Exploring the Remainder Theorem and Synthetic Substitution

The video tutorial explains the remainder theorem, emphasizing its connection to synthetic division. It begins by reviewing a previous example where a polynomial is divided by X-3, resulting in a remainder of 19, which is verified using the theorem. The tutorial then explores a new example with X-5, demonstrating the calculation and verification process, resulting in a remainder of 193. The video aims to solidify understanding of the remainder theorem through practical examples.

What prior knowledge is recommended before learning the remainder theorem?

• Knowledge of calculus

• Understanding of quadratic equations

• Familiarity with synthetic division

• Basics of trigonometry

What was the remainder when 3x^3 - 8x^2 + 4x - 2 was divided by X - 3?

• 12

• 3

• 19

• 7

According to the remainder theorem, what is f(3) for the polynomial 3x^3 - 8x^2 + 4x - 2?

• 12

• 3

• 19

• 7

What is the first step in verifying the remainder theorem for f(3)?

• Multiply the polynomial by 3

• Divide the polynomial by X - 3

• Substitute 3 into the polynomial

• Find the derivative of the polynomial

What is the remainder when 3x^3 - 8x^2 + 4x - 2 is divided by X - 5?

• 12

• 7

• 19

• 193

According to the remainder theorem, what is f(5) for the polynomial 3x^3 - 8x^2 + 4x - 2?

• 193

• 19

• 12

• 7

What is the first step in verifying the remainder theorem for f(5)?

• Divide the polynomial by X - 5

• Multiply the polynomial by 5

• Substitute 5 into the polynomial

• Find the derivative of the polynomial

What is the simplified form of 3 times 5 cubed minus 8 times 5 squared plus 4 times 5 minus 2?

• 20

• 193

• 375

• 200

What does the remainder theorem state about the remainder from synthetic division?

• It is the product of the coefficients

• It is the same as the leading coefficient

• It is always zero

• It is equal to f(h) where h is the constant in the binomial