🧮 algebra

1. The problem is to solve the cubic equation $$4x^{3}+3x^{2}+2x=12$$ or equivalently $$4x^{3}+3x^{2}+2x-12=0$$. 2. The solution correctly identifies this as a cubic equation and a

1. **State the problem:** Solve the system of linear equations using matrix inverse or Cramer's rule. Given:

1. The problem is incomplete as only "A=" is given without any expression or value. 2. To solve or simplify an algebraic expression, we need the full expression or equation.

1. The problem is to understand or find the value of the variable $A$. 2. Since the user only provided "A=", it appears incomplete and lacks context or an equation.

1. **Problem Statement:** We have a rectangle with length $6x - 1$ and breadth $x - 2$. Both length and breadth are increased by 4 meters, and the new area is three times the origi

1. **State the problem:** Solve the cubic equation $$4x^{3} + 3x^{2} + 2x = 12.$$ 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. The problem is to simplify the expression $2 \log_5 0.5 - \log_5 0.25$. 2. Recall the logarithm rules:

1. The problem involves verifying the algebraic identity and performing arithmetic and algebraic simplifications. 2. First, recall the difference of squares formula: $$(a+b)(a-b) =

1. Problem: Simplify and evaluate the given algebraic expressions and products. 2. Use the difference of squares formula for expressions like $(a+b)(a-b) = a^2 - b^2$.

1. The problem is to analyze the equation $y = -4$. 2. This is a horizontal line where the value of $y$ is always $-4$ regardless of $x$.

1. **State the problem:** Solve the equation $$(x + 4)\sqrt{2x} - 4 = (x + 4)(x - 1)$$ for $x$. 2. **Rewrite the equation:** The equation is $$(x + 4)\sqrt{2x} - 4 = (x + 4)(x - 1)

1. Let's solve each quadratic equation step-by-step. 2. For equation a) $(x - 4) = 0$:

1. **State the problem:** Show that $(x + 4)$ is a factor of the polynomial $5x^3 - 73x + 28$. 2. **Recall the Factor Theorem:** A polynomial $f(x)$ has a factor $(x - a)$ if and o

1. **Problem Statement:** Factorize the given polynomials. 2. **Formula and Rules:**

1. **Problem statement:** (a)(i) The first term $a_1$ of an arithmetic progression (AP) is 3 and the sum of its 8 terms $S_8$ is 164. Find the common difference $d$.

1. Solve $x^3 = 8$. The cube root formula is $x = \sqrt[3]{a}$ where $a$ is the number on the right side.

1. **Problem statement:** (a) Find $r^n$.

1. We are asked to rewrite each expression without brackets or negative exponents. 2. Recall the rules:

1. The problem is unclear as no table or data is provided to identify what is missing. 2. To assist effectively, please provide the table or specify the data or values you want to

1. **State the problem:** Simplify each expression of the form $\left(\frac{a}{b}\right)^{-n}$ or mixed fraction raised to a negative power, giving answers in simplest rational for

1. Problem: Misha and Masha eat together at a restaurant. The total cost including tax is 132000. The tax is 18000, and they split the food cost equally. Find how much each pays. S