🧮 algebra

1. **State the problem:** Add the polynomials \( (3x^3 + 3x^2 - 4x + 5) + (x^3 - 2x^2 + x - 4) \). 2. **Write down the polynomials:**

1. The problem is to understand the letter 'a' as a mathematical symbol or variable. 2. In algebra, 'a' is commonly used to represent a variable or a constant.

1. **State the problem:** Simplify the algebraic fraction $$\frac{6x + 8}{2}$$. 2. **Formula and rules:** To simplify a fraction, factor the numerator and denominator and cancel co

1. **Problem Statement:** Determine whether the related functions formed from polynomials $P(x)$ and $Q(x)$ (neither constant) are polynomial functions, choosing from Always, Somet

1. **State the problem:** Solve the quadratic equation $$x^2 + 14x - 15 = 0$$. 2. **Formula and rules:** To solve a quadratic equation of the form $$ax^2 + bx + c = 0$$, we can use

1. **State the problem:** Samantha withdrew 160 from her bank account, and the new balance is 379.52. We need to find the balance before the withdrawal. 2. **Formula and explanatio

1. The problem is to understand the function where for every input $x$, the output $y$ is the original input plus 2. 2. The formula for this function is $y = x + 2$.

1. **State the problem:** We are given two functions $f(x) = \frac{3 + x}{7}$ and $h(x) = 2x + 3$. We need to find: (a) $h(4)$

1. **State the problem:** Evaluate the expression $$(-9) - (-8) + 3 \times 4^2$$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division

1. **State the problem:** Given that $q$ varies inversely as the square of $p$, and the table: | p | 2 | 10 | 18 |

1. **State the problem:** Evaluate the expression $$8 \div (-4) \times (-6)^2 + 7$$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Divis

1. **State the problem:** Evaluate the expression $10 \times 3 - (-6)^2 + (-8)$.\n\n2. **Recall order of operations:** We follow PEMDAS (Parentheses, Exponents, Multiplication and

1. **State the problem:** Solve for $X$ in the equation $X = X$. 2. **Understand the equation:** The equation $X = X$ means that the variable $X$ is equal to itself.

1. **State the problem:** Solve the equation $-18 = 2a - 2|1 - 3a|$ for $a$. 2. **Understand the absolute value:** The absolute value expression $|1 - 3a|$ splits the problem into

1. **State the problem:** Calculate the value of the expression $(-5)^2 - 2 \times (-9) + 6$. 2. **Recall the order of operations:** We follow PEMDAS (Parentheses, Exponents, Multi

1. The problem is to solve number 8. Since the user did not provide the exact problem statement, I will assume a common algebra problem labeled as number 8. 2. Let's consider a typ

1. **Problem:** Solve the equation $y + 7 = 12$ for $y$. 2. **Formula and rules:** To solve for $y$, isolate the variable by performing inverse operations. Here, subtract 7 from bo

1. **State the problem:** Simplify the expression $-4[8 \div 4 + 3(3 - 6)^2]$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division fr

1. **State the problem:** Simplify the expression $3[(3 - 6)^3 + 5 \cdot 2]$. 2. **Apply the order of operations:** First, solve inside the parentheses.

1. **Problem statement:** Solve the equation $$\sqrt[5]{(3x^2 + 3x - 1)^3} = \sqrt[5]{x^3}$$ and choose all valid solutions. 2. **Step 1: Understand the equation**

1. **State the problem:** Simplify the expression $72-(8\times7+3)-5$. 2. **Recall order of operations:** We first do multiplication, then addition/subtraction from left to right.