Adding and Subtracting Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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 distributing the negative sign 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.

Front

How do you simplify the expression 7v + 2 - 12 - 2v?

Back

Combine like terms: 7v - 2v + 2 - 12 = 5v - 10.

Front

What is the result of (3a^2 + 1) - (4 + 2a^2)?

Back

Combine like terms: 3a^2 - 2a^2 + 1 - 4 = a^2 - 3.

Front

How do you find the perimeter of a rectangle with polynomial expressions?

Back

The perimeter P of a rectangle is given by P = 2(length + width). If length and width are polynomials, add them and multiply by 2.

Front

What is the perimeter of a rectangle if length = x^2 + 8x - 5 and width = x + 5?

Back

P = 2((x^2 + 8x - 5) + (x + 5)) = 2(x^2 + 9x) = 2x^2 + 18x.

Front

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

Back

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.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.