Solving Linear Equations and Polynomials

The video tutorial explains how to use the remainder theorem to solve a polynomial division problem. It begins by introducing the theorem and setting up the problem with a given polynomial. The tutorial then applies the remainder theorem to find the remainder when the polynomial is divided by a linear factor. Finally, it solves for the unknown variable K in the polynomial, concluding with the final answer.

What is the main goal of the problem discussed in the video?

• To find the roots of the polynomial.

• To factor the polynomial completely.

• To determine the degree of the polynomial.

• To find the value of K in a polynomial.

Which theorem is primarily used to solve the problem in the video?

• Pythagorean Theorem

• Factor Theorem

• Binomial Theorem

• Remainder Theorem

What does the remainder theorem help us find in this context?

• The roots of the polynomial

• The leading coefficient of the polynomial

• The remainder when the polynomial is divided by a linear factor

• The degree of the polynomial

What is the remainder when the polynomial is divided by X - 3?

• 81

• 54

• 27

• 0

What is the value of f(3) according to the remainder theorem?

• 81

• 54

• 27

• 0

What is the result of 3 to the third power?

• 81

• 27

• 243

• 9

What is the first step in solving for K after evaluating the polynomial?

• Divide both sides by 3

• Subtract 66 from both sides

• Multiply both sides by 3

• Add 15 to both sides

What is the value of 81 minus 15?

• 27

• 66

• 36

• 54

What equation do we get after subtracting 66 from both sides?

• 3K = 12

• 3K = -12

• K = -12

• K = 12

What is the final value of K after solving the equation?

• 4

• -4

• 12

• -12