Question 13218
1) Factor:

{{{7x^2+14x-21}}} First, factor a 7.
{{{7(x^2+2x-3)}}} Now factor the parentheses.
Look for two integers whose product is -3 and whose sum is 2.

Try 1 X (-3) = -3 and 1 + (-3) = -2 No, this won't do it.
Try -1 X 3 = -3 and -1 + 3 = 2 Aha!

So, {{{x^2+2x-3 = (x-1)(x+3)}}}

Putting it all together, we get:

{{{7x^2+14x-21 = 7(x-1)(x+3)}}} 

2) Factor:

{{{10x^2y+8xy^2+6xy}}} Factor the common factor in each term, 2xy.
{{{2xy(5x+4y+3)}}} I think that's as far as you can go with this.