Adding and Subtracting Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 3x^2 + 2x - 5 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves changing the signs of the terms in the polynomial being subtracted and then combining like terms.

Front

What are like terms?

Back

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

Front

How do you combine like terms?

Back

To combine like terms, add or subtract their coefficients while keeping the variable part the same. For example, 3x + 2x = 5x.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in 4x^3 + 2x^2 - x, the degree is 3.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 5x^4 + 3x^2, the leading coefficient is 5.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 2x^3 + 3x^2 - x + 5.

Front

How do you simplify (4a + 6ab - b) + (-2a - ab + 3b)?

Back

Combine like terms: (4a - 2a) + (6ab - ab) + (-b + 3b) = 2a + 5ab + 2b.

Front

How do you simplify (5x^4 - 4x^3 - 2x^2 + x - 19) - (x^4 + 5x^3 + 8x^2 + x + 5)?

Back

Distribute the negative sign and combine like terms: (5x^4 - x^4) + (-4x^3 - 5x^3) + (-2x^2 - 8x^2) + (x - x) + (-19 - 5) = 4x^4 - 9x^3 - 10x^2 - 24.