operations on Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. For example, 3x^2 + 2x - 5 is a polynomial.

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 and 5x are like terms, while 3x and 3x^2 are not.

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 + 5x = 8x.

Front

What is the degree of a polynomial?

Back

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

Front

What is the sum of (2x + 3) + (4x - 5)?

Back

The sum is 6x - 2.

Front

What is the difference of (5y^2 - 3y + 2) - (2y^2 + y - 4)?

Back

The difference is 3y^2 - 4y + 6.

Front

What is the product of (x + 2)(x - 3)?

Back

The product is x^2 - x - 6.

Front

What is the result of subtracting (3x^2 - 2x + 1) from (5x^2 + 4x - 3)?

Back

The result is 2x^2 + 6x - 4.

Front

What is an equivalent expression for 4x^2 + 2x - 3 + 3x^2 - x?

Back

An equivalent expression is 7x^2 + x - 3.

Front

What is the sum of (3y^2 + 2y) + (4y^2 - y)?

Back

The sum is 7y^2 + y.