#8x^214x+3#? I dont understand how to solve this using factoring grouping?
#8x^214x+3#
1 Answer
Please see below.
Explanation:
It is important to know that when you try to factorize a quadratic polynomial say

Remember you can do it, only if the determinant
#b^24ac# is a complete square of a number . This is generally not a big deal as generally in problems where factoring by grouping is desired, this is ensured. However, if you are unable to do this you can check for this. Here in#8x^214x+3# , we have#a=8# ,#b=14# and#c=3# . Hence#b^24ac=(14)^24xx8xx3=19696=100=10^2# and you can factorize the given polynomial by grouping. 
Now you have to split
#b# in two parts, whose sum is#b# and product is#axxc# . Here to make things easier look at the signs of#a# and#c# . If they are same, look at their sum equal to#b# and if signs are different, look at their difference equal to#b# .
Here, signs of#a=8# and#b=3# are same, as they are bot positive (an example of different signs given below), hence find two numbers whose sum is#14# and product is#8xx3=24# . 
For making things easier, particularly when
#axxc# is a large number, list factors as shown here#((1,24),(2,12),(3,8),(4,6))# and we end here as the factors are getting repeated there after. Here sum of#2# and#12# is equal to#14# , hence split accordingly.
Now
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