Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

The problem gives the general term of a sequence $a_n = \frac{1}{n(n+1)}$, and asks us to find the s...

Sequences and SeriesPartial FractionsTelescoping Sum

The problem presents the graph of the function $y = (x-2)^3$. The task is to analyze the function an...

Cubic FunctionsGraphingInterceptsFunction Analysis

We are given a geometric sequence $\{a_n\}$ with $a_1 = 4$ and $a_2 = 20$. We need to find the sum o...

Sequences and SeriesGeometric SequenceSum of Geometric Series

Given that $a$ is a real number and $a, 2a, 8$ form a geometric sequence, find the value of $a$.

Geometric SequencesSequences and SeriesAlgebraic Equations

We are given a sequence $a_n = 2n + 3$. We are also given that $a_n = 17$. We need to find the value...

SequencesLinear EquationsSolving Equations

Find the x-intercept of the line passing through the points A(-1, -2) and B(1, -1).

Linear Equationsx-interceptSlopeCoordinate Geometry

Find the $x$ and $y$ intercepts of the line $2x + \sqrt{3}y + 1 = 0$.

Linear EquationsInterceptsCoordinate Geometry

The problem states that $k<0$ and $b>0$. We are asked to determine which quadrant the line $y = kx +...

Linear EquationsCoordinate GeometryInequalitiesSlopeY-interceptQuadrants

The problem states that a line $l$ passes through the points $(2, -1)$ and $(-1, m)$. The slope of t...

Linear EquationsSlopeCoordinate Geometry

The problem is to factor the polynomial $x^3 - 7xy^2 - 6y^3$.

Polynomial FactorizationFactoringCubic Polynomials

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