Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We are asked to factor the polynomial $x^2 + 7x + 10$.

Polynomial FactorizationQuadratic Equations

The problem is to factor the polynomial $x^4 - 5x^2 - 50$.

Polynomial FactorizationQuadratic EquationsAlgebraic Manipulation

The problem is to factor the quadratic polynomial $x^2 - 6x + 8$. We need to find two binomials that...

Quadratic EquationsFactorizationPolynomials

We are given a system of equations involving real numbers $x$, $y$, and $z$: $x = \sqrt{y^2 - \frac{...

Systems of EquationsReal NumbersSquare Roots

The problem asks to factor the quadratic polynomial $x^2 + 6x + 5$.

Quadratic EquationsFactorizationPolynomials

We are given a system of equations: $x = \sqrt{y^2 - \frac{1}{16}} + \sqrt{z^2 - \frac{1}{16}}$ $y =...

Systems of EquationsSquare RootsAlgebraic Manipulation

We need to evaluate the expression $-x - \frac{1}{2}x + \frac{3}{2}$ when $x = -\frac{1}{4}$.

Algebraic ExpressionsSubstitutionFractionsSimplification

The problem is to decompose the rational function $\frac{4x-9}{(x-2)(x-3)}$ into partial fractions.

Partial FractionsRational FunctionsAlgebraic Manipulation

The problem asks to simplify two rational expressions. Expression (e): $\frac{2x^2 + 17x + 21}{(x+2)...

Rational ExpressionsSimplificationFactorizationPolynomials

We are asked to simplify the following two expressions: (e) $\frac{2x^2 + 17x + 21}{(x+2)(x^2-9)}$ (...

PolynomialsSimplificationRational ExpressionsFactorization

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