Thread: division

Hi all - me again,

I have a math exam in the morning. Lucky for me, I have some past papers, and only the numbers, not the questions, change each year.

I was wondering if someone could help me with the solution I have here:

1
a) Fully factorize:

3x -7x -3x+7

The solution which I have been given is to first of all do this:

1 I...3...............-7............-3..........7
....I
....I_________3_____-4_____7_____
.......3............... -4............-7..........0

Which then goes onto this:

3x - 4x -7 = (3x-7)(x+1)

so (x-1)(3x-7)(x+1)

Can someone please explain all of the above to me? I have no idea what the grid thing does, how the 4 gets in there? Basically, help? Please?

Cheers,

Martin

Originally Posted by Mathy

Hi all - me again,

I have a math exam in the morning. Lucky for me, I have some past papers, and only the numbers, not the questions, change each year.

I was wondering if someone could help me with the solution I have here:

1
a) Fully factorize:

3x -7x -3x+7

The solution which I have been given is to first of all do this:

1 I...3...............-7............-3..........7
....I
....I_________3_____-4_____7_____
.......3............... -4............-7..........0

Which then goes onto this:

3x - 4x -7 = (3x-7)(x+1)

so (x-1)(3x-7)(x+1)

Can someone please explain all of the above to me? I have no idea what the grid thing does, how the 4 gets in there? Basically, help? Please?

Cheers,

Martin

i don't see what you are doing here. it seems you were trying some sort of long division. that was completely unnecessary. this is a "nice" polynomial. it factors easily by grouping



factor out from the first two terms and -1 from the last two, we get:



now the 3x - 7 is common, so pull that out



the last part is the difference of two squares, so we have: