Question

Part 1: Tommy and Jessica are discussing how to factor 2x2 + 15x + 28. Tommy feels this trinomial is prime because he cannot find the factors of 28 that have a sum of 15. Jessica says he is incorrect and that it is factorable.

Using complete sentences, provide a convincing argument explaining who is correct and why. If this trinomial is factorable, factor it showing all work and explain your steps.

Answer 1

Here... I found this on the internet :
1)
4x^2 + 12xy + 2x + 2y
Experiment with factoring out alike terms:
4x(x + 3y) + 2(x + y)
That doesn't form any groupings. (x + y) won't group because the other terms won't factor into
(x + y)
This won't factor into groups. The number 2 is the only common factor:
2(2x^2 + 6xy + x + y)

3m^2 + 6mn + 7m + 14n
= 3m(m + 2n) + 7(m + 2n)
This can be grouped because of the common (m + 2n) in each:
(3m + 7)(m + 2n)

Part 2: Create your own polynomial that can be factored by grouping. Using complete sentences, explain how to factor the polynomial and show all work.
Do what was just shown in the second part of question 1.
2x^2 + 2xy + 3x + 3y is a good example. It will factor into groups because as common factors are gathered into parenthesis, it is shown that the terms will have (x + y) in common.
= 2x(x + y) + 3(x + y)
= (2x + 3)(x + y)

2) Part 1: The problem can be factored because there are terms which when multiplied will equal 28, and then when added or subtracted with create terms which equal 15x.
2x^2 + 15x + 28 = (x + 4)(2x + 7)

3) Part 1: Diana factored 75a^2 + 27d^2 using the following steps.
75a2 + 27d2 = 3(25a^2 + 9d^2)
= 3(5a + 3d)(5a − 3d)
75a2 + 27d2 = 3(25a^2 + 9d^2) is correct and would be the final factored answer.
The conclusion of 3(5a + 3d)(5a − 3d) is not correct.
The answer could be checked for errors by working out the problem and seeing if it equals what the problem was originally. At a glance, it is not likely to be correct since (3d)*(-3d) = -9d^2
3(5a + 3d)(5a − 3d)
3(25a^2 -15ad + 15ad - 9d^2)
= 75a^2 - 27d^2 (which would show her that it does not equal the original problem of (75a^2 + 27d^2).
The correct answer is that she should have stopped at the answer of:
75a2 + 27d2 = 3(25a^2 + 9d^2)

Answer 2

It was from yahoo answers :)

Answer 3

lol