x^2 + 12x + 9$$