Factoring Polynomials and Common Factors

What is the first step in any factoring problem?

• Multiply all terms by a constant

• Divide the polynomial into halves

• Factor out the greatest common factor

• Add like terms

Why can't factor by grouping be used when there is an odd number of terms?

• It requires a common factor

• It requires an even number of terms to divide into pairs

• Odd terms are harder to factor

• It only works with polynomials

In the first example, what is the greatest common factor of the four terms?

• 10y

• 3y

• 2y

• 5y

What is the result of factoring out 2y from 10y cubed?

• 5y

• 5y squared

• 10y

• 10y squared

What is the common polynomial factor found in the first example?

• 5y + 3

• y + 3

• y + 2

• 2y + 5

What is the purpose of dividing the polynomial into halves during factor by grouping?

• To eliminate terms

• To simplify the expression

• To make it easier to factor out common terms

• To find the greatest common factor

Why is it important to factor out a negative greatest common factor when the first term is negative?

• To make the polynomial even

• To eliminate negative terms

• To change the sign of each term

• To simplify the expression

What is the greatest common factor of the terms in the second example?

• 4x

• Negative 4x

• 5x

• Negative 5x

In the second example, what is the common binomial factor?

• x + 4

• x + 3

• 5x + 3

• 4x + 5

What is the final factored form of the second example?

• Negative 4x times (x + 4) times (5x + 3)

• 4x times (x + 4) times (5x + 3)

• Negative 4x times (x + 3) times (5x + 4)

• 4x times (x + 3) times (5x + 4)