Question 71157
Let's try the following.
Factor:
{{{10y^2+9y+2}}}
The factors, if this can be factored, will take the form:
{{{(ay+m)(by+n)}}} where:
a*b = 10 This is the coefficient of the first term.
m*n = 2 This is the constant term.
a*n+b*m = 9 This is the coefficient of the middle term.
Now you have to try a few combinations.
Try a = 5 and b = 2, so a*b = 10
Try m = 2 and n = 1, so m*n = 2
Then: an+bm = 5*1 + 2*2 = 5+4 = 9
Putting it all together, you'll get:
{{{10y^2+9y+2 = (5y+2)(2y+1)}}}
Check, using FOIL:
{{{(5y+2)(2y+1) = 10y^2+5y+4y+2}}} Simplify: {{{10y^2+9y+2}}}