Notes:
4/13 4/18 4/20

### 4/13

II. In text ch 3.1: polynomial, 3.2: continuous, discontinous
III. Use the leading coefficeint and the degree of the polynomial to determine the
end behavior of the function.

### 4/18

I. Sketch using your knowledge of single roots, double roots,
See dilation, polynomials.
1. y = (x - 3)(x + 1)
2. y = (x - 3)²(x + 1)
3. y = (x - 3)²(x + 1)²
Use your calculator to verify sketches.
II. Divide x5 + x3 + x2 - 12x + 8 by x - 1
see page 267 #1 then pg 283

### 4/20

I. Evaluate y = x5 + x3 + x2 - 12x + 8
when x is 1, -4, 2, -2
Use calculators/synthetic division to verify answers.
On 82 or 83, use table or
STO the x, then VARS then FUNCTION, then Y-VARS, then Y1, then ENTER
On 85, use EVAL then the number, after storing function in the y(x) menu

II. Sketch
2. y = (x + 5)2(x2 + 4)2
3. y = (x + 5)3(x + 4)2(x - 3)2
III. Solve
4. 0 = x4 - x2 - 20
IV. The Division Algorithm - Use division to rewrite a function as the
product of two factors plus a remainder.
f(x) = (quotient function) · (divisor function) + (remainder function)
If the remainder is 0, the divisor evenly divides the original function.
IV. Consider examples of the above.
ex 1. y = x2 + 4x + 4 = (x + 2)(x + 2) + 0
ex 2. y = x2 + 4x + 5 = (x + 2)(x + 2) + 1
ex 3. y = x2 + 6x + 4 = (x + 2)(x + 2) + 2x
ex 4. y = 2x2 + 4x + 4 = (x + 2)(x + 2) + x²
V. Text, pg 261. Sketch y = 3x4 - 4x3
Find roots.
y = 3x4 - 4x3 = 0
x3(3x - 4) = 0
x3 = 0 and 3x - 4 = 0
x3 = 0 and 3x - 4 = 0
x = 0 and x = 4/3
1st: Plot real roots.
2nd:Determine behavior of function about roots.
triple root at 0 -> passes through
single root at 4/3 -> passer through
3rd: Determine general shape & end behavior based on leading coefficient & degree of polynomial.
Quartic starts high, ends high.
From left to right,
• graph decreases from positive infinity,
• still decreasing passes through x-axis at 0
• next increases and passes through x-axis at x = 4/3 still increasing
• increases to positive infinity.

Last page     Next page     asquared@mathnstuff.com

http://www.mathnstuff.com/math/precalc/prec6.htm     Revised: 4/30/00