🧮 algebra

1. **Problem:** Identify which statement about the polynomial function $f(x) = -2x + \sqrt{3} x^2 - \frac{1}{2} x^4$ is not correct. 2. **Formula and rules:**

1. **State the problem:** Evaluate the expression $$\frac{(438)^3 \times \sqrt{0.056}}{(388)^4}$$ using logarithms. 2. **Recall the logarithm properties:**

1. **State the problem:** Simplify the expression $$\sqrt{9x^{8}y^{-4}} \times \sqrt[3]{8x^{6}y^{-3}}$$. 2. **Recall the formulas:**

1. **State the problem:** Find the equation of the perpendicular bisector of the line segment joining points $A(0,6)$ and $B(2,-2)$.\n\n2. **Find the midpoint of segment AB:** The

1. **Problem:** Solve the equation $$\sqrt[4]{0.04^x} = 125^{x-2}$$. 2. **Formula and rules:**

1. **State the problem:** Find the value of $x$ such that $\log_2 \left(\frac{1}{128}\right) = x$. 2. **Recall the logarithm definition:** $\log_b a = c$ means $b^c = a$.

1. **State the problem:** Simplify the expression $x^2 + 5x + 2x$. 2. **Identify like terms:** The terms $5x$ and $2x$ are like terms because they both contain $x$ to the first pow

1. Задача: Решить уравнение $$\sqrt[4]{0,04^x} = 125^{x-2}$$. 2. Формулы и правила:

1. The problem is to find the value of the square root of 3. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. The problem is to find a simple formula for expanding a bracket multiplied by 3. 2. When you have an expression like $3(a + b)$, the distributive property of multiplication over

1. **Problem statement:** Find the remainder when dividing the polynomial $4x^3 + 6x^2 + 3x + 4$ by $2x^2 + 1$. 2. **Formula and rules:** When dividing a polynomial $P(x)$ by a pol

1. **Nêu bài toán:** Tìm số các số tự nhiên $n$ sao cho biểu thức $$\frac{4x^5 y^2 - 3x^3 y + x^2 y}{3x^n y}$$ chia hết, tức là kết quả là một đa thức không có mẫu số. 2. **Phân tí

1. Bài toán yêu cầu tìm giá trị của $x$ sao cho phương trình $$x^3 - x^2 + \frac{1}{3}x - \frac{1}{27} = 0$$ được thỏa mãn. 2. Ta nhận thấy đây là phương trình bậc ba, có thể thử n

1. **State the problem:** Simplify the expression $$\frac{x^2}{x-3} - \frac{9}{x-3}$$. 2. **Identify the common denominator:** Both terms have the same denominator $x-3$, so we can

1. **State the problem:** Solve the linear equation $-3.25x + 6.31 = 10.52 + 5.42x$ for $x$. 2. **Formula and rules:** To solve for $x$, we want to isolate $x$ on one side of the e

1. Bài toán yêu cầu điền số thích hợp vào ô trống trong biểu thức \(x^3 + 27y^3 = (x + 3y)(x^2 - \square xy + 9y^2)\). 2. Đây là công thức phân tích tổng lập phương: \(a^3 + b^3 =

1. Bài toán yêu cầu tìm hệ số tự do trong khai triển của biểu thức $ (1 - 2x)^3 $. 2. Công thức khai triển nhị thức Newton cho $(a + b)^n$ là:

1. **State the problem:** Solve the equation $-(4-2X) = -(5X-3)$ for $X$. 2. **Apply the distributive property:** Remove the negative signs by distributing $-1$ inside the parenthe

1. **State the problem:** Find the fourth term in the expansion of $\left(2x - \frac{1}{x}\right)^{10}$.\n\n2. **Formula used:** The binomial expansion of $(a + b)^n$ is given by $

1. The problem is to understand how $\frac{1}{2} - \frac{1}{16}$ becomes $\frac{8}{16} - \frac{1}{16}$. 2. To subtract fractions, they must have the same denominator (bottom number

1. The problem is to understand how $\frac{1}{2} - \frac{1}{16}$ becomes $\frac{8}{16} - \frac{1}{16}$. 2. To subtract fractions, they must have the same denominator (bottom number