Determine if you have a factor of a polynomial using the factor theorem

The video tutorial explains the factor theorem and its connection to the remainder theorem. It covers polynomial factorization using long and synthetic division, emphasizing the application of the factor and remainder theorems to identify zeros and factors. The tutorial includes a step-by-step verification of the factor theorem through calculations, concluding with final remarks.

What is the relationship between the factor theorem and the remainder theorem?

• They are the same theorem with different names.

• The remainder theorem is a special case of the factor theorem.

• The factor theorem is a special case of the remainder theorem.

• They are completely unrelated.

Which method does the speaker suggest as easier for factoring the polynomial?

• Graphical method

• Remainder or factor theorem

• Synthetic division

• Long division

What value of x is used to check if x + 1 is a factor of the polynomial?

• x = 0

• x = 2

• x = -1

• x = 1

What does it mean if f(-1) equals zero for the polynomial?

• x = -1 is a zero and x + 1 is a factor.

• x = -1 is not a zero but x + 1 is a factor.

• x = -1 is not a zero and x + 1 is not a factor.

• x = -1 is a zero but x + 1 is not a factor.

What is the result of plugging x = -1 into the polynomial?

• The result is zero, but x + 1 is not a factor.

• The result is not zero, confirming x + 1 is not a factor.

• The result is zero, confirming x + 1 is a factor.

• The result is not zero, but x + 1 is a factor.