Synthetic Division

Front

What is synthetic division?

Back

A method for dividing a polynomial by a linear binomial of the form (x - c) without using long division.

Front

What is the first step in synthetic division?

Back

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

Front

In synthetic division, what does the left-hand box represent?

Back

The value of 'c' from the divisor (x - c) used in the division.

Front

How do you determine the number of zeros needed in synthetic division?

Back

Count the degree of the polynomial being divided and subtract the number of terms.

Front

What is the order of coefficients for the polynomial 6x^4 - 4x^3 + 0x^2 + 3x + 1?

Back

6, -4, 0, 3, 1.

Front

What is the result of dividing 2x^3 + 5x^2 + 9 by x + 3 using synthetic division?

Back

The quotient is 2x^2 - 1x + 6 with a remainder of 21.

Front

What do you do with the remainder in synthetic division?

Back

The remainder is added to the quotient as a fraction over the divisor.

Front

What is the significance of the coefficients in synthetic division?

Back

They represent the values of the polynomial at specific powers of x.

Front

How do you handle missing terms in synthetic division?

Back

Use a coefficient of 0 for any missing terms in the polynomial.

Front

What is the relationship between synthetic division and the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial by (x - c) is equal to the value of the polynomial at c.