🧮 algebra

1. **State the problem:** Simplify or analyze the polynomial $x^3 + x^2 - 10x + 8$. 2. **Identify the goal:** We can try to factor the polynomial to find its roots or simplify it.

1. The problem is to understand why we only find factors of 8 when factoring the polynomial $x^3 + x^3 - 10x + 8$ using the Rational Root Theorem. 2. The polynomial can be simplifi

1. The problem asks if the first number in the polynomial is 5, would you have to find the factors of 5 and 8 to determine possible zeros. 2. The answer is yes. When using the Rati

1. **State the problem:** We need to find which test point among (2,1), (3,0), (1,2), and (0,0) satisfies the system of inequalities: $$\begin{cases} 10y - 5x \leq 0 \\ 4x + 2y > 1

1. The problem is to graph the function $$y = 4 + \sqrt{x}$$. 2. Important note: The square root function $$\sqrt{x}$$ is only defined for $$x \geq 0$$, so the domain of this funct

1. Let's state the problem: We want to find the factors of the polynomial $$x^3 + x^2 - 10x + 8$$. 2. The Rational Root Theorem tells us that any rational root of a polynomial with

1. The problem is to understand and analyze the function $y = 4\sqrt{x}$.\n\n2. This function represents $y$ as four times the square root of $x$. The square root function $\sqrt{x

1. **State the problem:** Factor the polynomial $$P(x) = 3x^4 + x^3 - 14x^2 - 4x + 8$$ completely. 2. **List possible rational zeros:** By the Rational Root Theorem, possible zeros

1. **State the problem:** Simplify the expression $v - \frac{v}{3}$. 2. **Write the expression with a common denominator:** To combine the terms, express $v$ as $\frac{3v}{3}$.

1. **State the problem:** Simplify the algebraic expression $$\frac{x}{4} + \frac{2y}{3} - \frac{5y}{6} + \frac{4x}{3}$$. 2. **Group like terms:** Group the terms with $x$ and the

1. **State the problem:** Simplify the expression $-4(y+1)+2$. 2. **Apply the distributive property:** Multiply $-4$ by each term inside the parentheses.

1. **State the problem:** We need to solve the system of linear equations by graphing and fill in the tables for each equation at $x=0$ and $x=5$. 2. **Equations given:**

1. The problem asks to find the slope of the line passing through the points $(0,4)$ and $(0,6)$. 2. The formula for the slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is

1. Solve $42 = 18 - 4t$. Subtract 18 from both sides:

1. **Problem 1:** Solve the equation $2 - 16 = -32 - \frac{2}{5}f$. 2. First, simplify the left side: $2 - 16 = -14$.

1. Solve $42 \div 3 = 18 - 41 \div 9$. Start by simplifying each division:

1. **State the problem:** Solve the equation $$42 = 18 - 4l$$ for $l$. 2. **Isolate the term with $l$:** Subtract 18 from both sides:

1. **State the problem:** Simplify the expression $$5 - \frac{5}{12} - \frac{5}{28} \times 0.7$$. 2. **Recall the order of operations:** Multiplication comes before subtraction.

1. **State the problem:** Evaluate the expression $5 \cdot (-3) + ((-2)^3 - 2)^2$. 2. **Recall the order of operations:** We first calculate powers, then multiplication, then addit

1. **Problem Statement:** We want to find the amount of snow on the ground over time during and after a snowstorm with different rates of snowfall and melting. 2. **Initial Conditi

1. **State the problem:** Simplify the expression $$\frac{x}{4} + \frac{2y}{3} - \frac{5y}{6} + \frac{4x}{3}$$. 2. **Find a common denominator for the terms involving $x$ and $y$ s