Classifying Polynomials Flashcard

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, $$2x^2 + 3x + 1$$ is a polynomial.

A linear polynomial is a polynomial of degree 1, which can be expressed in the form $$ax + b$$ , where $$a$$ and $$b$$ are constants and @@a eq 0 $$. Example:$$ -4x + 2@@.

A quadratic polynomial is a polynomial of degree 2, which can be expressed in the form $$ax^2 + bx + c$$ , where @@a eq 0 $$. Example:$$ x^2 - 6x + 9@@.

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in $$4x^3 - 5x^2 + 7$$ , the degree is 3.

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. For example, in $$-3x^2 + 6x - 9$$ , the leading coefficient is $$-3$$ .

Polynomials can be classified as follows: 0 degree - constant, 1 degree - linear, 2 degree - quadratic, 3 degree - cubic, and so on.

A constant polynomial is a polynomial of degree 0, which has no variable term. For example, $$5$$ is a constant polynomial.

A cubic polynomial is a polynomial of degree 3, which can be expressed in the form $$ax^3 + bx^2 + cx + d$$ , where @@a eq 0 $$. Example:$$ x^3 - 2x^2 + 3x - 1@@.

The polynomial $$3x^2 - 4x + 1$$ has 3 terms.

A monomial has 1 term (e.g., $$3x$$ ), a binomial has 2 terms (e.g., $$x + 2$$ ), and a trinomial has 3 terms (e.g., $$x^2 - 4x + 1$$ ).