Remainder and Factor Theorems Quiz

What does the remainder theorem state about the remainder when a polynomial is divided by a binomial?

• The remainder is the sum of the polynomial's coefficients.

• The remainder is the same as the polynomial evaluated at the binomial's root.

• The remainder is always zero.

• The remainder is the product of the polynomial's coefficients.

What is synthetic substitution primarily used for?

• To integrate a polynomial.

• To find the derivative of a polynomial.

• To evaluate a polynomial at a specific value.

• To graph a polynomial.

When using synthetic substitution, what indicates that a number is a factor of the polynomial?

• The remainder is zero.

• The remainder is negative.

• The remainder is positive.

• The remainder is equal to the polynomial's degree.

How does direct substitution differ from synthetic substitution?

• Direct substitution is only used for linear polynomials.

• Direct substitution is faster.

• Direct substitution is more accurate.

• Direct substitution involves evaluating the polynomial directly.

What is the result of factoring x^2 + 7x + 6?

• (x + 3)(x + 2)

• (x + 6)(x + 1)

• (x + 5)(x + 1)

• (x + 4)(x + 2)

What is the significance of the last number in synthetic division?

• It is the leading coefficient.

• It is the constant term.

• It is the degree of the polynomial.

• It is the remainder.

What is the purpose of finding values of k in the context of the remainder theorem?

• To determine the degree of the polynomial.

• To ensure the polynomial is factorable.

• To achieve a specific remainder when dividing the polynomial.

• To find the roots of the polynomial.

What equation must be satisfied to find the value of k for a remainder of 5?

• -4k + 13 = 5

• 4k - 13 = 5

• -4k - 13 = 5

• 4k + 13 = 5

Which method can be used to verify the value of k found using synthetic substitution?

• Differentiation

• Direct substitution

• Integration

• Graphical method

What is the final step in the lesson on remainder and factor theorems?

• Integrating the polynomial.

• Calculating the polynomial's derivative.

• Summarizing the factorization process.

• Reviewing the polynomial's graph.