🧮 algebra

1. Problemet är att bestämma alla nollställen till polynomet $$p(x) = 2x^3 + x^2 - 8x + 3$$. 2. För att hitta nollställen löser vi ekvationen $$p(x) = 0$$, alltså:

1. **State the problem:** Solve the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. **Formula and rules:** To solve a quadratic equation of the form $$ax^2 + bx + c = 0$$, we can facto

1. **State the problem:** Solve the equation $$\log(2x + 3) + \log(x + 2) - 1 = 0$$ for $x$. 2. **Use the logarithm property:** The sum of logarithms is the logarithm of the produc

1. Bài toán yêu cầu tìm giá trị của $x$ thỏa mãn phương trình $ (x-2)(x-1) = x(2x+1) + 2$.\n\n2. Viết lại phương trình và mở rộng các biểu thức:\n$$ (x-2)(x-1) = x(2x+1) + 2 $$\n$$

1. Bài toán yêu cầu tìm giá trị của $x$ thỏa mãn phương trình $$3(2x-3)+2(2-x)=-3.$$\n\n2. Ta sẽ sử dụng quy tắc phân phối để khai triển các biểu thức trong dấu ngoặc.\n\n3. Khai t

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 18}{x^2 - 4x + 4} \cdot \frac{x - 2}{2(x + 3)}$$

1. The problem is to graph the function $y = x^2$. 2. The formula used is $y = x^2$, which is a quadratic function representing a parabola.

1. **State the problem:** We have a matrix of vehicle counts over three days and a charge matrix for each vehicle type. We want to find which revenue statement is true based on the

1. **State the problem:** We need to find the matrix $A$ given by the equation: $$A = 3.1 \begin{bmatrix} 1 & -4 & 0 \\ -2 & 2 & -1 \end{bmatrix} - 1.2 \begin{bmatrix} -1 & 2 & 5 \

1. El problema es reescribir la ecuación dada $$y = -\frac{1}{2}x - 2$$ en la forma estándar $$Ax + By = C$$, donde $$A$$, $$B$$ y $$C$$ son números enteros. 2. La forma estándar d

1. **State the problem:** Solve the equation $$0=36x^4+60x^3-696x^2-480x$$ algebraically using the factor theorem and polynomial long division. 2. **Rewrite the equation:**

1. **State the problem:** Simplify the expression $$\frac{\sqrt[3]{-125} \times (1 - 0.8)^2 + 0.3}{(\frac{1}{5})^{-1} - \sqrt{2.25}}$$. 2. **Recall formulas and rules:**

1. **State the problem:** Simplify the expression $$\frac{\sqrt[3]{-125} \times (1 - 0.8)^2 + 0.3}{(\frac{1}{5})^{-1} - \sqrt{2.25}}$$

1. El problema pide expresar cada operación como una sola potencia. 2. La regla importante es que para potencias con el mismo exponente $n$, se puede usar la propiedad:

1. **State the problem:** We need to find the total amount of money given to the three children as pocket money by their father. 2. **Analyze the problem:** The problem does not pr

1. Planteamos resolver la ecuación $$\frac{x^2}{5} - \frac{x}{2} = \frac{3}{10}$$ usando la forma general de la ecuación cuadrática. 2. Multiplicamos toda la ecuación por 10 para e

1. Planteamos la ecuación: $$\frac{x^2}{5} - \frac{x}{2} = \frac{3}{10}$$ 2. Multiplicamos toda la ecuación por 10 (mínimo común múltiplo de 5, 2 y 10) para eliminar denominadores:

1. **State the problem:** Simplify the expression $10 - 10 \times 10 + 10$. 2. **Recall the order of operations:** According to PEMDAS/BODMAS, multiplication is performed before ad

1. **Planteamiento del problema:** Dada la transformación lineal $T : \mathbb{R}^3 \to \mathbb{R}^3$ definida por

1. **Stating the problem:** Calculate the value of the expression:

1. Problema 2: Resolver la ecuación $2x + 3 = 11$. - Fórmula: Para resolver ecuaciones lineales, aislamos la variable $x$.