Polynomial Operations and Properties

Addition, subtraction, and division

Subtraction, division, and multiplication

Addition, subtraction, and multiplication

Addition, division, and multiplication

Multiply the coefficients

Combine like terms and be cautious with signs

Always subtract the coefficients

Ignore the constant terms

-x

x

5x

-5x

Because subtraction is commutative

Because it changes the degree of the polynomial

Because it affects the signs of the terms

Because it simplifies the calculation

x^2 + 3x - 4

-x^2 + 3x + 4

x^2 - 5x + 4

-x^2 + 5x + 4

Combine like terms

Add the coefficients

Subtract the coefficients

Distribute each term of the first polynomial to each term of the second

Two

Four

Six

Eight

2x^2

x^3

2x^3

2x

To automatically match up like terms

To increase the degree of the polynomial

To make the polynomial look neater

To decrease the degree of the polynomial

It simplifies the addition of polynomials

It helps in identifying the leading coefficient

It automatically aligns like terms for easier simplification

It reduces the number of terms