math
posted by tonya on .
factor the following expression completely 75x^4+35x^310x^2

75x^4 + 35x^3  10x^2
See your first post below for an example of how this is done.
Hint, factor out 5x^2 first, then factor the remaining expression.
You will never learn without practice :) 
75x^4+35x^310x^2=(5x^2)*(15x^2+7x2)
Factoring:
15x^2+7x2
Using the factor pair (3, 10) whose sum is 7, rewrite your equation replacing the term 7 x with
3 x and 10 x.
15x^2+7x2=15x^23x+10x2
Now group the first two terms and the last two terms on the left hand side:
(15x^23x)+(10x2)
Within each group, factor out common factors.
(15x^23x)+(10x2)=3x*(5x1)+2*(5x1)
Notice that the two quantities in parentheses are the same. This means that the quantity, (5x1), is a common factor and we can factor it out.
3x*(5x1)+2*(5x1)=(5x1)*(3x+2)
15x^2+7x2=(5x1)*(3x+2)
75x^4+35x^310x^2=(5x^2)*(15x^2+7x2)=
(5x^2)*(5x1)*(3x+2) 
Hvala