🧮 algebra

1. O problema pede para fatorar o polinômio $$4x^4 - 13x^3 - x^2 + 13x - 2$$ usando a regra de Ruffini. 2. A regra de Ruffini é usada para dividir polinômios por binômios da forma

1. **State the problem:** Simplify the expression $4x^4 - 13x^3 - x^2 + 13 - 2$. 2. **Combine like terms:** The constants $13$ and $-2$ can be combined.

1. The problem is to evaluate $\log 10$. 2. Recall that $\log$ without a base usually means $\log_{10}$, the logarithm base 10.

1. The problem asks to create a piecewise function that includes at least one absolute value and then graph it. 2. A piecewise function is defined by different expressions dependin

1. **State the problem:** We are given the function $$F(x) = a + \frac{b}{x+1} + \frac{c}{x-3}$$ and we want to understand its structure and behavior. 2. **Formula and rules:** Thi

1. **State the problem:** Simplify the expression $$\frac{3}{a^2-16} + \frac{2}{a+4}$$. 2. **Recall the formula and rules:** The denominator $a^2-16$ is a difference of squares, wh

1. **State the problem:** Simplify the expression $$\frac{4}{y^2-4} + \frac{1}{y-2}$$. 2. **Identify the formula and rules:** Recognize that $y^2-4$ is a difference of squares, whi

1. Planteamos el problema: dividir el polinomio $$4x^4 - 3 + 6x^2 - 852$$ entre el binomio $$x - 4$$. 2. Ordenamos el polinomio dividendos por grados descendentes y completamos tér

1. Problema: Reducir a un solo logaritmo las expresiones dadas. 2. Regla general: Para combinar logaritmos con la misma base, usamos las propiedades:

1. **State the problem:** Simplify the expression $$\frac{1}{2 - \frac{1}{3}}$$. 2. **Recall the rule:** To simplify a complex fraction, first simplify the denominator.

1. **Énoncé du problème** : Trouver l'expression de la fonction $f$ définie par $f(x) = \frac{1}{x} + 1$ et calculer $f(a)$ et $f(b)$ pour $a=1$ et $b=3$. 2. **Formule utilisée** :

1. Problem: Oblicz objętość prostopadłościanu o krawędziach długości $2 - \frac{7}{5}$, $\sqrt{2}$ oraz $\frac{1}{2 - \frac{1}{5}}$. 2. Wzór na objętość prostopadłościanu to:

1. **Problem statement:** Factor the expression $zac - bc$ using grouping. 2. **Formula and rules:** Grouping involves factoring common terms from parts of the expression.

1. **State the problem:** Calculate the new hourly rate given the number of hours worked per week and the new weekly earnings.

1. **State the problem:** Calculate (a)(i) the total hours Mrs. Tracey works per week, (a)(ii) her weekly earnings at $8.10 per hour, and (b) her new hourly rate given new weekly e

1. **State the problem:** Simplify the expression $$\frac{-20+V3-V1}{12}-\frac{\frac{2}{20+V3-V1}}{10}-\frac{V1}{10}$$. 2. **Rewrite the expression clearly:**

1. Problema afirmă că matricele nu comută neapărat, adică $AB \neq BA$ în general. 2. Se consideră matricele $A$ și $B$ și matricea identitate $I_n$ de dimensiune $n$.

1. Problema: Avem două matrice pătratice $A$ și $B$ de ordin $n$ cu elemente complexe, pentru care se știe că $$A^3 - B^3 = A(B - A)A$$ și $$\det(A + I_n) = \det(B + I_n).$$ Trebui

1. **State the problem:** Convert the mixed number percentages $3\ 7/8\%$ and $4\ 3/8\%$ into decimal form. 2. **Recall the formula:** To convert a mixed number percentage to a dec

1. We are asked to find the sum of the fractions: $\frac{2}{10} + \frac{5}{15} + \frac{2}{3} + \frac{1}{5} + \frac{2}{4}$.\n\n2. To add fractions, we need a common denominator. The

1. **State the problem:** Solve the equation exactly without rounding until the final answer. 2. **Identify the equation:** The user did not provide a specific equation, so I canno