Polynomial Operations

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 $$4x^3 + 2x^2 - x + 7$$ , the degree is 3.

The product of two binomials can be found using the distributive property or the FOIL method. For example, for the binomials $$(a + b)(c + d)$$ , the product is $$ac + ad + bc + bd$$ .

To multiply polynomials, use the distributive property to multiply each term in the first polynomial by each term in the second polynomial, then combine like terms.

The result is $$25n^2 - 64$$ .

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms.

The result is $$10x^2 - 6x + 8$$ .

The result is $$2x^3 + 5x^2 - x + 9$$ .

The square of a binomial $$(a + b)^2$$ is equal to $$a^2 + 2ab + b^2$$ .

The result is $$4x^2 + 12x + 9$$ .