Polynomial Division

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial, similar to long division with numbers.

Front

What is the result of dividing (2x^3 + 7x^2 - 6x - 8) by (x + 4)?

Back

The result is 2x^2 - x - 2.

Front

How do you perform polynomial long division?

Back

1. Divide the leading term of the dividend by the leading term of the divisor. 2. Multiply the entire divisor by the result and subtract from the dividend. 3. Repeat the process with the new polynomial until the degree of the remainder is less than the degree of the divisor.

Front

What is the quotient in polynomial division?

Back

The quotient is the result obtained from dividing one polynomial by another.

Front

What is the remainder in polynomial division?

Back

The remainder is what is left over after dividing one polynomial by another, when the degree of the remainder is less than the degree of the divisor.

Front

What is the end behavior of a polynomial function?

Back

The end behavior describes how the values of the function behave as x approaches positive or negative infinity.

Front

What does it mean for a polynomial to have a degree of at least 5?

Back

It means that the highest power of the variable in the polynomial is 5 or greater, which affects the shape and behavior of its graph.

Front

How do you determine the degree of a polynomial?

Back

The degree of a polynomial is determined by the highest exponent of the variable in the polynomial.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor and is generally faster than long division.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree and it affects the end behavior and the shape of the graph of the polynomial.