Factoring Polynomials and Verification

The video tutorial covers the process of factoring polynomials, emphasizing its importance and application. It begins with an introduction to factoring, followed by a detailed walkthrough of factoring a specific polynomial expression. The tutorial explains how to factor trinomials into binomials and verifies the correctness of the factored form. The video concludes with simplification steps and a summary of the factoring process.

Why is factoring an important skill to learn in algebra?

• It is not important in algebra.

• It is only used in calculus.

• It helps in solving equations.

• It is only useful for graphing.

What is the first step in factoring a polynomial?

• Divide the polynomial by a constant.

• Find the roots of the polynomial.

• Multiply all terms together.

• Check for a common factor in all terms.

In the example polynomial X^3 - 7X^2 - 18X, what common factor is identified first?

• X^2

• 7

• 18

• X

After factoring out the common factor X, what is the resulting expression?

• X^2 - 7X - 18

• X^2 - 7X + 18

• X^2 + 7X - 18

• X^2 + 7X + 18

What are the factors of -18 that combine to give -7 in the trinomial X^2 - 7X - 18?

• 6 and -3

• -6 and 3

• 9 and -2

• -9 and 2

What is the completely factored form of the polynomial X^3 - 7X^2 - 18X?

• X(X + 6)(X - 3)

• X(X + 9)(X - 2)

• X(X - 6)(X + 3)

• X(X - 9)(X + 2)

What is the purpose of verifying the factored form of a polynomial?

• To ensure the factors are correct.

• To graph the polynomial.

• To simplify the polynomial further.

• To find the roots of the polynomial.

Which method is preferred for verifying the factored form in the video?

• Foil the two binomials first.

• Distribute the X first, then foil.

• Graph the polynomial.

• Use synthetic division.

What is the result of distributing X in the expression X(X - 9)(X + 2)?

• X^2 + 9X * X - 2

• X^2 - 9X * X + 2

• X^2 - 9X + 2

• X^2 - 9X

What is the result of foiling the binomials (X^2 - 9X) and (X + 2)?

• X^3 + 2X^2 - 9X^2 + 8X

• X^3 - 2X^2 + 9X^2 + 8X

• X^3 - 2X^2 + 9X^2 - 8X

• X^3 + 2X^2 - 9X^2 + 18X