math
posted by Kent .
How do i factor?
a)5a^2b+ab^2
b)9k^21
c)2y^25y+2
If i can get an idea how to do these and i work the rest i have to do myself, thanks

math 
Reiny
The first is a simple case of "common factoring"
5a^2b+ab^2
= ab(5a+b)
these can be quickly verified by merely expanding your answers.
the second is a "difference of squares"
9k^21
= (3k+1)(3k1)
the third is a standard "quadratic trinomial factoring"
the most popular method these days seems to be "decomposition"
2y^25y+2
multiply the coefficients of the first and last terms ... 2x2 = 4
now find two numbers so that when multiplied will give you 4, and when added will give you the coefficient of the middle term, namely 5
those 2 numbers clearly are 4 and 1
so rewrite the middle term of 5y as
4y y , thus the name "decomposition"
= 2y^2  4y  y + 2
now factor by finding the highest common factor of the first two terms
= 2y(y  2)  y + 2
If you did everything correctly, that common factor of y2 MUST also appear at the end, and surely ....
= 2y(y2)  (y2)
and a common factor once more ....
= (y2)(2y1)
again you can always check your answer by expanding it, you must get the original question.
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