🧮 algebra

1. **State the problem:** Factor the expression $$16y^2z^2 - 16y^2z - 12y^2$$ completely. 2. **Identify common factors:** Notice that each term contains a factor of $$4y^2$$.

1. **State the problem:** We are given two functions $f(x)$ and $h(x)$ with their values at $x = -2, -1, 0, 1, 2$. We want to express $h(x)$ as a transformation of $f(x)$. 2. **Lis

1. The problem asks to find the degree of a monomial. 2. The degree of a monomial is the sum of the exponents of all variables in the monomial.

1. **Problemstellung:** Gegeben ist die Exponentialfunktion $f$ mit $f(x) = 4^x$. **a)** Welcher Punkt liegt auf dem Graphen von $f$?

1. **State the problem:** We are given two angles expressed as $4(x + 1)^0$ and $(7x + 3)^0$ and asked to find the value of $x$. 2. **Interpret the notation:** The notation $( ext{

1. **State the problem:** Evaluate the expression $$-12 - (14 + -15 \div 15) \times -9$$. 2. **Recall order of operations:** Parentheses first, then division and multiplication fro

1. **State the problem:** Find the roots and vertex of the quadratic function $$y = x^2 + 14x - 72$$. 2. **Formula for roots:** Use the quadratic formula $$x = \frac{-b \pm \sqrt{b

1. **Problem Statement:** Simplify the expression by combining like terms and using the distributive property. 2. **Key Concepts:**

1. **State the problem:** Find the roots and the vertex of the quadratic function $$y = x^2 - 8x - 48$$. 2. **Formula for roots:** The roots are the solutions to $$y=0$$, so solve

1. Let's start with basic arithmetic operations involving positive and negative numbers. For example, consider the expression $-3 + 7 - 2$. 2. We perform the operations from left t

1. The problem asks for the domain of a function represented by a line segment on the x-axis. 2. The graph shows a line segment starting at $x = -3$ with an open circle, meaning $-

1. The provided text is a comprehensive Danish math workbook covering algebraic reduction, equations, and word problems. 2. It starts with basic arithmetic operations involving pos

1. **State the problem:** We are given the quadratic function $$y = x^2 - 8x - 48$$ and want to analyze its graph. 2. **Formula and rules:** A quadratic function is generally writt

1. **Problem statement:** Josh starts with a whole number (not 8 or 11) and counts by a whole number (not 5). Some of his numbers are 11, 32, and 46, but 24 is not one of his numbe

1. The problem is to find the domain of the function represented by the blue line segment on the coordinate plane. 2. The graph shows a line segment starting at the point $(-4,-4)$

1. **State the problem:** Find the roots and vertex of the quadratic equation $$y = x^2 + 10x - 11$$. 2. **Formula for roots:** The roots of a quadratic equation $$ax^2 + bx + c =

1. **State the problem:** Find the roots and vertex of the quadratic function $$y = -x^2 + 12x - 11$$. 2. **Formula for roots:** The roots of a quadratic $$ax^2 + bx + c = 0$$ are

1. **Problem:** Determine if $f(a) = (2a^2 + 3a + 1)^2$ is equivalent to $g(a) = 4(a^4 + 1.5a^3 + 3a^2 + 2a + 0.25)$. Justify your answer using algebra. 2. **Formula and rules:** T

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **State the problem:** Find the roots and vertex of the quadratic function $$y = -x^2 - 16x + 36$$. 2. **Formula for roots:** Use the quadratic formula $$x = \frac{-b \pm \sqrt{

1. **Problem statement:** We will learn about "Reduktion og ligninger" which means "Reduction and equations" in Danish. This involves simplifying equations and solving for unknown