Question

Are the following polynomials irreducible over Q? Prove why or why not.

(a) 2x^13−25x^3+ 10x−30

(b) 5x^3+ 6x^2−9x+ 21

(c) x^4+ 7x^3+ 14

(d) x^5+ 18x + 6

Answer #1

solve for x using the factor theorem and long division. a.
2x^3-3x^2-5x+6=0 b. 8x^3+4x^2-18x-9=0 c.
2x^3+10x^2+13x+5=0 d. -2x^3-12x^2+x+60=0

Is f(x)=x^5+√6 x^4+2x^2-(3/2)x irreducible in R[x], why or why
not?
Is g(x)=x^3+x+1 irreducible in Z5[x] why or why not?

evaluate each indefinite integral
4) \int -(2*csc^(2)2x)/(cot(2x)*\sqrt(cot^(2)2x-1)); u=cot2x
5) \int (10x^(4))/(9+4x^(10)); u=2x^(5)
6) \int (20x^(3))/(\sqrt(25-25x^(8)))
7) \int (1)/(x\sqrt(25-(ln-2x)^(2)))

Find the greatest common divisor of the given polynomials over
the given field. Then write the greatest common
divisor as a linear combination of the given polynomials. That is,
given f(x) and g(x), find a(x) and b(x) so that d(x) = a(x)f(x) +
b(x)g(x), where d(x) is the greatest common divisor of f(x) and
g(x).
(a) x^10 − x^7 − x^5 + x^3 + x^2 − 1 and x^8 − x^5 − x^3 + 1
over Q.
(b) x^5 +...

NEED ANSWERS ASAP PLEASE
PROVIDE LETTERS ONLY
Part II. Multiple Choice:
Directions: Read each question carefully, and
then provide the answer that best fits the question.
1. What is the highest value of x that satisfies this equation
x(x+4) = -3
A. -1
B. 0
C. 1
D. -3
2. If x2 - 9x = -18, what are the possible values of
x?
A. -3 and -6
B. -3 and 6
C. 3 and -6
D. 3 and 6
3....

Sec 6.2
1.Write an augmented matrix for the following system of
equations.
9x-8y+6z=-1
7x-5y+2z=9
6y-8z=-9
The entries in the matrix are ?
2.use row operations on the augmented matrix as far as necessary
to to determine whether they system is independent, dependent, or
inconsistent ?
4x-6y+5x=-2
-8x+12y-10z=4
-12x+18y-15z=6
3. use row operations on the augmented matrix as far as
necessary to to determine whether they system is independent,
dependent, or inconsistent ?
5x-7y+4z=13
-5x+7y-4z=-15
-10x+14y-8z=-27
4. Solve the system by...

Verify the quotient rule for each of the following:
1. f(x)=4x^5-4x^4+13x^3-2x^2+7x+6/x^2-x+2
2. f(x)=20x^8-28x^6+29x^4-35x^2+5/5x^4-7x^2+1

Find the derivative of each of the following functions:
(a) y=x^12 (c) y=7x^5 (e) w=-4u^(1/2)
(b) y =63 (d) w=3u^(-1) (f) w=4u^(1/4)
2. Find the following:
(a) d/dx(-x^(-4)) (c) d/dw 5w^4 (e) d/du au^b
(b) d/dx 9x^(1/3) (d) d/dx cx^2 (f) d/du-au^(-b)
3. Find f? (1) and f? (2) from the following functions: Find the
derivative of each of the following functions:
(c) y=x^12 (c) y=7x^5 (e) w=-4u^(1/2)
(d) y =63 (d)w=3u^(-1) (f) w=4u^(1/4)
4.
(a) y=f(x)=18x (c) f(x)=-5x^(-2)...

3) If A = 3
1 and B
= 1 7
0
-2
5 -1
Find
a) BA
b) determinant
B
c) Adjoint A
d)
A-1
4) Using matrix method solve the following simultaneous
equations
5x – 3y = 1
2x – 2y = -2
5) Given that f(x) = 6x - 5 g(x) = 3x +
4 and h(x) = 4x – 6
2
Find:-
i)...

For each of the following pairs of polynomials f(x) and g(x),
write f(x) in the form
f(x) = k(x)g(x) + r(x)
with deg(r(x)) < deg(g(x)).
a) f(x) = x^4 + x^3 + x^2 + x + 1 and g(x) = x^2 −
2x + 1.
b) f(x) = x^3 + x^2 + 1 and g(x) = x^2 − 5x + 6.
c) f(x) = x^22 − 1 and g(x) = x^5 − 1.

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