🧮 algebra

1. **Problem statement:** Given the function $f(x) = 4x3^x$, find the value of $f(3)$. 2. **Formula and rules:** To find $f(3)$, substitute $x=3$ into the function.

1. The problem asks to find the value of #2, which is ambiguous but often interpreted as the number 2 itself or the second element in a sequence. 2. If the problem means to find th

1. **Planteamiento del problema:** Dividir el polinomio $$x^6 - 3x^4 + 2x^5 + 6x - 8$$ entre el binomio $$x - 3$$. 2. **Ordenar el polinomio dividendo:** Para facilitar la división

1. نبدأ بتحديد نوع الدالة الأسية بناءً على قاعدة الأساس في الدالة. 2. الدالة الأسية تأخذ الشكل العام $$y = a \times b^x$$ حيث:

1. **State the problem:** Solve the equation $$(x - 3)^2 = 24$$ for $x$. 2. **Recall the formula:** To solve an equation of the form $$(x - a)^2 = b$$, take the square root of both

1. **State the problem:** Solve the equation $$(x - 1)^2 = 3$$ for $x$. 2. **Recall the formula:** To solve equations of the form $$(x - a)^2 = b$$, take the square root of both si

1. **State the problem:** Solve the inequality $$\frac{x - 1}{3} > 3x - \frac{4}{3}$$. 2. **Write the inequality clearly:**

1. **Problem statement:** Factor the quadratic expressions given in part 21, starting with (a) 4y^2 - 20y - 56. 2. **Formula and rules:** To factor a quadratic expression of the fo

1. **Problem:** Simplify the expression $$(5x - 2)(x + 4) - (2x + 1)(5x - 3) + 5x^2.$$ 2. **Formula and rules:** Use distributive property (FOIL) to expand each product, then combi

1. The problem is to rationalize the expression, which means to eliminate any radicals from the denominator of a fraction. 2. The general formula for rationalizing a denominator wi

1. Problem: For the function $f(x) = -2x^3$, analyze the behavior as $x \to -\infty$. The leading term dominates the behavior of the polynomial for large $|x|$. Since the leading t

1. **State the problem:** Simplify the expression $$\frac{12}{2 - \sqrt{3}}$$. 2. **Formula and rule:** To simplify expressions with radicals in the denominator, multiply numerator

1. **State the problem:** Multiply the polynomials $ (x + 6)(x - 2) $ and simplify the result. 2. **Formula used:** To multiply two binomials, use the distributive property (also k

1. **State the problem:** Multiply the polynomials $ (v - 5)(v + 4) $ and simplify the result. 2. **Recall the formula:** To multiply two binomials, use the distributive property (

1. **State the problem:** Simplify each expression involving squares and square roots. 2. **Recall the rule:** For any positive number $a$, $(\sqrt{a})^2 = a$ because squaring and

1. **State the problem:** Simplify the fraction $\frac{602}{20}$. 2. **Formula and rules:** To simplify a fraction, divide the numerator and denominator by their greatest common di

1. **State the problem:** We analyze the rational function $$f(x) = \frac{3x^2 - 13x - 10}{x^2 - 2x - 15}$$ to find points of discontinuity, vertical and horizontal asymptotes, and

1. **State the problem:** Solve for $x$ in the equation $$\frac{6}{x+2} = \frac{1}{4} + \frac{x-7}{x+2}.$$

1. **State the problem:** We are given the area of a playground as 504 square yards. The length is expressed as $x + 8$ and the width as $x - 2$. We need to find the values of leng

1. **State the problem:** We need to find the polynomial that represents the area of a rectangle whose length is 5 inches longer than its width. 2. **Define variables:** Let the wi

1. The problem is to understand the decimal 0.90 and its equivalent fraction form. 2. We know that decimals can be converted to fractions by considering the place value. Here, 0.90