Long and Synthetic Division

Front

What is long division in algebra?

Back

Long division is a method used to divide polynomials by breaking down the division process into a series of simpler steps, similar to numerical long division.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor of the form (x - c). It is faster and requires less writing than long division.

Front

How do you determine if a division problem is correct?

Back

To determine if a division problem is correct, check if the product of the divisor and the quotient plus the remainder equals the original polynomial.

Front

What is the remainder theorem?

Back

The remainder theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).

Front

What is the quotient in the division of (10n² - 37n - 12) by (n - 4)?

Back

The quotient is (10n + 3).

Front

What is the remainder when x² + 3x + 7 is divided by x + 2?

Back

The remainder is 5.

Front

How do you perform synthetic division?

Back

1. Write the coefficients of the polynomial. 2. Use the root of the divisor (c) to set up synthetic division. 3. Bring down the leading coefficient, multiply, and add down the columns.

Front

What is the result of dividing (2x³ + 4x² - 5) by (x + 3)?

Back

The result is 2x² - 2x + 6 with a remainder of -23.

Front

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

Back

The leading coefficient determines the degree of the polynomial and influences the behavior of the polynomial as x approaches infinity.

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.