Polynomial Remainders and Evaluations

The video tutorial explains how to solve a polynomial division problem. It starts by introducing the problem of finding the remainder when a polynomial P(x) is divided by x - 3 and 3x + 2. The tutorial then calculates the value of K using the given conditions and proceeds to find the remainder for the division by 3x + 2. The process involves simplifying the polynomial expression and performing calculations to arrive at the final answer. The tutorial emphasizes the importance of checking calculations with a calculator and understanding the steps involved.

What is the initial polynomial P(x) given in the problem?

• x^3 + kx^2 + 17x - 6

• x^3 - kx^2 + 17x + 6

• x^3 + kx^2 - 17x + 6

• x^3 - kx^2 - 17x - 6

What is the remainder when P(x) is divided by x - 3?

• 6

• 12

• 18

• 24

What is the first step in solving the problem?

• Find the value of K

• Find the remainder when P(x) is divided by x - 3

• Find the remainder when P(x) is divided by 3x + 2

• Simplify the polynomial

How do you find the value of K from the given remainder?

• By setting P(-3) equal to 12 and solving for K

• By setting P(0) equal to 12 and solving for K

• By setting P(1) equal to 12 and solving for K

• By setting P(3) equal to 12 and solving for K

What is the value of K after solving the equation?

• 9

• 7

• 6

• 8

What is the expression for P(3) in terms of K?

• 27 - 9K + 51 + 6

• 27 + 9K - 51 + 6

• 27 - 9K - 51 - 6

• 27 + 9K + 51 - 6

What is the value of P(3) when K is found?

• 12

• 24

• 36

• 48

What is the next step after finding P(3)?

• Simplify the expression

• Verify with a calculator

• Find P(-2/3)

• Solve for K

What is the next step after finding the value of K?

• Substitute K into the polynomial and find P(-3)

• Substitute K into the polynomial and find P(3)

• Substitute K into the polynomial and find P(-2/3)

• Substitute K into the polynomial and find P(2/3)

What is the expression for P(-2/3) after substitution?

• -2/3^3 - 8(-2/3)^2 - 17(-2/3) + 6

• -2/3^3 + 8(-2/3)^2 - 17(-2/3) + 6

• -2/3^3 + 8(-2/3)^2 + 17(-2/3) + 6

• -2/3^3 - 8(-2/3)^2 + 17(-2/3) + 6