Factor each of the following polynomials. Answer the questions that follow.

1. 2xsquared-8x
2. -3s squares+9s
3. 4s+20x squared
4. 5t-10t squared
5. s squared+8s+12
6. x squared-10x+21
7.x squared+5x-6
8.4r squared+20r+25
9. 9r squared-4
10. 2x squared+3x-14

questions
a. how did you factor each polynomial
b..what factoring technique did you use to come up with the factors of each polynomial? explain how you used this technique
c.how wouldyou know i the factors you got are the correct ones?
d. Which of the polynomials did you find difficult to factor? why?

1

Answers

2016-07-12T20:24:08+08:00
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.
2 5 2
Thankyou so muchhhh.
what is the answwr in the QuestionsB and D?
For B... 1 - 4: factoring polynomials with common monomial factor, 5-7: I don't know, actually but this is how I understand what our teacher taught us, sorry. 8: Perfect square rule thingy; 9: Special product thingy - sum and difference of two terms; 10 - ac method...simply do a research by yourself. I'm not sure about it anyway... and lastly, for D, I think someone's opinion is needed and I don't know what to answer :3