MAT 171 1.3–1.5 Review: Polynomials, Absolute Value, and Equations

Vocabulary flashcards covering key terms from polynomials, exponents, factoring, absolute value, and solving linear and quadratic equations.

Polynomial

A sum of terms separated by plus or minus signs, where each term is a monomial in a variable; written in descending powers of the variable.

Coefficient

The numerical factor multiplying a variable in a term (the ai in an x^n + … + a_0).

Term

A summand in a polynomial; can be a monomial, consisting of a coefficient and a variable(s) raised to a power.

Leading coefficient

The coefficient of the highest-degree term in a polynomial.

Degree

The highest exponent of the variable in the polynomial.

Constant term

The term without any variable; the a_0 term.

Descending order

Writing terms from highest degree to lowest degree.

Leading term

The term with the highest degree in a polynomial.

Like terms

Terms that have the same variable raised to the same power; can be combined.

Monomial

A single term, such as 5x^3 or -7.

Binomial

A polynomial with exactly two terms.

Trinomial

A polynomial with exactly three terms.

Quadratic trinomial

A trinomial of the form ax^2 + bx + c, where a ≠ 0.

Factor

A number or polynomial that divides another polynomial exactly; a product in a factorization.

Greatest Common Factor (GCF)

The largest factor that divides all terms of a polynomial.

Difference of squares

A^2 − B^2 = (A − B)(A + B).

Distributive property

The rule a(b + c) = ab + ac (and a(b − c) = ab − ac).

FOIL

First-Outer-Inner-Last method for multiplying two binomials.

Zero Product Property

If AB = 0, then A = 0 or B = 0.

Absolute value

The distance of a number from zero; |x| ≥ 0.

Absolute value equation

An equation that contains an absolute value expression.

Solve by splitting absolute value

Rewrite |expression| = k as two equations: expression = k and expression = −k.

Inverse operations

Operations that undo each other (addition/subtraction; multiplication/division).

Linear equation

An equation in which the variable has degree 1; graphs as a straight line.

Quadratic equation

An equation of degree 2, of the form ax^2 + bx + c = 0 with a ≠ 0.

Factor completely

Factor until no further factoring over the integers is possible.

Factoring by grouping

A method for factoring polynomials with four terms by grouping terms to factor common factors.