Help! I've been having troubles on these questions and really need some help. 1. A strategy got factoring trinomials of the form x^2+bx+c was developed by exploring the product of binomials (x+p) and (x+q).
a) Explain how the development of this factoring strategy is an example of working backwards to solve a problem
b) Explain why px+qx=(9+q)x
c) Explain why the expression x^2+(p+q)x+pq leads to the need to determine integers that add to b and have a product of c when factoring a trinomial of the form x^2+bx+c.

2. Juan is trying to factor x^2+7x+3 and makes the following table (in photo)
Juan concluded that x^2+7x+3 cannot be factored using integers.
a) Is Juan Correct?
b) Comment on Juan's strategy and improve it if possible.

3. Factor each of the following expressions.
a) x^2+9x+20 (My answer I got was (x+5)(x+4))
b) 10n^2+n-3 (For this, I think I got (2n-1)(5n+3)
c) 2(d^2-4de+3e^2 (My answer was 2(d^2-4de+3e^2))