🧮 algebra

1. **Énoncé du problème :** Décomposer le polynôme $P(x) = 2x^3 - 5x^2 + 3x - 1$ en facteurs, identifier les coefficients des termes, et donner la forme canonique.

1. **Problem Statement:** Translate the polygon with vertices D(0,4), E(-3,-1), F(1,-5), and G(1,0) 3 units right and 3 units up. 2. **Translation Matrix:** Translation moves point

1. **State the problem:** Simplify the expression $$(-192k)^{20}$$. 2. **Recall the rule for powers:** When raising a product to a power, raise each factor to that power: $$ (ab)^n

1. **State the problem:** Simplify the expression $$\frac{3(x^2 + 2x + 4)}{6}$$. 2. **Formula and rules:** When simplifying fractions, divide numerator and denominator by their gre

1. **State the problem:** Solve the quadratic equation $x^2 - 45 = 0$ for $x$. 2. **Formula and rules:** The equation is in the form $x^2 = c$, where $c$ is a positive number. To s

1. The problem is to verify if the equation $-3x - 3y + 4z - 6 = 0$ can be a valid answer. 2. This equation is a linear equation in three variables $x$, $y$, and $z$. It represents

1. **State the problem:** Solve the quadratic equation $3x^2 - 48 = 0$ for $x$. 2. **Rewrite the equation:**

1. **State the problem:** We need to sketch the graph of the linear equation using intercepts for the equation $$y = -2x - 4$$. 2. **Recall the formula and rules:** The equation is

1. Stating the problem: Solve the quadratic equation $x^2 - 25 = 0$. 2. Formula and rules: This is a difference of squares equation, which can be factored using the identity $a^2 -

1. **State the problem:** We need to sketch the graph of the linear equation $$y = -2x - 4$$ using intercepts. 2. **Recall the formula and rules:** A linear equation in slope-inter

1. **State the problem:** We are given the system of equations:

1. Diberikan matriks $$B = \begin{pmatrix}4 & 0 \\ 9 & -2\end{pmatrix}$$. 2. Kita diminta mencari nilai eigen dan vektor eigen dari matriks ini.

1. **State the problem:** Solve the quadratic equation $x^2 - 25 = 0$. 2. **Formula and rules:** This is a difference of squares equation, which can be factored using the identity

1. Let's clarify why we add terms when simplifying expressions. 2. When you have like terms, which means terms with the same variable and exponent, you can add or subtract their co

1. **Problem Statement:** Given real numbers $a, b, c, d, e$, consider the expressions: $$a(b-c),\quad b(c-d),\quad c(d-e),\quad d(e-a),\quad e(a-b)$$

1. **State the problem:** Find the equation of the plane containing the lines \(L_1\) and \(L_2\).\n\n2. **Write parametric equations of the lines:**\n\(L_1:\ x = t,\ y = 2 - t,\ z

1. **State the problem:** Solve the quadratic equation $x^2 = 81$. 2. **Formula and rules:** To solve $x^2 = a$, we take the square root of both sides, remembering that both positi

1. **Problem:** Write any one relation that satisfies AM, GM, and HM between any two unequal positive numbers. 2. **Formula and Explanation:** For two positive numbers $a$ and $b$,

1. **State the problem:** We are given the function $$f(x) = - \frac{5}{4} \left(\frac{4}{5}\right)^{x + 4} + 2$$ and need to analyze it.

1. **State the problem:** We are given the function $f(x) = x^2 - 2x + 5$ and asked to analyze it on the interval $x = 0$ to $x = 3$. 2. **Formula and rules:** This is a quadratic

1. **Problem (a): Factorise completely** $3x(4a - 5b) - 2y(5b - 4a)$. 2. Notice that $-2y(5b - 4a)$ can be rewritten as $+2y(4a - 5b)$ because $5b - 4a = -(4a - 5b)$.