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# Rational Zero's Theorem 4 Lessons and Multiple Assignments for PDF

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Included in this zip folder are 11 PDF files. 4 are Instruction files, 2 are student reference sheets and 5 are assignments. A brief description of each:

PDF instruction file #1 is a 92 page file dedicated to polynomial synthetic division. Numeric division is related to polynomial long division which is suppressed into synthetic division.

PDF instruction file #2 is a 52 page file that introduces the learner to the Fundamental Theorem of Algebra and the Complex Conjugates Zero's Theorem.

PDF Instruction File # 3 is a 52 page file that breaks down the rational Zero's Theorem into tiny pieces. Part of this file is in the preview.

PDF Instruction file #4 is an 18 page file that continues the Rational Zero's Theorem through synthetic division and the quadratic formula.

Student Reference sheet #1 emphasizes recognizing polynomial graphs not relative to the x-axis.

Student Reference sheet #2 emphasizes recognizing polynomial graphs relative to the x-axis.

PDF Assignment A is a 24 question assignment. The emphasis is synthetic division. It is on 1 page for easy printing.

PDF Assignment B is a 24 question assignment. The emphasis is using the 2 student reference sheets to identify graphs, the number of real and non-real zeros of graphs.. It is on 1 page for easy printing.

PDF Assignment C is a 15 question assignment. The emphasis is classifying complex numbers into the sub-sets of complex numbers. It is on 1 page for easy printing.

PDF Assignment File #1 is 20 degree 3 Rational Zero's problems. Each problem is on 1 page and formatted for the student to:
1. Find all the complex zero's. Some are imaginary numbers and some are real numbers.
2. State the degree of the polynomial.
3. Determine if the zero's are rational, irrational, integers, whole numbers etc...
4. Determine if the degree is odd or even
5. State the linear factorization of the polynomial.
6. Draw a sketch(graph) of the function.

PDF Assignment file #2 has 10 assignments in it. Below is a description:

Assignment #1 is 4 problems each degree 3. All Zero’s are Real. All have 1 Rational Zero and 2 Irrational Zero’s. There are 2 problems with positive lead coefficients and 2 problems with negative lead coefficients.

Assignment #2 is 4 problems each degree 3. All Zero’s are Real. 1 has all Rational Zero’s. The other 3 have 1 Rational and 2 Irrational Zero’s. There are 2 problems with positive lead coefficients and 2 problems with negative lead coefficients.

Assignment #3 is 4 problems each degree 3. 1 Zero is Real and Rational and the other 2 Zero’s are Imaginary. There are 2 problems with positive lead coefficients and 2 problems with negative lead coefficients.

Assignment #4 is 4 problems each degree 3. 1 Zero is Real and Rational and the other 2 Zero’s are Imaginary. There are 2 problems with positive lead coefficients and 2 problems with negative lead coefficients.

Assignment #5 is 4 problems each degree 3. 2 problems have 1 Real, Rational Zero and 2 Imaginary Zero’s. The other 2 problems have all Real Zero’s with 1 being Rational and the other 2 Irrational. There are 2 problems with positive lead coefficients and 2 problems with negative lead coefficients.

Assignment #6 is 4 problems each degree 3. 2 problems have 1 Real, Rational Zero and 2 Imaginary Zero’s. The other 2 problems have all Real Zero’s with 1 being Rational and the other 2 Irrational. There are 2 problems with positive lead coefficients and 2 problems with negative lead coefficients.

Assignment #7 is 3 problems each degree 4. All Zero’s are Real. 2 zero’s are Rational and 2 are Irrational. All lead coefficients are positive.

Assignment #8 is 3 problems each degree 4. All Zero’s are Real. 2 zero’s are Rational and 2 are Irrational. All lead coefficients are negative.

Assignment #9 is 3 problems each degree 4. 2 Zero’s are Real and 2 Zero’s are Imaginary. 2 problems have lead coefficients positive.

Assignment #10 is 3 problems each degree 4. 2 Zero’s are Real and 2 Zero’s are Imaginary. 2 problems have lead coefficients negative.

Thank you for looking.

Total Pages
80+
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Teaching Duration
1 Week
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