1. Page 248 1) Yes; Degree: 3, LC: 1, Constant: 1 3)5)
Yes; Degree: 2, LC: 1, Constant: -1 7) No 9)
3x3 – 2x2 – 4x (7/x – 2)
10)
4x2 + 5x (29/x - 2)
11)
2x3 - x2 + 3x (25/x + 3)
12)
3x2 - 17x (433/x + 5)
15)
x3 – 4x2 – 4x – 6 – (19/x – 2)
17)
3x3 – 3x2 + 5x – 11 + (12/x + 1)
18)
x4 + 2x3 + 3x2 + 6x + (13/x – 2)
21)
5x2 + 5x + 5
22)
x4 + x3 + x2 + x + 1
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4.1A - Related Theorems

2. Grade Distribution 2nd 5th A 5 6 B C 3 D 1 F No Shows 2 100+ Range3 D 1 F
No Shows 2
100+
Range
56-99
Average
79.94
81.27
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4.1A - Related Theorems

3. Pre–Calculus PreAP/Dual, Revised ©2015
Related Theorems
Section 4.1a
Pre–Calculus PreAP/Dual, Revised ©2015
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4.1A - Related Theorems

4. Identifying Polynomials
Identifying where the graph crosses at the x-axis
Rewriting it as a linear factor
Multiply it as a polynomials
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4.1A - Related Theorems

5. Example 1
With a degree of 5 whose leading coefficient of 1, write the equation in linear factors and determine the polynomial.
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4.1A - Related Theorems

6. Your Turn
With a degree of 3 whose leading coefficient of 1, write the equation in linear factors and determine the polynomial. Write it as a linear factor.
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4.1A - Related Theorems

7. Remainder and Factor Theorem
Remainder Theorem is where a polynomial f(x) is divided by x – c, then the remainder is f(c).
Factor Theorem uses the remainder and determine whether the factor is part of the polynomial or not. The remainder has to be ZERO for the factor to work.
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4.1A - Related Theorems

8. Example 2
Determine 4, –2, and –5 are zeros of the given polynomial f(x) = x3 – x2 – 22x + 40.
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4.1A - Related Theorems

9. Example 3
Find the remainder when x3 + 2x2 – 5x – 1 is divided by x – 2. Then, use the factor theorem to prove whether the factor is polynomial.
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4.1A - Related Theorems

10. Your Turn
Find the remainder when x4 + 7x3 + 8x2 + 11x + 5 is divided by x Then, use the factor theorem to prove whether the factor is polynomial.
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4.1A - Related Theorems

11. Example 4
What is the value of k such that x – 5 is a factor of x3 – x2 + kx – 30?
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4.1A - Related Theorems

12. Example 5
What is the value of k such that x + 2 is a factor of x3 + 4x2 – 11x + k?
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4.1A - Related Theorems

13. Your Turn
What is the value of k such that x – 2 is a factor of x3 + kx2 + 5x + k?
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4.1A - Related Theorems

14. Assignment Worksheet – Theorems 11/27/2018 3:49 AM
4.1A - Related Theorems