Polynomial Division

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial of the same or lower degree, resulting in a quotient and a remainder.

Front

What are the two main methods of polynomial division?

Back

The two main methods of polynomial division are long division and synthetic division.

Front

When is synthetic division preferred over long division?

Back

Synthetic division is preferred when dividing by a linear factor of the form (x - c), as it is generally faster and simpler.

Front

What is the first step in polynomial long division?

Back

The first step is to divide the leading term of the dividend by the leading term of the divisor.

Front

What is a zero placeholder in synthetic division?

Back

A zero placeholder is used in synthetic division to represent missing terms in the polynomial, ensuring that all degrees are accounted for.

Front

How do you determine the remainder in polynomial division?

Back

The remainder is determined by evaluating the polynomial at the root of the divisor (for example, for (x - c), evaluate at c).

Front

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

Back

The result is 2x^3 + 4x^2 + 4x + 6 with a remainder of 10.

Front

What is the significance of the degree of a polynomial in division?

Back

The degree of a polynomial determines the highest power of the variable, which affects the number of terms in the quotient and the remainder.

Front

What is the quotient in polynomial division?

Back

The quotient is the result of the division, representing how many times the divisor fits into the dividend.

Front

What does it mean if the remainder is zero in polynomial division?

Back

If the remainder is zero, it means that the divisor is a factor of the dividend.