How to Find All Zeros of a Polynomial, Given the Graph Using Synthetic Division

The video tutorial explains how to graph polynomials and find zeros using synthetic division. It covers the process of synthetic division, including handling coefficients and place values, and demonstrates finding factors and zeros. The tutorial concludes with a solution set and a method to verify results using a calculator.

What is the relationship between zeros and x-intercepts in a polynomial?

• Zeros are unrelated to x-intercepts.

• Zeros are the opposite of x-intercepts.

• Zeros are the same as x-intercepts.

• Zeros are always positive values.

In synthetic division, what is the first step after writing down the coefficients?

• Add all coefficients together.

• Multiply the first coefficient by the zero.

• Bring down the first coefficient as a freebie.

• Divide the first coefficient by the zero.

What is the zero-product property used for in polynomial equations?

• To add zeros to the polynomial.

• To find the zeros of a polynomial.

• To multiply all terms by zero.

• To divide the polynomial by zero.

If x = -2 is a zero, what is the corresponding factor of the polynomial?

• x - 2

• x + 2

• x - 3

• x + 3

What is the result of synthetic division when the remainder is zero?

• The divisor is not a factor.

• The polynomial has no zeros.

• The divisor is a factor of the polynomial.

• The division is incorrect.

How can you verify the zeros of a polynomial using a calculator?

• By multiplying all coefficients by zero.

• By graphing the polynomial and checking the x-intercepts.

• By dividing the polynomial by its degree.

• By adding all zeros together.

What is the factor form of a polynomial if one of its zeros is 3?

• x - 3

• x + 2

• x - 2

• x + 3