🧮 algebra

1. El problema es factorizar el trinomio $x^2 + 13x + 40$. 2. Para factorizar un trinomio de la forma $x^2 + bx + c$, buscamos dos números que multiplicados den $c$ y sumados den $

1. Planteamos el problema: Encontrar dos números cuya suma sea $-10$ y cuyo producto sea $24$. 2. Sea $x$ y $y$ los dos números. Entonces, tenemos el sistema:

1. **Planteamiento del problema:** Factorizar por agrupación el polinomio $$y^2 + 5y + 9y + 45$$. 2. **Agrupamos términos:** Agrupamos los términos en dos pares para facilitar la f

1. **Planteamiento del problema:** Factorizar la expresión $12 a^2 + 15 b + 21$ usando el Factor Común Mayor (FCM). 2. **Regla para factorizar por FCM:** Se busca el mayor número y

1. El problema es encontrar el factor común mayor (FCM) de los términos $60y^8$, $40y^4$, $20y^5$ y $80y^4$. 2. Para hallar el FCM, debemos encontrar el máximo común divisor (MCD)

1. **Planteamiento del problema:** Queremos calcular cuánto se debe pagar por una camiseta y una pelota de fútbol después de aplicar sus respectivos descuentos.

1. El problema es calcular cuánto se debe pagar por unas tijeras y una pala considerando sus descuentos respectivos. 2. La fórmula para calcular el precio con descuento es:

1. **Problem 1:** Find the standard form of a line through $(-1,-4)$ parallel to the line through $(-2,-5)$ and $(2,7)$. 2. Find the slope of the given line using points $(-2,-5)$

1. **State the problem:** We need to divide the polynomial $$3x^3 + 5x^2 + 10x - 4$$ by the binomial $$3x - 1$$. 2. **Formula and rules:** Polynomial division can be done using lon

1. **State the problem:** We are given the function $$f(x) = \frac{x^3}{x^2 - x - 2}$$ and asked to analyze its properties including domain, asymptotes, and behavior. 2. **Identify

1. **State the problem:** We need to perform polynomial division for two expressions: a) $$\frac{8x^3 - 22x^2 + 11x + 6}{2x - 3}$$

1. **Stating the problem:** A quadratic equation is any equation that can be written in the form $$ax^2 + bx + c = 0$$ where $a$, $b$, and $c$ are numbers and $a \neq 0$. The goal

1. **State the problem:** Find the possible rational zeros of the polynomial $$f(x) = x^4 + 4x^3 - x^2 - 16x - 12$$ and test them to find actual zeros. 2. **Use the Rational Root T

1. **State the problem:** Factor the polynomial $$2x^3 - 6x^2 - 4x + 12$$ by grouping. 2. **Step 1: Group the terms into two halves:**

1. **State the problem:** Find the possible rational zeros of the polynomial $$f(x) = x^4 - 5x^3 + 5x^2 + 5x - 6$$ and test them to find actual zeros. 2. **Factors of the constant

1. The problem asks which inequality represents temperatures $t$ that are greater than $-2$ degrees Fahrenheit. 2. The inequality symbol $>$ means "greater than," and $<$ means "le

1. **State the problem:** We are given that over four days in Alaska, the temperature remained below 5°F. We want to determine which temperatures from the list \(-4^\circ F, -3^\ci

1. **Determine if** $f(x) = \left(\frac{3}{2}x^2 + \frac{1}{4}x - 5\right) + \left(3x^2 - \frac{5}{2}x + 6\right)$ **and** $g(x) = \left(\frac{5}{2}x^2 - \frac{3}{8}x - \frac{1}{4}

1. **State the problem:** We are given the linear function $f(x) = -2x + 5$ and asked to analyze its intercepts and end behavior. 2. **Find the x-intercept:** The x-intercept occur

1. **State the problem:** Solve the equation $$4x - 9 + 9x + 6 = 7x^2 - 3x - 54$$ for $x$. 2. **Combine like terms on the left side:**

1. **State the problem:** We need to find values of $x$ that cannot be solutions to the equation $$\frac{1}{x - 3} - \frac{1}{x + 8} = 10.$$ These values are those that make the eq