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Question

How do you factor 3x2+8x+4 by using the grouping method?


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Solution

Factor the quadratic polynomial 3x2+8x+4 by using the grouping method:

Find the product of the quadratic term 3x2 and the constant term 4, 3x2√ó4=12x2 .

By a hit and trial process, we have to find two factors that give this product 12x2, such that the factors add up to the linear term 8x.

The two factors that satisfy these conditions are 2x and 6x, because their sum gives the linear term 8x and their product gives 12x2.

Rewrite 8x as 6x+2x in the expression 3x2+8x+4.

Then factorize by grouping the terms.

3x2+8x+4=3x2+6x+2x+4=3x2+6x+2x+4=3xx+2+2x+2=x+23x+2

Therefore, 3x2+8x+4 is factorized to (x+2)(3x+2) by using the grouping method as shown above.


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