🧮 algebra

1. **Problem statement:** Find the zeros (Nullstellen) of the function given in factor form: $$f(x) = x(x-2)(x+3)$$ 2. **Formula and rules:** The zeros of a function in factor form

1. We are asked to graph the function $f(x) = x^4 - 3x^2 + 2$. 2. The function is a polynomial, so it is continuous and smooth everywhere.

1. Let's start by stating the problem: You want to understand how to apply the difference of squares to simplify a denominator. 2. The difference of squares formula is: $$a^2 - b^2

1. The problem is to understand how to perform the third difference of squares. 2. The difference of squares formula is $a^2 - b^2 = (a-b)(a+b)$.

1. Let's start by stating the problem: You want to understand how to factor expressions using the difference of squares method. 2. The difference of squares formula is:

1. **State the problem:** Simplify the expression $$6^3 \times \frac{1}{9^2}$$. 2. **Recall the formulas and rules:**

1. **State the problem:** Simplify the rational expression $$\frac{4r^2 + 24r + 32}{16r^2 - 16r - 96}$$. 2. **Factor numerator and denominator:**

1. **State the problem:** Factor the expressions $t^2 - 49$ and $t^2 - 14t + 49$. 2. **Recall formulas:**

1. State the problem. Problem: Rewrite the quadratic equation $$x^2 - 6 = 11x$$ in standard form and identify $a$, $b$, and $c$.

1. We are asked to find the value of $y$ in the equation $$-\frac{3}{7} y = \frac{2}{3}.$$ 2. To isolate $y$, we need to divide both sides of the equation by $-\frac{3}{7}$. The fo

1. **State the problem:** Solve for $t$ in the equation $5 = \frac{10.3}{1 + 12.8 e^{-0.036t}}$. 2. **Rewrite the equation:** Multiply both sides by the denominator to eliminate th

1. **State the problem:** Factor the polynomial expression $4x^3 - 20x^2$ completely. 2. **Identify the greatest common factor (GCF):** Both terms have a factor of $4x^2$.

1. **State the problem:** Solve for $x$ in the equation $100 = 85 \times 1.005^x$. 2. **Write the formula and explain:** We want to isolate $x$. The equation involves an exponentia

1. **Problem statement:** Given points $P(6|6)$ and $Q(8|3)$ on a parabola $p$ with equation $y = -0.25x^2 + bx + c$, find $b$ and $c$.

1. **Problem statement:** Given a parabola $p$ passing through points $P(6|6)$ and $Q(8|3)$ with equation form $y = -0.25x^2 + bx + c$, find $b$ and $c$.

1. El problema es dividir el polinomio $2x^2 + 3x$ entre el binomio $2x + 3$. 2. La división de polinomios se realiza como la división larga: dividimos el término de mayor grado de

1. The problem is to factor the polynomial expression $2x^3 - 6x$ by factoring out the common factor. 2. The formula used is factoring out the greatest common factor (GCF): $$a b +

1. **State the problem:** We need to find the equation of line K in the form $y = mx + c$. 2. **Identify points on the line:** From the graph description, line K passes through poi

1. **State the problem:** We are given the linear function $$y = -2x - 1$$ and a table with some known and unknown values: $$\begin{array}{c|ccccc}

1. Il problema è analizzare la funzione razionale $$y = \frac{x^2 + 1}{2x + 1}$$ e determinarne il dominio, i segni e i punti notevoli. 2. Il dominio è dato da tutti i valori di $x

1. Il problema chiede di trovare le intersezioni della funzione razionale fratta $$y=\frac{x^2+1}{2x+1}$$ con gli assi cartesiani. 2. Intersezione con l'asse y: si trova ponendo $$