Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

The problem is to divide the polynomial $-21a^2b^3 + 21ab^3 - 7ab^2$ by the monomial $7ab^2$. We nee...

Polynomial DivisionSimplificationMonomial Division
2025/3/22

The problem asks us to divide the polynomial $9b^4 - 12b^3 - b^2$ by the monomial $3b^2$.

Polynomial DivisionMonomial DivisionAlgebraic Manipulation
2025/3/22

We are given the profit function $P(q) = 1200 - 10q - q^2$, where $q$ is the quantity of units produ...

Quadratic EquationsProfit FunctionFactoringProblem SolvingOptimization
2025/3/22

The problem asks us to divide the polynomial $24x^4 - 8x^3 + 48x^2$ by the monomial $-8x$.

Polynomial DivisionMonomialAlgebraic Manipulation
2025/3/22

The problem asks us to divide the polynomial $20x^2 - 16x - 24$ by $4$. We need to simplify the expr...

PolynomialsDivisionSimplification
2025/3/22

The problem asks for the slope of the line that is perpendicular to the line $3x + 12y = 6$.

Linear EquationsSlopePerpendicular LinesSlope-intercept form
2025/3/22

The problem asks us to find the slope of the line passing through the points (3,4) and (4,2).

Linear EquationsSlopeCoordinate Geometry
2025/3/22

The problem provides two functions, $f(x) = \sqrt{x-2}$ and $g(x) = x^2 - 1$. The goal is to find th...

Function CompositionFunctionsAlgebraic Manipulation
2025/3/22

The problem requires us to simplify the expression $(a-5)(4+a)(3-2a)$ by first multiplying two of th...

PolynomialsExpansionSimplification
2025/3/22

We need to find the equation of a line that passes through the point $(4, 5)$ and is parallel to the...

Linear EquationsSlopeParallel LinesPoint-Slope Form
2025/3/22