Question

Given the polynomial f(x) = 3x^4 -7x^3 -3x^2 + 17x + 10, and given the zeros of -1 and -2/3,

A). Write the polynomial in linear and irreducible quadratic factors

B). Write the linear factorization of the polynomial.

Answer #1

**(b)**

1. a) For the polynomial f(x) = ?4 − 4?^3 + 22?^2 + 28?− 203,
find the following:
a. Find all the zeros using the given zero ? = 2 − 5?. Write the
zeros in exact form.
b. Factor f(x) as a product of linear factors.
Zeros: x = x = x= x=

f(x)=x^3+8x^2+14x+4 (given that -2 is a zero)
find all zeros of the polynomial function

form a polynomial F(x) with real coefficients having the given
degree and zeros
degree 4
zeros 2-3i; -3 multiplicity 2

5.
All the real zeros of the given polynomial are integers. Find
the zeros. (Enter your answers as a comma-separated list. Enter all
answers including repetitions.)
P(x) = x4 − 13x2 + 36
x =
Write the polynomial in factored form.
P(x) =
15.
All the real zeros of the given polynomial are integers. Find
the zeros. (Enter your answers as a comma-separated list. Enter all
answers including repetitions.)
P(x) = x3 + 5x2 − x − 5
x =...

Find (f −1 (a))' :
(a) f(x) = 2x 3 + 3x 2 + 7x + 4, a = 4
(b) f(x) = 2x + cos(x), a = 1

Consider the polynomial f(x) = x ^4 + x ^3 + x ^2 + x + 1 with
roots in GF(256). Let b be a root of f(x), i.e., f(b) = 0.
The other roots are b^ 2 , b^4 , b^8 .
e) Write b 4 as a combination of smaller powers of b.
Prove that b 5 = 1. f) Given that b 5 = 1 and the factorization
of 255, determine r such that b = α...

Form a polynomial f(x) with the real coefficients having the given
degree and zeros
Degree 4; zeros: -1,2 and 1-2i

6. For the given polynomial, find all zeros of the polynomial
algebraically. Factor the
polynomial completely.
P(x) = x^5 − 3x^4 + 12x^3 − 28x^2 + 27x − 9

1.Determine all the zeros and their multiplicities of the
polynomial function f(x) = x 5 − 6x 3 + 4x 2 + 8x − 16
2. Find all the zeros of the function f(x) = x 5 − 4x 4 + x 3 −
4x 2 − 12x + 48 given that −2i and 4 are some of the zeros.

Form a polynomial f(x) with real coefficients having the given
degree and zeros.
Degree 4;
zeros:-5+3i, -4 multiplicity 2
please show all steps and explain

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