Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

a) Find the gradient and y-intercept of the line given by the equation $x + 2y = 14$. b) Find the eq...

Linear EquationsSlope-Intercept FormPartial FractionsCoordinate Geometry
2025/6/9

We are given a set of math problems. a) (i) Express 5630 in standard form. (ii) Express 16346000000 ...

Scientific NotationEngineering NotationPolynomialsSimplificationRemainder TheoremSimultaneous EquationsLogarithmsLinear Equations
2025/6/9

The problem provides two real numbers $a$ and $b$ such that $a = 2 + \sqrt{3}$ and $ab = -\sqrt{3}$....

Algebraic ManipulationInequalitiesRationalizationSquare Roots
2025/6/9

The problem consists of two parts. Part 1: There are three different equilateral triangles made of c...

Algebraic ExpressionsGeometric PatternsProblem Solving
2025/6/9

We are given four problems: a) i. Show that $f(x) = \sqrt{x}$ is not a function using the vertical l...

FunctionsVertical Line TestRangeLinear FunctionsInverse Functions
2025/6/9

Solve the quadratic equation $x^2 + 4x + 1 = 0$ by completing the square.

Quadratic EquationsCompleting the SquareAlgebraic Manipulation
2025/6/9

The problem asks us to resolve the rational function $\frac{4x-3}{(x+1)^2}$ into partial fractions.

Partial FractionsRational FunctionsAlgebraic Manipulation
2025/6/9

The problem asks to simplify the given expression: $\frac{x^2y^3 + xy^2}{xy}$.

SimplificationAlgebraic ExpressionsFactoringPolynomials
2025/6/9

The problem asks us to evaluate the expression $3pq^3r^3$ when $p=\frac{2}{3}$, $q=-2$, and $r=-1$.

Algebraic ExpressionsSubstitutionExponentsEvaluation
2025/6/9

The problem is to factor the given expression $9m^5n^2 + 12m^3n$.

FactoringGreatest Common FactorPolynomials
2025/6/9