Factoring out a GCF and then a prime polynomial

The video tutorial covers the process of factoring a polynomial expression. It begins with an introduction to the importance of completing factoring problems. The teacher explains a specific problem, 3X^3 - 12X^2 - 45X, and demonstrates the initial steps in factoring by identifying the greatest common factor (GCF). The process of factoring using the GCF is detailed, and the teacher discusses the possibility of further factoring. The concept of prime factors is introduced, and the tutorial concludes with a brief mention of finding roots when further factoring is not possible.

What is the primary goal when asked to factor an expression?

• To divide it by the largest coefficient

• To write it as a product of its factors

• To subtract the smallest term from the largest

• To add all the terms together

What is the first step in factoring an expression?

• Multiplying all terms by a constant

• Identifying the greatest common factor

• Rewriting the expression in standard form

• Finding the sum of all coefficients

What is the greatest common factor (GCF) in the expression 3X^3 - 12X^2 - 45X?

• 3X

• 12X

• 3

• X

When is an expression considered to be in its prime factored form?

• When it cannot be factored any further

• When it is divided by its smallest coefficient

• When it is written as a sum of terms

• When it can be factored further

What should you do if an expression cannot be factored further?

• Multiply all terms by a variable

• Leave it as it is, as it is in its prime form

• Divide the expression by its largest term

• Add a constant to the expression