🧮 algebra

1. **Problem 1:** Factorize the cubic polynomial $x^3 - 13x^2 + 24x + 108$ given that one factor is $(x + 2)$. We want to find the other two factors. 2. Use polynomial division or

1. **State the problem:** Simplify the complex nested fraction expression given: $$\frac{\frac{1 + \frac{1}{3}}{1 + \left(2 - \frac{1}{3}\right)}}{\frac{1 - \left(2 - \frac{1}{2}\r

1. **State the problem:** We need to rewrite the given expression in a clean, readable format. 2. **Given expression:**

Let's look at the graph edges step by step! 🎉 **Step 1:** Imagine you have 6 vertices: $v_1, v_2, v_3, v_4, v_5, v_6$.

1. **State the problem:** Solve the equation $\frac{x}{2} + 1 = 3$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by performing invers

1. **Problem Statement:** A trader mixes 26 kg of rice costing 20 per kg with 30 kg of rice costing 36 per kg. He sells the mixture at 30 per kg. We need to find his profit percent

1. **Problem statement:** For the number 252, find the smallest whole number to multiply it by to get a perfect square, then find the square root of that perfect square. 2. **Step

1. **State the problem:** Factor the expression $x^7$. 2. **Recall the rule:** Any power of a variable can be expressed as the variable multiplied by itself the given number of tim

1. **State the problem:** We need to find the cost per square foot to lease office space for January, February, and March, given the price increases each month. 2. **Given data:**

1. **Problem Statement:** A trader mixes 26 kgs of rice costing 720 per kg with 30 kgs of rice costing 36 per kg. He sells the mixture at 30 per kg. We need to find his profit perc

1. The problem is to solve the equation or expression given by the user, but since no specific problem was provided, I will demonstrate solving a simple algebraic equation as an ex

1. The problem is to identify the pattern in the sequence of alphanumeric strings and predict the next element. 2. The given sequence is: 3R7, R8M, 8N2, N3T, 7K6, 3U6, U7J, K7Y.

1. **Problem Statement:** A trader mixes 26 kgs of rice costing 20 per kg with 30 kgs of another variety costing 36 per kg. He sells the mixture at 30 per kg. We need to find his p

1. **Problem Statement:** Find the square roots of 100 and 169 using the method of repeated subtraction. 2. **Method Explanation:** The method of repeated subtraction to find the s

1. **Problem Statement:** Find the square roots of 1000 and 169 using the method of repeated subtraction. 2. **Method Explanation:** The method of repeated subtraction for square r

1. Let's start by understanding the problem: calculating percentage increase or decrease, or both in the same problem. 2. The formula for percentage increase is:

1. **State the problem:** Find the range of values of $x$ satisfying the inequality $$|x - 1| - |2x + 1| \geq -4.$$\n\n2. **Recall the definition of absolute value:** For any real

1. **State the problem:** Solve the system of inequalities: $$2 \geq 1 - 2x + 3 < 4x$$

1. **Statement of the problem:** Given a ratio of 4:7 for two quantities (Anna's and Toneli's), find the value of Anna's quantity if the total is known or if one part is given. 2.

1. **State the problem:** Simplify the expression $6x^2 - 54$. 2. **Identify the formula or rule:** We can factor out the greatest common factor (GCF) from the terms.

1. **State the problem:** Simplify the expression $25x + 3y + 7z - 10x + 5y + 2z + 18$. 2. **Identify like terms:** Like terms are terms that have the same variable raised to the s