4/13
 I. Review answers from test
 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,
 leading coefficient, degree of polynomial.
 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 x^{5} + x^{3} + x^{2}  12x + 8 by x  1
 see page 267 #1 then pg 283
4/20
 I. Evaluate y = x^{5} + x^{3} + x^{2}  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 YVARS, then Y_{1}, then ENTER
 On 85, use EVAL then the number, after storing function in the y(x) menu

 II. Sketch
 2. y = (x + 5)^{2}(x^{2} + 4)^{2}
 3. y = (x + 5)^{3}(x + 4)^{2}(x  3)^{2}
 III. Solve
 4. 0 = x^{4}  x^{2}  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 = x^{2} + 4x + 4 = (x + 2)(x + 2) + 0
 ex 2. y = x^{2} + 4x + 5 = (x + 2)(x + 2) + 1
 ex 3. y = x^{2} + 6x + 4 = (x + 2)(x + 2) + 2x
 ex 4. y = 2x^{2} + 4x + 4 = (x + 2)(x + 2) + x²
 V. Text, pg 261. Sketch y = 3x^{4}  4x^{3}
 Find roots.
 y = 3x^{4}  4x^{3} = 0
 x^{3}(3x  4) = 0
 x^{3} = 0 and 3x  4 = 0
 x^{3} = 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 xaxis at 0
 next increases and passes through
xaxis at x = 4/3 still increasing
 increases to positive infinity.
