Dividing Polynomials with Synthetic Division

What is the first step in synthetic division?

• Set the divisor equal to zero and solve for x

• List down the coefficients of the polynomial

• Multiply the divisor by the dividend

• Arrange the polynomial in ascending order

How do you solve for x when given a divisor in the form of x + a?

• Add a to both sides

• Subtract a from both sides

• Multiply both sides by a

• Divide both sides by a

What is the role of the coefficients in synthetic division?

• They are ignored in the process

• They are subtracted from the divisor

• They are multiplied by the divisor

• They are used to set up the division box

What is the correct setup for synthetic division?

• Divisor and coefficients mixed together

• Divisor on the left, coefficients on the right

• Coefficients only, divisor is not needed

• Coefficients on the left, divisor on the right

What does the quotient of the first example become?

• x^3 + 3x + 7

• x^3 + 3x^2 + 7x

• x^2 + 3x - 7

• x^2 + 3x + 7

How do you determine the degree of the quotient in synthetic division?

• It is the same as the degree of the divisor

• It is one less than the degree of the dividend

• It is one more than the degree of the dividend

• It is the same as the degree of the dividend

Why is it important to check for missing terms in polynomials for synthetic division?

• To make the polynomial look complete

• To simplify the divisor

• To increase the degree of the polynomial

• To ensure the division is performed correctly

What happens if a term is missing in the polynomial during synthetic division?

• Synthetic division cannot be performed

• The missing term is ignored

• The polynomial is considered invalid

• A zero is placed for its coefficient

What do you do with the remainder in synthetic division?

• Subtract it from the quotient

• Place it over the divisor in the quotient

• Ignore it as it is not important

• Add it to the highest degree term

What signifies the end of the synthetic division process?

• When the quotient is fully written out

• When the divisor is no longer needed

• When the remainder is zero

• When all coefficients have been used