Polynomial Operations

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

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 sum is $$x^2 + x + 1$$ .

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

The result is $$b^3 + 5b^2 + 7b + 3$$ .

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

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

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

Combining like terms involves adding or subtracting the coefficients of like terms to simplify a polynomial expression.

A monomial is a polynomial with only one term, while a polynomial can have multiple terms.