Get Expert Help with Polynomials: Examples, Word Problems, and Practice Questions

To prove $f = x^{4} + x^{3} + x^{2} + x^{1} + 1$ is irreducible over the $Q$

Arraryeldergox2 2022-06-26

I want to prove that
$f (x, y) = (x - 2 y)^{4} + 64 x y + 16 \geq 0$

boloman0z 2022-06-24

If a is a root of $x^{2} (x - 5) + 2$ , then what is $[a^{4}]$ ?

protestommb 2022-06-24

Solve in integers the equation: $(x^{2} - 4 y) + (y^{2} - 4 x) + x y (x - 4) (y - 4) = 2021$

Leland Morrow 2022-06-24

Let $f (x) = x^{3} - 3 x^{2} + 3 x + 1, g (x) = x^{3} + 3 x^{2} + 3 x + 3$ . I would like to show that $Q [x] / ⟨ f (x) ⟩ ≅ Q [x] / ⟨ g (x) ⟩$

Villaretq0 2022-06-24

What is the Galois group of $27 x^{8} - 72 x^{4} - 16$ over the rationals?

doodverft05 2022-06-24

$P (x)$ is a polynomial and it is equal to $2 x^{3} + 2 a x^{2} + b x + c$ . It is given that $P (x)$ can be divided by $(x - 1)^{3}$ with zero remainder. Then , what is c?

Mara Cook 2022-06-22

Find the remainder of f divided by $g (x) = x^{4} + x^{2} + 1$ if the remainder of f divided by $h_{1} (x) = x^{2} + x + 1$ is $- x + 1$ and the remainder of f divided by $h_{2} (x) = x^{2} - x + 1$ is $3 x + 5$

Layla Velazquez 2022-06-22

How to show this formal identity (or you can assume $| x | < 1$

Sattelhofsk 2022-06-22

Show that $f (t) = t^{5} - 5 t + 1$ has no repeated roots.

Celia Lucas 2022-06-22

Prove that $t_{n} = 1 + \frac{\ln (2 n)}{2 n} + o (\frac{1}{n})$ as n tends to infinity.

Garrett Black 2022-06-21

Let $S = {- 1, 0, 1}$ and $T : P_{2} (R) \to Fun (S)$ be the transformation $T (p (x)) = p^{'} (x)$
and consider the ordered bases
$\begin{aligned} E & = {1, x, x^{2}} the standard basis of P_{2} (R), \\ F & = {1 - x, x + x^{2}, 2 + x^{2}} a basis of source P_{2} (R), \\ E^{'} & = {χ_{- 1}, χ_{0}, χ_{1}} the standard basis of Fun (S), \\ G & = {χ_{- 1}, χ_{1} - 2 χ - 1, χ_{- 1} + χ_{0} - 2 χ_{1}} a basis of target Fun (S) . \end{aligned}$

pokoljitef2 2022-06-21

Proving $X^{4} - 14 X^{2} + 9$ is irreducible

Mara Cook 2022-06-21

How to find all the real roots of $x^{9} - 2021 x^{3} + \sqrt{2020}$

opepayflarpws 2022-06-20

If $α, β, γ$ are roots of the cubic equation $2 x^{3} + 3 x^{2} - x - 1 = 0$

Celia Lucas 2022-06-20

If $x \geq - 1$ , prove that $(x + 1)^{3} = x$ has no solutions

varitero5w 2022-06-20

Give a complete non-redundant list of elements $x \in C$ such that $x^{10} + x^{5} + 1 = 0$

Finley Mckinney 2022-06-20

Find the value of $\int_{0}^{1} P (x) d x$

excluderho 2022-06-18

Find all real solutions for:
$\frac{3 x}{2 x^{2} - 7 x + 7} + \frac{27 x}{2 x^{2} + 6 x + 7} = 8$

Ezekiel Yoder 2022-06-16

Suppose the roots to $z^{4} + a z^{3} + b z^{2} + c z + d = 0$ all have the property that $| z | = 2$

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Precalculus

Get Expert Help with Polynomials: Practice Questions and Examples