Synthetic Division Techniques and Applications

What type of polynomial division is synthetic division?

• A method for dividing by quadratic factors

• A method for dividing by linear factors

• A method for dividing by cubic factors

• A method for dividing by constant factors

What is the first step in setting up synthetic division?

• Setting the divisor equal to zero and solving for x

• Identifying the coefficients of the polynomial

• Multiplying the coefficients by the divisor

• Writing down the polynomial in standard form

In synthetic division, what do you do with the first coefficient?

• Multiply it by the divisor

• Add it to the next coefficient

• Drop it down to the bottom row

• Subtract it from the next coefficient

What is the result of adding the first column in synthetic division?

• The divisor

• The remainder

• The next term in the quotient

• The next coefficient

How do you determine the next number to write under the division bracket?

• By subtracting the previous result from the next coefficient

• By multiplying the previous result by the divisor

• By dividing the previous result by the divisor

• By adding the previous result to the next coefficient

What does a remainder of zero indicate in synthetic division?

• The divisor is not a factor of the polynomial

• The polynomial is prime

• The polynomial has no real roots

• The divisor is a factor of the polynomial

How do you write the quotient after performing synthetic division?

• By keeping the powers of x the same

• By decreasing the powers of x by one

• By increasing the powers of x by one

• By using the original powers of x

What must be considered when writing the final answer as a fraction?

• The denominator must be a constant

• The numerator must be a polynomial

• The denominator must not be zero

• The numerator must be zero

What is an alternative way to express the result of synthetic division?

• As a quotient and remainder

• As a difference of polynomials

• As a product of factors

• As a sum of polynomials

Why is it important to ensure the x value is not equal to 3 in this example?

• Because it would make the quotient undefined

• Because it would make the numerator zero

• Because it would make the denominator zero

• Because it would make the remainder non-zero