1. ALGEBRA II HONORS/GIFTED @
ALGEBRA II HONORS/GIFTED - SECTION 5-2 (Polynomials, Linear Functions, and Zeros)
2/17/2019
ALGEBRA II HONORS/GIFTED @
SECTION 5-2 : POLYNOMIALS, LINEAR FUNCTIONS, and ZEROS

2. With your graphing calculator, graph f(x) = x3 – 2x2 – 15x.
1) What are the x-intercepts?
ANSWERS : -3, 0, 5
2) Now, substitute -3, 0, and 5 into f(x). What happens?
ANSWER : f(x) = 0
4) Finally, solve using the factors you found in number 3.
3) Factor f(x).
ANSWER : x(x – 5)(x + 3)
ANSWERS : 0, 5, -3

3. The summary…………
Given the polynomial P(x), if x – b is a linear factor then
*b is a zero of P(x)
*b is a root of P(x)
*b is an x-intercept of P(x).
FACTOR THEOREM : x – b is a factor of P(x) if and only if b is a zero of P(x).

4. RELATIVE MINIMUM : The value of a function at a down to up point.
Let’s go back and find the relative minimum and relative maximum of P(x) using the MAXIMUM and MINIMUM functions of your calculator.
RELATIVE MAXIMUM : The value of a function at an up to down turning point.
RELATIVE MINIMUM : The value of a function at a down to up point.
See page 291 of your book.

5. 6) Find the zeros of y = (x – 3)(x + 4)(x – 3)
5) Factor. x3 + x2 – 12x
ANSWER : x(x + 4)(x – 3)
6) Find the zeros of y = (x – 3)(x + 4)(x – 3)
ANSWER : 3, -4
We can say that 3 has a multiplicity of 2. That is, 3 appears twice as a zero. Negative four has a multiplicity of one.

6. 7) What is a cubic polynomial function in standard form with zeros 1, -1, and 4?
ANSWER : x3 – 4x2 – x + 4
8) What are the zeros of f(x) = x3 – 5x2 + 3x + 9? What are their multiplicities? How do the graphs behave at the zeros?
ANSWERS : 3 with a multiplicity of 2, there is a vertex at that point; -1 with a multiplicity of one, the graph crosses through the x-axis at that point.

7. Why did the imaginary number turn red?
It ran out of i-drops.