Given a list of zeros, learn how to write the equation of a polynomial

The video tutorial reviews the process of factoring polynomials and introduces the concept of reversing these steps to form equations. It explains the zero product property and demonstrates how to multiply binomials using both the FOIL method and the box method. The tutorial emphasizes understanding the difference of squares and provides a step-by-step guide to solving polynomial equations.

What is the factored form of the quadratic equation y = X^2 - 7X + 12?

• (X - 3)(X - 4)

• (X + 2)(X + 6)

• (X - 2)(X - 6)

• (X + 3)(X + 4)

When working backwards from zeros, what is the first step?

• Set all zeros equal to zero

• Set all zeros equal to X

• Multiply the factors

• Use the box method

Why do we set each factor equal to zero when forming a polynomial?

• To use the box method

• To find the degree of the polynomial

• To apply the zero product property

• To simplify the equation

What is the reverse process of factoring called?

• Division

• Addition

• Multiplication

• Subtraction

What is a key characteristic of a difference of squares?

• Terms are the same but with opposite signs

• Both terms are negative

• Both terms are positive

• Terms are different with the same sign

What method can be used instead of FOIL for multiplying polynomials with many terms?

• The lattice method

• The column method

• The grid method

• The box method

What is the final polynomial obtained using the box method in the example?

• X^4 + 2X^3 - 3X^2 - 2X

• X^4 - 2X^3 + 3X^2 + 2X

• X^4 - X^3 + 4X^2 + 4X

• X^4 + X^3 - 4X^2 - 4X