Polynomials(Adding, subtracting, and multiplying)

Front

Define a polynomial.

Back

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.

Front

What is the degree of a polynomial?

Back

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

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, while 3x^2 and 4x are not.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5x) = (2x^2 + 4x^2) + (3x + 5x) = 6x^2 + 8x.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (5x^2 + 3x) - (2x^2 + 4x) = (5x^2 - 2x^2) + (3x - 4x) = 3x^2 - x.

Front

What is the product of two polynomials?

Back

The product of two polynomials is found by using the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

Front

Simplify: 5(3x + 2)

Back

15x + 10.

Front

Find the sum: (2x^2 + 5x - 7) + (3 - 4x^2 + 6x)

Back

-2x^2 + 11x - 4.

Front

Find the area of a rectangle with length (x - 5) and width (3x + 1).

Back

3x^2 - 14x - 5.

Front

Combine Like Terms: 4y + 3x^3 + 2y + 8x^3 - 6y

Back

11x^3.