Polynomial Operations

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, along with 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.

To add polynomials, combine like terms. 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 + 2x) - (x^2 + 4) = (3x^2 - x^2) + 2x - 4 = 2x^2 + 2x - 4.

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 $$-2x^2 + 11x - 4$$ .

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

The expression simplifies to $$5p + 4$$ .

The quotient is $$4n^2$$ .

The perimeter P is given by P = 2(length + width) = 2(5x + 1) = 10x + 2.