Synthetic Division

Front

What is Synthetic Division?

Back

A method used to divide a polynomial by a linear divisor of the form (x - c) without using long division.

Front

What is the first step in Synthetic Division?

Back

Write down the coefficients of the polynomial in descending order of degree.

Front

How do you set up Synthetic Division for (2x^3 - 5x^2 + 3x + 7) ÷ (x - 2)?

Back

Use 2 as the divisor and write the coefficients: 2, -5, 3, 7.

Front

What is the result of Synthetic Division if the polynomial is (x^3 - 3x^2 - 10x + 24) and the divisor is (x + 3)?

Back

The result is x^2 - 6x + 8.

Front

What does the remainder represent in Synthetic Division?

Back

The remainder represents the value of the polynomial at the divisor's root.

Front

How do you find the coefficients of the quotient in Synthetic Division?

Back

Perform the division process, bringing down coefficients and multiplying by the divisor's root.

Front

What is the significance of the order of coefficients in a polynomial?

Back

The order of coefficients corresponds to the descending powers of x in the polynomial.

Front

What is the formula for the quotient when dividing a polynomial by a linear factor?

Back

If P(x) is the polynomial and (x - c) is the linear factor, then P(x) = (x - c)Q(x) + R, where Q(x) is the quotient and R is the remainder.

Front

What is the result of (2x^3 + 5x^2 + 9) ÷ (x + 3)?

Back

The result is 2x^2 - x + 3.

Front

What is the relationship between the degree of the dividend and the degree of the quotient in Synthetic Division?

Back

The degree of the quotient is one less than the degree of the dividend.