🧮 algebra

1. **Problema:** hacer el paso a paso del primer ejercicio, desde el inciso $a$ hasta el inciso $s$.\n2. No se incluyó el enunciado ni los resultados de esos incisos, así que no pu

1. **Planteamiento del problema:** Multiplicar los polinomios dados. 2. **Polinomios:**

1. Planteamos el problema: calcular el resto de la división del polinomio $$x^6 + 2\sqrt{2}x^5 + 2\sqrt{2}x^3 - 2x^2 - 2\sqrt{2}x + 4$$ entre el binomio $$x - \sqrt{3} + \sqrt{2}$$

1. **State the problem:** Simplify the expression $x^2 + x^2$. 2. **Formula and rules:** When adding like terms, add their coefficients and keep the variable part the same.

1. **State the problem:** Solve the system of equations by graphing: $$y = x - 8$$

1. The problem is to evaluate the expression $(-11)^8 \times (-11)^5$. 2. We use the rule of exponents that states $a^m \times a^n = a^{m+n}$ when the bases are the same.

1. **State the problem:** Multiply the expression $3u \cdot 3u^3 v^3 \cdot 4v^5$ and simplify it. 2. **Recall the product rule for exponents:** When multiplying terms with the same

1. **State the problem:** Multiply and simplify the expression $2x \cdot 3y^9 \cdot 7x^5y^3$. 2. **Write the expression:**

1. **State the problem:** Solve the logarithmic equation $$3 \log_2 - 2 \log_2 \frac{x}{3} = 2 \log_2 3 + 1$$. 2. **Rewrite the equation clearly:** Note that $$\log_2$$ without an

1. **State the problem:** Solve for $x$ in the equation $x - 7(2x + 1) = 2(6 - 5x) - 13$. 2. **Write the equation and apply distributive property:**

1. **Énoncé du problème :** Simplifier les expressions exponentielles suivantes :

1. **State the problem:** Solve the inequality $$|x+1| - 4 > 9$$. 2. **Isolate the absolute value:** Add 4 to both sides:

1. **State the problem:** Divide the polynomial $29x^4 - 7x - 5x^2 + 7x^3 + 20$ by the binomial $5x - 7$. 2. **Arrange the dividend in descending powers of $x$:**

1. El problema és trobar una funció logarítmica que es pugui resoldre. 2. La forma general d'una funció logarítmica és $$y = a \log_b(x - h) + k$$, on:

1. **State the problem:** Simplify the expression $$\frac{2x^4 + 2x^3 - 7x^2 + 5x + 10}{x^2 - 1}$$. 2. **Recall the formula and rules:** The denominator can be factored using the d

1. **State the problem:** Simplify the expression $$\frac{2x^4 + 2x^3 - 7x^2 + 5x + 10}{x^2 - 1}$$. 2. **Recall the formula and rules:** The denominator is a difference of squares:

1. **State the problem:** Simplify and understand the expression $-2x^2 + 80$. 2. **Identify the terms:** The expression consists of two terms: $-2x^2$ (a quadratic term) and $80$

1. **State the problem:** Solve the quadratic equation $3x^2 - 7x = 20$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. The problem is to solve for $x$ in the equation $\log_x \left( \frac{4}{9} \right) = -2$. 2. Recall the definition of logarithm: $\log_a b = c$ means $a^c = b$.

1. El problema no está explícito, pero resolveré una ecuación común para ilustrar. 2. Supongamos que la ecuación es $$2x + 3 = 7$$.

1. **State the problem:** Solve the inequality $$\left|\frac{x+9}{x-9}\right| \le 2.$$\n\n2. **Rewrite the absolute value inequality:** This means \(-2 \le \frac{x+9}{x-9} \le 2\).