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Factoring by grouping given polynomial group terms

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What is factoring by grouping? What is a prime polynomial? Please show examples for both.

What is a common factor? Where do you use the common factor in an expression consisting of various terms?

What is a zero factor property? How does this help in solving equations?

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What is factoring by grouping?  What is a prime polynomial?  Please show examples for both. 

Factoring by grouping given polynomial group terms and find the factors
Eg x2 + 5x + 6 = 0
This equation can be written as x2 +3x +2x + 6 ( ie 5x = 3x + 2x)
Group the terms x2 ,3x and 2x, 6
(x2 +3x) + (2x + 6) = 0
Now take common factors from each group
x(x +3) +2(x +3) = 0
x(x +3) is one ...

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