Understanding Factors of Polynomials

The video tutorial explains how to determine if a polynomial has a specific factor using the remainder theorem. It begins by defining a factor as a divisor that leaves no remainder. The remainder theorem is introduced, which involves substituting a value into the polynomial to check if the result is zero. A detailed example is provided, demonstrating the process of substituting and calculating to verify if X-3 is a factor. The tutorial concludes by confirming the factor through arithmetic operations, emphasizing the importance of accurate calculations.

What is a factor of a polynomial?

• A number that multiplies with the polynomial.

• A number that divides the polynomial without a remainder.

• A number that divides the polynomial with a remainder.

• A number that adds to the polynomial.

What does the remainder theorem help determine?

• If a number is a factor of a polynomial.

• If a polynomial is prime.

• If a polynomial is even.

• If a polynomial is odd.

What value should be plugged into the polynomial to check if X-3 is a factor?

• -3

• 3

• 0

• 1

What is the result of 3 to the power of 4?

• 243

• 27

• 81

• 9

What is the product of 27 and -11?

• -297

• 243

• 297

• -243

What is the result of 3 to the power of 2 multiplied by 15?

• 45

• 135

• 90

• 60

What is the sum of 162 and -297?

• -135

• 135

• 0

• 12

What is the final result of the polynomial evaluation when X is replaced by 3?

• 3

• -12

• 0

• 12

What conclusion can be drawn if the remainder is zero?

• X-3 is not a factor.

• The polynomial is even.

• X-3 is a factor.

• The polynomial is prime.

What does it mean if X-3 is a factor of the polynomial?

• The polynomial is even.

• The polynomial is odd.

• The polynomial can be divided by X-3 without a remainder.

• The polynomial can be divided by X-3 with a remainder.