Classifying, Adding and Subtracting Polynomials 5.2.1

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, $$2x^2 + 3x - 5$$ is a polynomial.

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial $$x^4 + 9x^3 - 2x - 7$$ , the degree is 4.

To add polynomials, combine like terms. For example, $$(2x + 3) + (4x + 5) = (2x + 4x) + (3 + 5) = 6x + 8$$ .

To subtract polynomials, distribute the negative sign and then combine like terms. For example, $$(5x^2 + 3) - (2x^2 + 1) = (5x^2 - 2x^2) + (3 - 1) = 3x^2 + 2$$ .

Like terms are terms that have the same variable raised to the same power. For example, $$3x^2$$ and $$5x^2$$ are like terms, while $$3x^2$$ and $$4x$$ are not.

The result is $$-8n^2-8n+3$$ .

The result is $$a^2+8a+7$$ .

The result is $$11rt-7rw-6tw$$ .

The result is $$9xy+4x+3y$$ .

A coefficient is a numerical factor in a term of a polynomial. For example, in the term $$7x^3$$ , 7 is the coefficient.