Vicky factored 30x2 + 76x + 48 as follows:

Line 1 30x2 + 76x + 48
Line 2 30x2 + 36x + 40x + 48
Line 3 6x(5x + 6) + 8(5x +6)
Line 4 (6x + 8)(5x + 6)
Did Vicky completely factor the polynomial? Justify your response by explaining why it is is factored completely or by showing the correct solution if it is not factored completely.
Would the problem produce a different result if Line 2 was written as 30x2 + 40x + 36x + 48? Explain why or why not.

Question

Vicky factored 30x2 + 76x + 48 as follows:

Line 1	30x2 + 76x + 48
Line 2	30x2 + 36x + 40x + 48
Line 3	6x(5x + 6) + 8(5x +6)
Line 4	(6x + 8)(5x + 6)
Did Vicky completely factor the polynomial? Justify your response by explaining why it is is factored completely or by showing the correct solution if it is not factored completely.
Would the problem produce a different result if Line 2 was written as 30x2 + 40x + 36x + 48? Explain why or why not.

anonymous · Answer

A two can be factored out of 6x+8 to make 2(3x+4).
Correct solution: 2(3x+4)(5x+6)

It wouldn't produce a different end result, but there would be different work in between.
30x^2 +76x +48
30x^2 +40x +36x +48
10x(3x+4) + 12(3x+4)
(10x+12)(3x+4)
A 2 can still be factored out at this point.
2(5x+6)(3x+4)

2(3x+4)(5x+6)=2(5x+6)(3x+4), so they are the same.