Adding and Subtracting Polynomials Flashcard

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

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power. For example, $$(2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5$$ .

Subtracting polynomials involves combining like terms after changing the signs of the terms in the polynomial being subtracted. For example, $$(3x^2 + 2x) - (x^2 + x) = (3x^2 - x^2) + (2x - x) = 2x^2 + x$$ .

Like terms are terms that have the same variable raised to the same power. For example, in the polynomial $$4x^2 + 3x - 2x^2 + 5$$ , the like terms are $$4x^2$$ and $$-2x^2$$ .

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

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in $$4x^3 + 2x^2 - 5$$ , the leading coefficient is 4.

To combine like terms, add or subtract their coefficients while keeping the variable part the same. For example, $$3x + 5x = (3 + 5)x = 8x$$ .

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

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

The result is $$3x^2 - x$$ .