Long Division and Synthetic Division Practice

What does it mean if the remainder is zero after performing synthetic division?

• The divisor is not a factor of the polynomial.

• The polynomial is not divisible by the divisor.

• The divisor is a factor of the polynomial.

• The polynomial has no roots.

What is the next step after confirming that 2/3 is a root of the polynomial?

• Performing another synthetic division.

• Setting the polynomial equal to zero.

• Factoring the resulting quadratic polynomial.

• Finding the greatest common factor.

Why can't synthetic division be used when the denominator is x squared?

• Because synthetic division is only for cubic polynomials.

• Because the numerator must be a higher degree.

• Because x squared is not a polynomial.

• Because synthetic division only works with linear factors.

What is the first step in long division of polynomials?

• Combining like terms.

• Dividing the first term of the numerator by the first term of the denominator.

• Multiplying the divisor by the first term of the quotient.

• Subtracting the terms.

In the third example, what is unusual about the given root?

• It is a square root.

• It is a fraction.

• It is a negative number.

• It is a complex number.

What is the result of multiplying root 3 times 2 plus root 3?

• 2 root 3 plus 3

• 2 root 3 plus root 9

• 2 plus root 3

• 3 root 3 plus 2

What are the roots of the polynomial after factoring x squared plus 2 plus root 3 x plus 2 root 3?

• Positive 2 and positive root 3

• Negative 2 and negative root 3

• Positive 2 and negative root 3

• Negative 2 and positive root 3

What does the remainder theorem state?

• The remainder is the sum of the coefficients.

• The remainder is the product of the roots.

• The remainder is always zero.

• The remainder is the same as the value of the polynomial at the given root.

Why is it useful to check the remainder when dividing polynomials?

• To verify if the divisor is a factor.

• To find the degree of the polynomial.

• To simplify the polynomial.

• To determine the leading coefficient.

What should be the remainder when dividing a polynomial by a factor?

• The same as the leading coefficient.

• Zero.

• The same as the degree of the polynomial.

• The same as the constant term.