Question

Help!!! I need someone to explain step by step how to do this problem. I will fan and medal

Answer 1

Factor completely
48y^2 + 82y -70

Answer 2

First, write out the problem:
\[48y^2 + 82y - 70\]
Then, remove the common factor:
\[2*(24y^2 + 41y - 35)\]

Answer 3

Now, focus on the part in parenthesis:
\[24y^2 + 41y - 35\]
In order to factor this, it needs to be written in the following form:
\[(ay + c)(by - d)\]
Where a, b, c, and d are constants.

Answer 4

Next, we list the products of 24 to find the possibilities of a and b:

24 = 2 * 12 = 3 * 8 = 4 * 6

So a and b could equal 2 and 12, 3 and 8, or 4 and 6 (not necessarily respectively).

Answer 5

Do the same to 35 to find the possible values for c and d:

35 = 5 * 7

So either c = 5 and d = 7, or c = 7 and d = 5.

Answer 6

Sorry, it's -35, so this is the proper product listing:

35 = -5 * 7 = 5 * -7

So c and d could equal -5 and 7, or 5 and -7 (again, not necessarily respectively).

Answer 7

Since the middle term (41y) is positive, we'll guess that c = -5 and d = 7, since if the larger number were negative, the middle term would most likely be negative too.

This leaves us with:
\[(ay - 5)(by + 7)\]

Answer 8

At this point, we try combinations of a and b until it fits the given value:
a = 2, b = 12
\[(2y - 5)(12y + 7) = 24y^2 - 60y + 14y - 35 = 24y^2 - 46y - 35\]
a = 12, b = 2
\[(12y - 5)(2y + 7) = 24y^2 + 84y - 10y - 35 = 24y^2 + 74y - 35\]
a = 3, b = 8
\[(3y - 5)(8y + 7) = 24y^2 - 40y + 21y - 35 = 24y^2 - 19y - 35\]
a = 8, b = 3
\[(8y - 5)(3y + 7) = 24y^2 - 15y + 56y - 35 = 24y^2 + 41y - 35\]

Answer 9

it would be a=8 , b=3 right?

Answer 10

Yes, so:
\[24y^2 + 41y - 35 = (8y - 5)(3y+7)\]
Those are its factors.