🧮 algebra

1. **Problem 1:** Find the remainder when $P(x) = 4x^3 - 4x + 1$ is divided by $2x - 3$. 2. Use the Remainder Theorem: The remainder when a polynomial $P(x)$ is divided by a linear

1. The statement "All quartic polynomial equations have at least one real solution" is false. Explanation: Quartic polynomials are degree 4 polynomials. According to the Fundamenta

1. The problem asks: "All quartic polynomial equations have at least one real solution. True or False?" 2. A quartic polynomial is a polynomial of degree 4, generally written as $$

1. **State the problem:** Find the remainder when the polynomial $$x^4 + 2x^2 - 3x + 7$$ is divided by $$x + 2$$. 2. **Formula used:** According to the Remainder Theorem, the remai

1. **State the problem:** Emma made a punch using 4 cups of mango juice and 12 cups of lemonade. She wants to keep the same ratio of mango juice to lemonade but only has 9 cups of

1. **State the problem:** Emma used a scale drawing with the scale 5 inches : 2 feet. The actual width of the closet is 8 feet. We need to find the width of the closet in the drawi

1. The problem is to simplify the expression involving terms with $x$. 2. The expressions given are $3(5x)$, $3x$, $3x + 5x$, and $5x$.

1. El problema nos pide hallar el costo total en dólares de $n$ cornetas y $n$ portarretratos. 2. Sabemos que cada corneta cuesta $1.50$ y cada portarretratos cuesta $3$. Si compra

1. The problem is to solve an inequality while keeping the greater than or less than symbol intact. 2. When solving inequalities, remember that multiplying or dividing both sides b

1. **State the problem:** Simplify the expression $$(8 - 2m - 3) + 6m - 14$$. 2. **Apply the distributive property and combine like terms inside the parentheses:**

1. **State the problem:** Solve the quadratic equation $x^2 + 25 = 10x + 4$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Melanie uses 5 screws per plank and buys 100 screws. We need to find how much wood she buys, then compare costs at Home Depot and Rona with discounts, and

1. **State the problem:** Evaluate the expression $3 + a^2$ when $a = 5$. 2. **Recall the order of operations (PEMDAS):** Parentheses, Exponents, Multiplication and Division (left

1. **State the problem:** Evaluate the expression $15 - z^2$ when $z = 3$. 2. **Recall the order of operations (PEMDAS):**

1. **State the problem:** Evaluate the expression $n + 15 \div 3$ when $n = 2$. 2. **Recall the order of operations (PEMDAS):** Parentheses, Exponents, Multiplication and Division

1. **State the problem:** Evaluate the expression $x^2 \cdot 3$ when $x=2$. 2. **Recall the order of operations (PEMDAS):** Parentheses, Exponents, Multiplication and Division (lef

1. **State the problem:** Evaluate the expression $y^2 - 5$ when $y = 3$. 2. **Recall the formula and order of operations:** The expression is $y^2 - 5$. According to PEMDAS (Paren

1. **State the problem:** Evaluate the expression $10 - k^2 + 2$ when $k = 3$. 2. **Substitute the value of $k$ into the expression:**

1. **State the problem:** We want to understand and simplify the formula for $H$ given by

1. The problem is to analyze the equation $x = -1$ and understand its graph. 2. This equation represents a vertical line where the $x$-coordinate is always $-1$, regardless of the

1. **State the problem:** Simplify the expression $$67 + 41 - 93047294792 + \frac{48927492472429}{4729472947} - 67$$. 2. **Identify the operations:** The expression involves additi