🧮 algebra

1. Stated problem: Find the remainder when the polynomial $$2x^3 + 3x^2 - 2x + 2$$ is divided by $$x+3$$. 2. According to the Remainder Theorem, the remainder of a polynomial $$f(x

1. Stating the problem: Decompose the rational function $$F(X) = \frac{1}{X^{3}(X^{2} - 1)(X^{2} + 1)}$$ into partial fractions over $\mathbb{R}(X)$. 2. Factor the denominator: Not

1. Énoncé du problème 1.1 : Résoudre dans ℝ les systèmes (E1) : $ (x+1)^2 + y + x -1=0 $ et (E2) : $ (x+y)^2 = 1 $, puis (E1) alternatif : $ \frac{x}{1} + x + y -1=0 $ et (E2) : $

1. Problemet handlar om att beräkna hur många procent räntesatsen höjdes när den tidigare räntan var 0,5% och den höjdes med 0,2 procentenheter. 2. Vi börjar med att skriva den gam

1. **State the problem:** We are given two inequalities involving variables $\beta_{ji}$, $\theta_{ji}$, $x_{ij}$, and constants $b_{ij}$, $A_{ij}$: $$\beta_{ji} x_{ij} \leq \theta

1. Écrire sous forme canonique les expressions suivantes. a) Pour $A(x) = 2x^2 - 6x + 5$ :

1. Problème: Décomposer en éléments simples dans \(\mathbb{R}(X)\) \(F(X) = \frac{1}{X^{3}(X^{2} - 1)(X^{2} + 1)}\). 2. Factorisation des dénominateurs: \(X^{2} - 1 = (X-1)(X+1)\)

1. The problem is to simplify the expression $(2\sqrt{2})^2$. 2. First, recognize that $(a b)^2 = a^2 b^2$ for any real numbers $a$ and $b$.

1. The problem asks to simplify the expression $\sqrt{2} + 3\sqrt{2}$.\n2. Notice that both terms have the same radical part, $\sqrt{2}$, so we can treat the problem like combining

1. **Question 1: Calculate the exact value of** $$Q = \frac{(\sin 2x + b)(2 \sin x - 1)}{a^2 - 4 \tan x}$$

1. نبدأ بتعريف الدوال: الدالة $g(x) = x^3 + 6x - 4$ وهي كثيرة حدود تكعيبية.

1. **State the problem:** A student must attend at least 160 days but not more than 200 days to meet attendance requirements. 2. **Write the inequality:** Let $d$ be the number of

1. Énonçons le problème : Calculons $C = 3\sqrt{75} - 2\sqrt{139} + 3\sqrt{182} - \sqrt{432}$ en simplifiant chaque terme radical. 2. Simplifions radicaux un par un.

1. **Find the 10th term of the arithmetic sequence where $a_1=5$ and $d=3$.** The $n$th term of an arithmetic sequence is given by:

1. Simplifions les nombres donnés. a = \frac{\sqrt{18} \times \sqrt[3]{256} \times \sqrt[4]{64}}{\sqrt[3]{1024} \times \sqrt[6]{64} \times 10^{6}}

1. **Stating the problem:** Let's understand arithmetic sequences and series step-by-step. 2. **Arithmetic Sequence:** It is a list of numbers with a constant difference between co

1. Diberikan limit $$\lim_{x \to 1} \frac{x^4 - 1}{x^2 + 5x - 6}$$. 2. Faktorkan pembilang: $$x^4 - 1 = (x^2 - 1)(x^2 + 1) = (x - 1)(x + 1)(x^2 + 1)$$.

1. The problem is to convert the repeating decimal $1.8\overline{8}$ into a fraction. 2. Let $x = 1.8\overline{8}$ represent the number.

1. Pernyataan masalah: Tentukan pernyataan yang bersesuaian dengan $$\lim_{x \to 4} \frac{2-\sqrt{x}}{4-x}$$. 2. Perhatikan bahwa jika kita substitusi langsung $x=4$, maka pembilan

1. Classify the following statements as true or false: (a) $-2 \in \mathbb{N}$: False, natural numbers are positive integers starting from 1.

1. Stated problem: Calculate $9 \frac{1}{6} \div \left(2 \frac{5}{6} - 1 \frac{1}{2}\right)$. 2. Convert mixed numbers to improper fractions: