Adding and Subtracting Polynomials HW

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, $$4x^2 - x + 14$$ is a polynomial.

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial $$4x^2 - x + 14$$ , the degree is 2.

To add polynomials, combine like terms by adding their coefficients. For example, $$(2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5$$ .

To subtract polynomials, distribute the negative sign and then combine like terms. For example, $$(3x^2 + 4) - (2x^2 + 1) = (3x^2 - 2x^2) + (4 - 1) = x^2 + 3$$ .

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 $$4x^3 + 2x + 4$$ .

The result is $$3x^2 + 4x - 6$$ .

The coefficients are 7, 4, -5, and 2, corresponding to the terms $$7x^3$$ , $$4x^2$$ , $$-5x$$ , and $$2$$ respectively.

The constant term is 5, which is the term without a variable.

You simplify it by combining like terms: $$(2x + 4x) + (3 - 5) = 6x - 2$$ .