There is a small error in the first example: the factored form should be x^3(a - b + c - d^2*x^3)
In this lesson on common factors, we learn how to remove the greatest common factor of each term in a polynomial expression. The trick is to find the smallest common factor, and divide each term by it, writing the expression inside a bracket. We can then verify our answer by multiplying the two factors together, which should give us the original expression. By taking out the common factors one by one, we can simplify polynomial expressions effectively.
The Common Factor factoring method.
Questions answered by this video:
What is factoring?
What is a common factor?
How do you find the greatest common factor of terms of a polynomial?
How can you factor out the GCF from a polynomial?
What is the greatest common factor of ax^3 - bx^3 + cx^3 - d^2x^6?
How do you factor ax^3 - bx^3 + cx^3 - d^2x^6 by finding the GCF?
How do you factor xy - 6x^2y^2 + 9xy^3 - 12x by taking out the greatest common factor?
How do you factor ax^2 + a^3x^2 - ax^3 by taking out the GCF?
How do you factor 17ax^2 - 34a^2x^3 - 51a^3x^4 by finding the greatest common factor?
How do you know if you factored a polynomial correctly?
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This lesson is a great introduction to factoring by showing how to take out the greatest common factor of a polynomial. This series of videos on factoring does a great job and is very understandable.