🧮 algebra

1. **Problem statement:** Prove that if the sum of two integers $a$ and $b$ is even, then at least one of the summands $a$ or $b$ is even. 2. **Recall definitions:**

1. បញ្ហា៖ ដោះស្រាយសមីការជាដើម $x^3 + 4x^2 - 17x - 60 = 0$។ 2. យើងប្រើវិធីសាស្រ្ត Factorization ដើម្បីស្វែងរកឬស។

1. 题目要求求函数 $f(x) = \sqrt{x+1} - \frac{1}{x}$ 的定义域。 2. 函数定义域的限制条件：

1. Problem: Simplify the expression $$2(a^4 + 6)^2$$ given that $$a < 6$$ and the expression $$\sqrt{a - 6}$$ is mentioned but not directly related to simplification. 2. Formula an

1. **State the problem:** Simplify the expression $$\frac{x^2 - 36}{x^2 - 24x + 144} \cdot \left(\frac{x+6}{x-12}\right)^{-2}$$. 2. **Recall important formulas and rules:**

1. **State the problem:** Factor the trinomial $$4x^2 - 13x + 10$$ into the form $$(4x - a)(x - b)$$ where $a$ and $b$ are numbers to be found. 2. **Recall the factoring method:**

1. **State the problem:** Simplify the expression $\frac{1}{3} + 8$. 2. **Recall the rule:** To add a fraction and a whole number, convert the whole number to a fraction with the s

1. The problem is to simplify the expression $\frac{a}{b}1 3 + 6$.\n\n2. First, clarify the expression. It seems to be $\frac{a}{b} \times 1 \times 3 + 6$.\n\n3. Use the multiplica

1. **State the problem:** Divide the polynomial $$P(x) = x^4 - x^3 + 4x + 2$$ by the divisor $$D(x) = x^2 + 3$$ using polynomial long division. 2. **Recall the formula:** Polynomia

1. The problem is to solve the equation $5$. 2. Since $5$ is a constant and not an equation or expression to solve, it means the value is simply $5$.

1. **Problem Statement:** Divide the polynomial $P(x) = 3x^2 + 5x - 4$ by $D(x) = x + 3$ using synthetic or long division, and express $P(x)$ in the form $$P(x) = D(x) \cdot Q(x) +

1. **Problem statement:** Prove that if the sum of two integers $a + b$ is even, then at least one of the summands $a$ or $b$ is even. 2. **Recall definitions:**

1. **State the problem:** We need to prove two statements:

1. **State the problem:** Simplify the expression $$(4x^2 + x + 3)(x + 2)$$ and find the coefficients of the resulting cubic polynomial in the form $$ax^3 + bx^2 + cx + d$$. 2. **F

1. **State the problem:** We need to find the value of $b - a$ for an integer point $(a,b)$ with $a > 9$ that satisfies the system of inequalities: $$x + y < 50$$

1. **State the problem:** We have two perpendicular lines T and K intersecting at point (3,2). Line T passes through (3,2) and (2,5). We need to find which of the given points lies

1. **State the problem:** Simplify and solve the equation $$\frac{2p}{5} + \frac{5}{p} = 3$$. 2. **Identify the formula and rules:** To solve this, we need to combine the fractions

1. **State the problem:** Simplify the expression $$\frac{2p}{5} + \frac{5}{p}$$. 2. **Find a common denominator:** The denominators are 5 and $p$. The least common denominator (LC

1. **State the problem:** An electronic weighing scale balances two batteries and one casing with eight screens. Also, one battery balances one casing and one screen. We need to fi

1. **State the problem:** We need to find the solution for each linear equation and match it to one of the numbers: -3, -2, 3, or 7. 2. **Equation 1:** $$\frac{1}{4} x + \frac{5}{3

1. **Problem:** Evaluate $4 + 5^2 \times 7$ using order of operations. 2. **Recall order of operations:** Parentheses, Exponents, Multiplication/Division (left to right), Addition/