🧮 algebra

1. **Problem:** Factor the polynomial $6x^3 + 15x^2 + 3x$ over the integers. 2. **Step 1: Find the greatest common factor (GCF).**

1. Stating the problem: We are given two piecewise functions: $$f(x) = \begin{cases} 2x + 1, & x < 0 \\ x + 3, & x \geq 0 \end{cases}$$

1. **State the problem:** Solve the system of equations: $$\text{(1) } x + y = 4$$

1. The problem asks to convert the number 0.0000006 into standard form. 2. Standard form (also called scientific notation) expresses a number as $a \times 10^n$ where $1 \leq |a| <

1. **Problem (a):** Find the range of values of $x$ such that $$x^2 - 4x - 5 > 0$$ using the table method. 2. **Step 1:** Factorize the quadratic expression:

1. **State the problem:** We are given an equation involving terms with variable $h$: $$\frac{h}{21.0 + 1} + \frac{\frac{h}{21.0}}{21.0 + E} \times xos = gk$$

1. **Problem 1: Find the standard form of the hyperbola with center (0,0), focus at (\sqrt{74},0), and directrix x=\frac{49}{\sqrt{74}}.** 2. Since the focus is on the x-axis and t

1. **Problem 1: Find the standard form of the hyperbola with center (0,0), focus at (\sqrt{74},0), and directrix at x = \frac{49}{\sqrt{74}}.** 2. The hyperbola is horizontal becau

1. The user requests to write mathematical content, not theoretical explanations. 2. Since no specific problem or topic is given, I will provide a simple example of a mathematical

1. **State the problem:** Solve the system of equations: $$8x - y - 2x = 0$$

1. The problem asks for the equations of vertical and horizontal lines passing through the point $(-9, -6)$. 2. A vertical line has the form $x = a$, where $a$ is the x-coordinate

1. The problem asks to write equations for vertical and horizontal lines represented by symbols || and — respectively. 2. A vertical line has the form $x = a$, where $a$ is the con

1. **State the problem:** Find the equation of the line passing through the points $(-6, -2)$ and $(4, 3)$. 2. **Calculate the slope $m$:** The slope formula is $$m = \frac{y_2 - y

1. **State the problem:** We need to find the equation of a line given two points on the line: $(0,4)$ and $(-3,7)$. The line crosses the y-axis at $y=4$ and has a negative slope.

1. **State the problem:** We need to write the equation of a line in point-slope form that passes through the point $(-6,4)$ and has a slope of $-\frac{4}{3}$. 2. **Recall the poin

1. **State the problem:** We need to find the equation of a line in slope-intercept form $y = mx + b$ that passes through the point $(4, 8)$ and has a slope $m = \frac{5}{4}$. 2. *

1. The problem is to convert the number 0.00005401 into standard form. 2. Standard form (also called scientific notation) expresses a number as a product of a number between 1 and

1. **State the problem:** We are given three lines: Line 1: $2y = -5x + 7$

1. The problem asks for the equation of a line in slope-intercept form given the slope and y-intercept. 2. Recall the slope-intercept form of a line is $$y = mx + b$$ where $m$ is

1. **State the problem:** We are given the linear equation $$2x - 4y = 16$$ and need to find the slope and y-intercept, then use them to graph the line. 2. **Rewrite the equation i

1. **State the problem:** Find the y-intercept and slope of the line given by the equation $$9x + 3y = -3$$. 2. **Rewrite the equation in slope-intercept form** $y = mx + b$, where