Polynomial Operations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents of variables. 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 -9x are like terms.

Front

How do you combine like terms?

Back

To combine like terms, add or subtract the coefficients of the terms that have the same variable and exponent. For example, 5a + 2a = 7a.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c). It is faster than long division and uses only the coefficients of the 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 4x^3 + 2x^2 - x, the degree is 3.

Front

What is the leading coefficient?

Back

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

Front

What is the result of (3x^3 + 5x - 1) ÷ (x + 1)?

Back

The result is 3x^2 - 3x + 8 - 9/(x + 1).

Front

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

Back

Combine like terms to get 9v + 14.

Front

What is the process of polynomial long division?

Back

Polynomial long division involves dividing the leading term of the dividend by the leading term of the divisor, multiplying the entire divisor by the result, and subtracting from the dividend, repeating until the degree of the remainder is less than the degree of the divisor.

Front

What are the steps to perform synthetic division?

Back

1. Write the coefficients of the polynomial. 2. Write the zero of the divisor (x - c). 3. Bring down the leading coefficient. 4. Multiply and add down the column.