Synthetic division

3 problems of synthetic division, remainder theroum, polynomials

22-9
35. For the rational function f (x)
answer the followings. Make sure to
22-2-3
explain how you get the answer, if there is any. If there is no answer, explain why.
(a) Zeros of the numerator:
(b) Zeros of the denominator:
(c) Domain:
(d) Holes:
(e) Vertical asymptotes:
(f) Horizontal asymptotes:
(g) Oblique asymptotes:
(h) y-intercept:
(i) x-intercepts:
(j) Symmetry:
(k) Range:
(1) Using all of the above information graph the function on a graphing paper.
is a factor of f(x) and that f (-5)
0.
(a) All zeros of the function and their multiplicities.
(b) The y-intercept of the graph of the function:
(c) The x-intercepts:
(d) Sketch of the graph of the function on a graphing paper.
22. The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2
at x=1 and x=0, and a root of multiplicity 1 at x==3
Find a possible formula for P(x). Explain each step.
23. The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=2 and a root of
multiplicity 1 at x=-4. The y-intercept is y=-1.6.
Find a formula for P(x). Explain each step.
24. The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2
at x=4 and x=0, and a root of multiplicity 1 at x=-2.
Find a possible formula for P(x). Explain each step.