Factoring Polynomials and GCF Concepts

The video tutorial covers two methods of factoring polynomials. The first method involves factoring out the greatest common factor from a polynomial, resulting in a prime polynomial. The second method demonstrates factoring by grouping, where terms are grouped to identify common factors, leading to a factorization of the polynomial into two binomials.

What is the first step in factoring a polynomial?

• Identify the greatest common factor

• Multiply all terms

• Add all coefficients

• Divide by the smallest term

Which number is the greatest common factor in the first example?

• 2

• 3

• 4

• 5

What is the smallest exponent for x in the first polynomial?

• x

• x squared

• x cubed

• x to the fourth

What is left behind from the first term after factoring out the greatest common factor?

• 5x squared

• 3y

• x cubed

• y

What is a prime polynomial?

• A polynomial with only one term

• A polynomial with all positive coefficients

• A polynomial that can be factored further

• A polynomial with no common factors

What method is introduced in the second example?

• Factoring by substitution

• Factoring by addition

• Factoring by elimination

• Factoring by grouping

What common factor is extracted from the first two terms in the second example?

• x

• w

• y

• z

What is left behind after factoring out a y from the first two terms?

• x cubed plus ten

• x squared minus ten

• x squared plus ten

• x cubed minus ten

What factor is extracted from the second two terms?

• Positive ten

• Negative ten

• Negative three

• Positive three

Why is the plus sign changed to a minus sign in the second example?

• To balance the equation

• To correct a mistake

• Because negative three times negative ten gives a positive 30

• To simplify the expression