How to apply the remainder theorem by evaluating and synthetic division

The video tutorial explains the remainder theorem and its application in polynomial division. It covers the concept of factors and zeros, and demonstrates synthetic division. The tutorial shows how to verify results using the remainder theorem and evaluate polynomials by substituting values. The lesson concludes with a discussion on verifying remainders and understanding the relationship between synthetic division and polynomial evaluation.

What does the remainder theorem state about the relationship between the remainder and f(k) when x minus k divides a polynomial?

• The remainder is always zero.

• The remainder is equal to f(k).

• The remainder is equal to k.

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

In synthetic division, what indicates that a given k is a zero of the polynomial?

• The quotient is zero.

• The remainder is zero.

• The polynomial is zero.

• The divisor is zero.

What is the first step in synthetic division?

• Add the coefficients

• Multiply the divisor by the first coefficient

• Subtract the coefficients

• Bring down the first coefficient

What was the remainder when synthetic division was performed with k equals 2 in the example?

• 0

• 2

• -4

• 4

What does the remainder theorem help verify when using synthetic division?

• The leading coefficient of the polynomial

• The factors of the polynomial

• The degree of the polynomial

• The remainder and f(k) are the same

How can you determine if a function is a zero of the polynomial using the remainder theorem?

• By checking if the remainder is non-zero

• By checking if the remainder is zero

• By checking if the polynomial is even

• By checking if the polynomial is odd

What is the purpose of using synthetic division in the context of the remainder theorem?

• To simplify the polynomial

• To calculate the leading coefficient

• To determine if a value is a zero of the polynomial

• To find the degree of the polynomial