Algebra 2 5-6 Guided Practice: The Fundamental Theorem of Algebra

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Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It! The first graph shows the three complex number solutions of the equation: 

The second graph shows the six solutions of the equation: 

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Graph a parabola that represents a quadratic function with no real zeros.

Instructions

Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.

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Take Note: How many linear factors can a 4th-degree polynomial be factored into? Enter only a number.

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Take Note: For each function graphed on the right, identify its number of roots, numbers of real and complex roots, and the related equation.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

has 2 roots
has 1 real root & 1 complex root
has 2 real roots & 0 complex roots
has 2 complex roots & 0 real roots
represents y=x^{2}+2x+2
represents y=x^{2}-4
represents y=x^{2}-2x+1

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Problem 1 Got It?

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Summarize the four-step process used in Problem 1 to find all of the roots of the polynomial equation. You may use the canvas to help illustrate your written summary.

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Problem 2 Got It? What are all the zeros of the function?
Select all that apply.

Problem 2 Got It? The graph of f(x) is shown. 

Recall: The maximum number of turning points of a polynomial function is always one less than the degree of the function.

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Problem 2 Got It? Use turning points to explain why the graph does not show all of the real zeros of the function.

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Algebra 2 5-6 Guided Practice: The Fundamental Theorem of Algebra

Video Check: Select all that apply with regards to the video embedded directly above this item.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Graph a parabola that represents a quadratic function with no real zeros.

Take Note: How many linear factors can a 4th-degree polynomial be factored into? Enter only a number.

Problem 1 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the four-step process used in Problem 1 to find all of the roots of the polynomial equation. You may use the canvas to help illustrate your written summary.

Problem 2 Got It? What are all the zeros of the function?
Select all that apply.

Problem 2 Got It? Use turning points to explain why the graph does not show all of the real zeros of the function.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It: How many complex number solutions does this equation have?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Graph a parabola that represents a quadratic function with no real zeros.

Take Note: How many linear factors can a 4th-degree polynomial be factored into? Enter only a number.

Take Note: Summarize The Fundamental Theorem of Algebra.

Problem 1 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the four-step process used in Problem 1 to find all of the roots of the polynomial equation. You may use the canvas to help illustrate your written summary.

Problem 2 Got It? What are all the zeros of the function?
Select all that apply.

Problem 2 Got It? Use turning points to explain why the graph does not show all of the real zeros of the function.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Solve It: How many complex number solutions does this equation have?

Take Note: Summarize The Fundamental Theorem of Algebra.

Algebra 2 5-6 Guided Practice: The Fundamental Theorem of Algebra

Algebra 2 5-6 Guided Practice: The Fundamental Theorem of Algebra

Video Check: Select all that apply with regards to the video embedded directly above this item.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Graph a parabola that represents a quadratic function with no real zeros.

Take Note: How many linear factors can a 4th-degree polynomial be factored into? Enter only a number.

Problem 1 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the four-step process used in Problem 1 to find all of the roots of the polynomial equation. You may use the canvas to help illustrate your written summary.

Problem 2 Got It? What are all the zeros of the function? Select all that apply.

Problem 2 Got It? Use turning points to explain why the graph does not show all of the real zeros of the function.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It: How many complex number solutions does this equation have?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Graph a parabola that represents a quadratic function with no real zeros.

Take Note: How many linear factors can a 4th-degree polynomial be factored into? Enter only a number.

Take Note: Summarize The Fundamental Theorem of Algebra.

Problem 1 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the four-step process used in Problem 1 to find all of the roots of the polynomial equation. You may use the canvas to help illustrate your written summary.

Problem 2 Got It? What are all the zeros of the function? Select all that apply.

Problem 2 Got It? Use turning points to explain why the graph does not show all of the real zeros of the function.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Solve It: How many complex number solutions does this equation have?

Take Note: Summarize The Fundamental Theorem of Algebra.

Problem 2 Got It? What are all the zeros of the function?
Select all that apply.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Problem 2 Got It? What are all the zeros of the function?
Select all that apply.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?