Factoring Polynomials Techniques

The video tutorial explains how to factor polynomial expressions with four or more terms using the factor by grouping technique. It begins by identifying the greatest common factor and proceeds to divide the polynomial into two halves. If no common factor is found, the terms are rearranged to facilitate grouping. The process is completed by factoring out the common binomial factor, resulting in a fully factored polynomial expression.

What is the first step in any polynomial factoring problem?

• Divide the polynomial into two halves

• Factor out the greatest common factor

• Rearrange the terms

• Apply the quadratic formula

When should you consider using the factor by grouping technique?

• 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 linear

• When the polynomial is quadratic

What should you do if the initial factor by grouping attempt fails?

• Use the quadratic formula

• Rearrange the terms and try again

• Try a different factoring technique

• Conclude that the polynomial cannot be factored

Which terms share a common factor of X in the rearranged polynomial?

• XY and -63

• 9Y and -63

• XY and -7X

• XY and 9Y

What is the greatest common factor of the terms 9Y and -63?

• 1

• 3

• 7

• 9

What is the common binomial factor in the final step of factor by grouping?

• x - 7

• x + 9

• y - 7

• y + 9

What is the result after factoring out the common binomial factor?

• x + 9

• y - 7

• y + 7

• x - 9

Why is it sometimes necessary to rearrange the terms in a polynomial?

• To change the polynomial's degree

• To successfully apply the factor by grouping technique

• To simplify the polynomial

• To make the polynomial longer

What is the purpose of the factor by grouping technique?

• To find the roots of a polynomial

• To factor polynomials with four or more terms

• To simplify expressions

• To solve quadratic equations

What is the final expression after completing the factor by grouping?

• (x - 7)(y + 9)

• (x + 7)(y - 9)

• (x - 9)(y + 7)

• (x + 9)(y - 7)