Polynomial Division and Remainder Theorem

The video tutorial explains polynomial division using the remainder theorem. It begins with an introduction to polynomial division and the remainder theorem, followed by solving simultaneous equations using the theorem. The tutorial then delves into understanding polynomial remainders and their degrees. It applies the remainder theorem to solve polynomial division problems and concludes with solving example problems.

What theorem is primarily used to solve the polynomial division problem introduced in the video?

• Binomial Theorem

• Factor Theorem

• Remainder Theorem

• Fundamental Theorem of Algebra

What is the first step in applying the remainder theorem to a polynomial?

• Find the roots of the polynomial

• Identify the degree of the polynomial

• Set the polynomial equal to zero

• Substitute the divisor into the polynomial

What is the value of p(3) according to the first simultaneous equation?

• 54

• 63

• 120

• 117

What is the second simultaneous equation derived in the video?

• 3a + b = 120

• 2x - 1 = -8

• 2x + 7 - a + b = -8

• 2x + 7 = 120

What is the degree of the remainder when dividing by a linear divisor?

• Two

• One

• Three

• Zero

When dividing by a quadratic divisor, what is the expected degree of the remainder?

• One

• Three

• Two

• Zero

What is the remainder when dividing by x - 4 and x + 3?

• x + 4

• x - 4

• 2x + 4

• 2x - 4

What is the value of 'a' in the final solution?

• 2

• 14

• 4

• 7

What is the value of 'b' in the final solution?

• 0

• 4

• 8

• -4

What happens to the polynomial when the divisor is substituted in the remainder theorem?

• It vanishes

• It becomes zero

• It becomes a constant

• It doubles