🧮 algebra

1. **State the problem:** Find values of $l$ and $m$ such that the polynomial $$x^4 + 4x^3 + 16x^2 + lx + m$$ is a perfect square. 2. **Assume the polynomial is a perfect square of

1. Stating the problem: Solve the equation $ (x-2)(x+3) = 0 $ for $ x $. 2. Use the zero product property: If the product of two factors is zero, then at least one of the factors m

1. **State the problem:** Find the truth set of the equation $$3x + 5x - 2 = 0$$. 2. **Combine like terms:** Add the terms with $x$ together:

Problem: Solve the quadratic equation $2x^2 - 3x - 5 = 0$. 1. Level 1 — Identify coefficients and apply the quadratic formula.

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Identify coefficients:** The quadratic is in the form $ax^2 + bx + c$ where $a=1$, $b=5$, and $c=6$.

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 25$. 2. **Identify coefficients:** Here, $a=1$, $b=5$, and $c=25$.

1. **Classer dans l’ordre croissant les nombres** $\sqrt{2}$, $\sqrt[3]{4}$, $\sqrt[6]{5}$.\n - Calculons les valeurs approchées :\n

1. State the problem: Multiply the numbers $0.05$ and $1.38$. 2. Write the multiplication expression: $$0.05 \times 1.38$$

1. The problem is to multiply the two numbers: $0.05$ and $1.38$. 2. Multiply the numbers directly: $$0.05 \times 1.38 = 0.069$$

1. **State the problem:** We need to evaluate the expression $6.8 \times 1.3 \times 204 + 68$ and check why the answer 2.72 is incorrect. 2. **Calculate the multiplication part:**

1. **Stating the problem:** We want to understand the laws of indices (exponents) and how they relate to repeated multiplication, which can be seen as a form of repeated addition i

1. The problem asks to find the solution set of the inequality $$|x - 2| \leq -4$$ in the real numbers $\mathbb{R}$. 2. Recall that the absolute value $|x - 2|$ represents the dist

1. The problem asks for the domain of the function $$f(x) = \sqrt{x^2 - 1}$$. 2. The expression inside the square root, called the radicand, must be non-negative for the function t

1. The problem asks to identify the false statement among the given options about absolute values and square roots. 2. Let's analyze each statement:

1. **State the problem:** Given that $a > 0$ and $b < 0$, determine which of the following expressions is always negative: (a) $|ab|$

1. **State the problem:** We need to find which value among $-1$, $0$, $3$, and $4$ does not satisfy the equation $$|x - 3| + |x + 1| = 4.$$ 2. **Analyze the absolute value express

1. The problem is to solve a system of linear equations. 2. A linear system typically looks like:

1. The problem involves matching algebraic expressions and logarithmic equations to their corresponding graphs and solving exponential and logarithmic equations. 2. For the algebra

1. **State the problem:** Solve the equation $4x = 5y - 140$ for $x$ in terms of $y$. 2. **Isolate $x$:** To express $x$ in terms of $y$, add $140$ to both sides and then divide bo

1. The problem involves adding and subtracting fractions with different denominators. 2. First, convert all fractions to have a common denominator where necessary.

1. **State the problem:** We need to write an inequality involving pixels per inch (ppi) that relates the lab's average finger width in pixels to the manufacturers' widths. 2. **Gi