🧮 algebra

1. **State the problem:** Find the domain of the function $f(x) = x^3$. 2. **Recall the definition of domain:** The domain of a function is the set of all possible input values ($x

1. **State the problem:** We are given the quadratic function $$y = -\frac{1}{16}(x-6)^2 + 7$$ and we want to analyze its properties. 2. **Formula and explanation:** This is a quad

1. **State the problem:** Solve the inequality $2x^2 - 8 \ge 0$. 2. **Rewrite the inequality:** Factor out the common factor 2:

1. **Stating the problem:** Solve the inequality $x^2 + x - 6 \ge 0$. 2. **Formula and rules:** To solve quadratic inequalities, first find the roots of the quadratic equation $x^2

1. **State the problem:** Solve the inequality $x^2 - x - 2 \ge 0$. 2. **Formula and rules:** To solve quadratic inequalities, first find the roots of the quadratic equation $x^2 -

1. **Stating the problem:** Solve each linear equation for $x$. 2. **General approach:** Use the distributive property to expand parentheses, combine like terms, and isolate $x$ on

1. **Stating the problem:** We have a polynomial $$P(x) = x^4 - 6x^3 + ax^2 + bx + c$$ with conditions:

1. The problem involves simplifying and understanding two sets of polynomials given as: Top-left set: (d) $16x + 24 + 2x^2$, (a) $35x^2 + 43x + 12$, (b) $-21x^2 + 58x - 21$, (c) $1

1. **Stating the problem:** Vi skal løse ligninger med parenteser, hvor vi enten kan ophæve plusparenteser direkte eller minusparenteser ved at ændre fortegn. 2. **Regler:**

1. We are given two sets of quadratic expressions and asked to analyze or simplify them. 2. The general form of a quadratic expression is $ax^2 + bx + c$.

1. **State the problem:** We are given the polynomial $$2x^4 - 9x^3 + 6x^2 + 11x - 6$$ and want to express it in the form $$(x - 1)(Ax^3 + Bx^2 + Cx + D)$$ to find constants $A$, $

1. **Stating the problem:** Solve the linear equations with multiple terms for $x$. 2. **Formula and rules:** To solve equations like these, combine like terms (all $x$ terms toget

1. **State the problem:** We need to divide the cubic polynomial $$2x^3 + 2$$ by the binomial $$2x + 2$$ and express the quotient in the form $$Ax^2 + Bx + C$$. 2. **Recall the div

1. **Problem Statement:** Understand and apply the Laws of Indices including fractional indices. 2. **Laws of Indices:**

1. **State the problem:** Simplify the expression $$\frac{2x^3 - 7x^2 + 9}{2x - 3}$$ into the form $$Ax^2 + Bx + C + \frac{R}{2x - 3}$$ where $A$, $B$, $C$, and $R$ are constants.

1. **State the problem:** Simplify the expression $$\sqrt{\frac{35}{20}}$$. 2. **Recall the property of square roots:** $$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$$ for posit

1. **Stating the problem:** We need to expand and simplify each of the expressions a) to f) by multiplying the parentheses and then compare the results to find which expressions ar

1. **State the problem:** We need to divide the cubic polynomial $$x^3 + 8x^2 + 19x + 12$$ by the linear polynomial $$x + 4$$ using algebraic long division to find constants $$A$$,

1. **Stating the problem:** We need to expand and simplify the products of binomials given in expressions a) through f) and then match them with the provided expressions A) through

1. **Stating the problem:** We are given two expressions: the first is a fraction $$\frac{x^2 + x - 6}{x - 3x^2 + 10}$$ and the second is an expression $$x + 3x - 2$$. We need to a

1. The problem involves understanding how to graph functions, find key features such as intercepts and extrema, and determine points of intersection between two curves or lines usi