These problems are from different books and the page
numbers do not correspond to the ones of your book .
P. 295 Exercises
2.
Let a be a positive number .
Sketch the graph of . g(x) = -ax4.
14. Divide, using algebraic long division. Write the quotient, and indicate the
remainder.
21. Use the synthetic division to write the quotient P(x) ÷ (x - r) in the form
, where R is a constant.
26.
Use the synthetic division and the remainder theorem.
Find P(-3), given P(x) = 5x3 + 14x2 + 3x + 10
The coefficient
Therefore, P(-3) = -8
36.Divide, using synthetic division. Write the quotient,
and indicate the remainder. As coefficients get more involved, a calculator
should prove helpful. Do not round off-all quantities are exact.
Quotient: Q(x) = x5 + 2x3 - 3, Remainder, R = 0
54.Either give an example of a polynomial with real
coefficients that satisfies the given conditions or explain why such a
polynomial cannot exist.
Condition: P(x) is a fourth-degree polynomial with no x- intercepts .
An example: P(x) =x4 + 4
58.
Divide, using algebraic long division. Write the quotient, and indicate the
remainder.
Quotient: Q(x) = x2 + 2x + 1
Remainder, R = 0
P. 308
2.
Write the zeros of the polynomial and indicate the multiplicity of each if over
1.
What is the degree of the polynomial?
P(x) = (x + 6)2(x - 5)3
Zeros:
-6 withmultiplicity2
5 withmultiplicity3
Thedegree of the polynomials5.
6.
Find a polynomial of lowest degree with leading coefficient 1, that has the
indicated set of zeros. Leave the answer in a factored form. Indicate the degree
of the polynomial.
Zeros are – 4 (multiplicity 2), 0, 2(multiplicity 3)
P(x) = x(x + 4)2(x - 2)3
Degree = 6
16.
Find the polynomial of lowest degree, with leading coefficient 1, that has the
indicated graph. As sume all zeros are integers. Leave the answer in a factored
form. Indicate the degree.
P(x) = x(x - 2)2(x + 2)2
Degree = 5
24.
List all possible rational zeros .
28.
Write as a product of linear terms .
P(x) = x3 - 4x2 - 3x + 18; 3 is a double zero
36.
Find all the roots exactly (rational, irrational, and imaginary) for each
polynomial equation.
x4 - 11x2 + 12x + 4 = 0
Possible zeros are ±1, ±2, ±4
Continue…
The other roots are from the roots of x2 + 4x + 1 = 0
Use the quadratic formula ,
Therefore, the roots are 2 and
46.
Find all zeros exactly (rational, irrational, and imaginary) for each
polynomial.
P(x) = x4 + 9x3 + 23x2 + +8x - 16
Use the synthetic division to find the first zero.
The other zeros are from the zeros of x2 + x - 1 = 0
Use the quadratic formula,
Therefore the zeros are –4 and
56.
Solve the inequality : x2 > 2x + 1
x2 > 2x + 1
x2 - 2x - 1 > 0
Use the quadratic formula to find the zeros of x2 - 2x - 1 and factor it.
The interval notation of the solution set is
66.
Find the all the zeros of P(x), given the indicated zero.
P(x) = x3 + 2x2 - 3x - 10, -2 + i is a zero.
Note that -2-i is also a zero.
P(x) = (x - 2)(x + 2 - i)(x + 2 + i)
Zeros are 2, -2 + i, -2 - i
