Understanding Synthetic Division

The video tutorial explains synthetic division, a method for dividing polynomials. It begins with setting up the division using coefficients and solving for X. The process involves multiplying and subtracting to simplify the polynomial. The tutorial concludes by interpreting the results, showing how exponents decrease by one in the final expression.

What is the primary purpose of synthetic division?

• To multiply polynomials

• To divide polynomials more efficiently

• To find the roots of polynomials

• To add polynomials

In synthetic division, what do the coefficients represent?

• The variables in the polynomial

• The numbers in front of the variables

• The exponents in the polynomial

• The roots of the polynomial

What should be placed in the box during synthetic division?

• The sum of all coefficients

• The solution to the divisor set to zero

• The constant term of the polynomial

• The highest degree of the polynomial

What is the first step in performing synthetic division?

• Add all coefficients

• Bring down the first coefficient

• Multiply all coefficients

• Subtract the exponents

During synthetic division, what operation is performed after multiplying?

• Multiplying the result by the next coefficient

• Subtracting the result from the next coefficient

• Adding the result to the next coefficient

• Dividing the result by the next coefficient

What indicates a correct result in synthetic division?

• The remainder is zero

• The quotient is a constant

• The divisor is unchanged

• The coefficients are all positive

How does the degree of the polynomial change after synthetic division?

• It increases by one

• It remains the same

• It doubles

• It decreases by one

What is the final step in writing the result of synthetic division?

• Adding the original polynomial

• Writing the coefficients with reduced exponents

• Multiplying the coefficients by the divisor

• Subtracting the divisor from the result

What happens to the zero in the final polynomial result?

• It is multiplied by the divisor

• It is subtracted from the first term

• It is ignored

• It is added to the constant term

What is the role of the divisor in synthetic division?

• It is added to the final polynomial

• It is set to zero to find the box value

• It determines the degree of the result

• It is used to multiply the coefficients