🧮 algebra

1. Let's state the problem: We want to find when $3\cdot(x+1)$ is a factor of $x^n + 1$. 2. Note that to check if $(x+1)$ is a factor of $x^n + 1$, by the Factor Theorem, $(x+1)$ i

1. **State the problem:** We are given the equation $x^2 + kx + 6 = (x + 2)(x + 3)$ and need to find the value of $k$ such that the equality holds for all $x$. 2. **Expand the righ

1. Stating the problem: We are given that 12 sheets of thick paper weigh 40 grams, and we need to find how many sheets weigh 1 gram. 2. Find the weight of one sheet by dividing the

1. We are asked to solve the inequality $$7 - x \leq 9$$. 2. Start by isolating $x$ on one side. Subtract 7 from both sides:

1. We are asked to find the cube root of 8. 2. The cube root of a number $x$ is a number $y$ such that $y^3 = x$.

1. Énonçons le problème : résoudre l'exercice 2 (sans indication spécifique, supposons un problème algébrique classique). 2. S'il s'agit d'une équation à résoudre (exemple : $2x +

1. **State the problem:** Simplify the expression $$6a + 6b + 9c - 4a + 9b - 2c$$. 2. **Group like terms:** Combine terms with the same variables.

1. Énoncé du problème : Vous souhaitez pratiquer les mathématiques. Voici un problème simple d'algèbre pour commencer. 2. Problème : Résoudre l'équation linéaire suivante : $$2x +

1. We are given the inequality $5 > 3$ and asked to multiply both sides by $-3$ and then compare the results. 2. Multiplying both sides by $-3$, we get:

### Exercice 1 1) Problème : Trouver la bonne équation dont $\sqrt{5}$ est solution.

1. **Stating the problem:** We know the weight of 12 sheets of thick paper is 40 kg. We want to find how many sheets would weigh 1 g. 2. **Convert all weights to the same units:**

1. Stating the problem: Factorise the expression $$-32h^5j^3y^4 + 64h^2j^4y^7$$.\n\n2. Identify the greatest common factor (GCF) for each part:\n- Numerical coefficients: GCF of 32

1. The problem is to solve the inequality: $$3x + 4 < 8$$. 2. Subtract 4 from both sides to isolate the term with $$x$$:

1. The problem is to factorise the quadratic expression $$6x^{2} + 35x + 49$$. 2. First, identify the coefficients: $$a = 6$$, $$b = 35$$, and $$c = 49$$.

1. The user has provided a long list of numbers ending with an underscore, suggesting the need to find the correct continuation or next number in the sequence. 2. Since the given s

1. Simplify $3^4 \times 3^2$. Using the product of powers rule: $a^m \times a^n = a^{m+n}$,

1. The problem requires us to simplify the expression $a^{-9} \times a^{-3}$. 2. Recall the exponent multiplication rule: when multiplying like bases, add the exponents.

1. **State the problem:** Simplify the expression $b^{-5} \times \sqrt[5]{b^3}$. 2. **Rewrite the radical as an exponent:** Recall that $\sqrt[5]{b^3} = b^{\frac{3}{5}}$.

1. **Minimize area of a closed cylinder with volume 250\pi ml** Given volume $V = 250\pi$, volume formula: $$V = \pi r^2 h = 250\pi \implies r^2 h = 250$$

1. The problem involves analyzing the parabola given by the equation $y^2 = 8x$. 2. We identify the parabola as one that opens to the right because it is in the form $y^2 = 4ax$.

1. The problem asks to simplify the expression $b^{-5} \times \sqrt[5]{b^3}$. 2. Recall that $\sqrt[5]{b^3}$ can be written as $b^{\frac{3}{5}}$.