Factoring Polynomials Techniques

The video tutorial explains how to factor a polynomial with four or more terms using the factor by grouping technique. It begins by identifying the greatest common factor, then divides the polynomial into two halves. Each half is factored separately, and a common binomial factor is identified and factored out. The tutorial concludes with the polynomial in its factored form.

What is the first step in any polynomial factoring problem?

• Find the common binomial factor

• Factor out the greatest common factor

• Divide the polynomial into halves

• Factor by grouping

When is factor by grouping a suitable technique?

• When the polynomial has no common factors

• When the polynomial has an odd number of terms

• When the polynomial has four or more terms and the number of terms is even

• When the polynomial is quadratic

How do you divide a polynomial for factor by grouping?

• Into individual terms

• Into four quarters

• Into two halves

• Into three equal parts

What is the common factor in the first half of the polynomial XY + 9Y?

• Y

• X

• None

• 9

What is the greatest common factor in the second half of the polynomial -5X - 45?

• 45

• 5

• -5

• X

Why do we factor out a negative five instead of a positive five in the second half?

• To make the polynomial simpler

• To increase the polynomial's degree

• To eliminate negative signs

• To achieve a common binomial factor

What is the common binomial factor in the expression after adjusting the factors?

• 5X - 45

• X - 9

• X + 9

• Y + 5

What is the final step in factor by grouping?

• Factor out the common binomial factor

• Factor out the greatest common factor

• Multiply the factors

• Divide the polynomial into halves

What is the result of factoring the polynomial using factor by grouping?

• A factored form with two binomials

• A quadratic equation

• A single term

• An unfactored polynomial

What is the purpose of factor by grouping?

• To increase the polynomial's degree

• To simplify the polynomial

• To find the roots of the polynomial

• To express the polynomial in a factored form