Given One Zero or Factor Find the Remaining Zeros

The video tutorial explains the role of factors in polynomials, highlighting how they help determine zeros. It covers synthetic division and the use of conjugates for irrational factors. The tutorial demonstrates finding zeros by setting factors to zero and verifies them using synthetic division and the square root method.

What is the significance of knowing the factors of a polynomial?

• They indicate the polynomial's leading coefficient.

• They show the polynomial's constant term.

• They allow us to use synthetic division.

• They help in determining the degree of the polynomial.

If a polynomial has a factor of (x - sqrt(5)), what can be inferred?

• The polynomial is linear.

• The polynomial has a factor of (x - 5).

• The polynomial has a factor of (x + sqrt(5)).

• The polynomial is quadratic.

How do you find the zeros of a polynomial from its factors?

• By setting each factor equal to zero.

• By multiplying the factors together.

• By dividing the factors by the polynomial's degree.

• By adding the factors together.

What is the first step in synthetic division?

• Bring down the leading coefficient.

• Multiply the divisor by the dividend.

• Add the coefficients together.

• Subtract the divisor from the dividend.

What does a remainder of zero in synthetic division indicate?

• The divisor is not a factor of the polynomial.

• The polynomial is quadratic.

• The divisor is a factor of the polynomial.

• The polynomial has no real zeros.