Exam Review Understanding roots, zeros, factors of a polynomial

The video tutorial explores the concept of polynomial roots and factors, emphasizing the factor theorem. It discusses how to identify true statements about polynomial factors and the role of conjugates. The tutorial also covers the multiplication of polynomial factors and explains why certain expressions are factors. The conclusion focuses on why the expression X^2 + 3 is not necessarily a factor, depending on the polynomial's degree.

What does it mean if F(sqrt(3)) equals zero in terms of polynomial characteristics?

• sqrt(3) is a root or zero

• sqrt(3) is an exponent

• sqrt(3) is a coefficient

• sqrt(3) is a factor

According to the Factor Theorem, what is true if a value is a root of a polynomial?

• The polynomial is linear

• The value is a coefficient

• The corresponding expression is a factor

• The polynomial has no roots

If X - sqrt(3) is a factor, what must also be a factor due to the conjugate root theorem?

• X^2 - 3

• X + sqrt(3)

• X - 3

• X + 3

What is the result of multiplying the factors (X - sqrt(3)) and (X + sqrt(3))?

• X^2 - 6

• X^2 + 6

• X^2 - 3

• X^2 + 3

Why is X^2 + 3 not necessarily a factor of the polynomial?

• It depends on the polynomial's degree

• It is always a factor

• It is a coefficient

• It is a root