Find the polynomial function with integer coefficients that has given zeros

The video tutorial explains how to write polynomials from given zeros, emphasizing the transition from zeros to factors. It highlights common mistakes in polynomial multiplication, particularly when using the difference of two squares method. The instructor guides through the correct application of this method and demonstrates the final steps in calculating the polynomial, ensuring all terms are multiplied correctly.

What is the factor form of a polynomial if X = A is a zero?

• X - A

• X + A

• X * A

• X / A

When multiplying factors to form a polynomial, what common mistake should be avoided?

• Ignoring the constant term

• Only multiplying the first and last terms

• Forgetting to add terms

• Using the wrong variable

What is the difference of two squares?

• A method to add two squares

• A method to subtract two squares

• A technique to divide two squares

• A technique to multiply two identical terms

How can you correctly apply the difference of two squares?

• By ignoring the middle terms

• By adding all terms together

• By rewriting parentheses to group terms

• By multiplying only the first terms

What is the result of multiplying X - 4 by X - 4?

• X^2 - 16

• X^2 + 16

• X^2 + 8X + 16

• X^2 - 8X + 16

What is the final polynomial expression after combining like terms?

• X^3 - 8X^2 + 17X - 34

• X^3 + 10X^2 - 33X + 34

• X^3 + 8X^2 - 17X + 34

• X^3 - 10X^2 + 33X - 34

What should you do to ensure you have the correct polynomial expression?

• Use the distributive property

• Add all terms together

• Ignore the constants

• Only multiply the first terms