1. 2x^2 - 8x = (2x)(x - 4)
2. -3s^2 + 9s = (3s)(-s + 3)
3. 4s + 20x^2 = (4)(5x^2 + s)
4. 5t - 10t^2 = (5t)(1 - 2t)
5. s^2 + 8s + 12 = (s + 2)(s + 6)
6. x^2 - 10x + 21 = (x - 3)(x - 7)
7. x^2 + 5x - 6 = (x + 2)(x + 3)
8. 4r^2 + 20r + 25 = (2r + 5)(2r + 5) or (2r + 5)^2
9. 9r^2 -4 =(3r + 2)(3r - 2)
10. 2x^2 + 3x - 14 = (x - 2)(2x + 7)
a. For numbers 1 - 4, I simply find the GCMF or Greatest Common Monomial Factor, which will be the first factor and Polynomial given over (or divided by) the GCMF, which will be the second factor.
5 - 7, I just simply factor them. The square root of the first term then the factors of the last term, but their sum (I'm actually referring the numerical coefficients) should be the second term. (Not sure but this is how I factor quadratic trinomials, actually.)
8, I just use the perfect square rule.
9, (√first term + √second term)(√first term - √second term)
10, by grouping. Split the mid term 3x = 7x - 4x
2x^2 + 7x - 4x - 14
x(2x + 7) - 2(2x + 7)
Final answer: (x - 2)(2x + 7)
c. Simply multiply them with any methods you know, specifically latice or the vertical ones (not sure if I heard it right... that it was called traditional method)
Sorry, I wasn't able to answer the questions clearly.