Question

Explain the grouping method of factoring. Describe a scenario when the grouping method would be preferred over other methods and provide an example of this type of problem.

Answer 1

I just need a better understanding!

Answer 2

@ganeshie8

Answer 3

@Hero

Answer 4

@Microrobot Can u help please :)

Answer 5

When you group it is more organized, allowing there to be a lower chance of you making errors, it allows shows the steps done perfectly.

Answer 6

Thank youuu

Answer 7

Wait it says to provide an example

Answer 8

So it's both needed

Answer 9

yeah im gonna find an example

Answer 10

like 10x^2 + 8x+ 4 ?

Answer 11

@crystelle, Did you make that one up?

Answer 12

yes!

Answer 13

You shouldn't have....because it doesn't factor....at least not the way you need it to. If you want it to factor properly you have to make sure the value of the discriminant is square. Otherwise it won't factor.

Answer 14

Oh how do I make number that will factor?

Answer 15

Are you familiar with the discriminant?

Answer 16

a little bitt..my teacher was explaing a lil

Answer 17

\[b^2 - 4ac\]

Answer 18

All you have to do is make sure that whatever values of a, b, c you pick

if \(b^2 - 4ac\) produces a perfect square, then the quadratic will be factorable.

Answer 19

Ohhh okay soo hm lemme see

Answer 20

For example, suppose a =3 b = 2, c = -1

Then 2^2 - 4(3)(-1) = 4 + 12 = 16

And 16 is a perfect square.

Answer 21

Therefore, you can write the following quadratic
3x^2 + 2x - 1

And it is factorable

I created this one myself

Answer 22

To factor it by grouping you would have to think of two numbers that multiplied to get -3, yet added to get 2. For this one, those two numbers would obviously be 3 and - 1

So you replace 2 with 3 - 1

3x^2 + 2x - 1 becomes 3x^2 + (3 - 1)x - 1

Then you distribute the x to get

3x^2 + 3x - 1x - 1

Then factor the first two terms to get
3x(x + 1)

and the last two terms to get
-1(x + 1)

And as you can see x + 1 is common to both factorizations
3x(x + 1) - 1(x + 1)

So factor out x + 1 :
(x + 1)(3x - 1)

Answer 23

Any questions?

Answer 24

I undertand it! Thanks so muchhH!! ur really good in math

Answer 25

I learned some of these techniques on this site.

Answer 26

wow! thats pretty tightt

Answer 27

hmm im a little confused on one part

Answer 28

So you replace 2 with 3 - 1

3x^2 + 2x - 1 becomes 3x^2 + (3 - 1)x - 1

Answer 29

@Hero

Answer 30

Correct

Answer 31

no that is what u said but i dont get the x -1 at the end

Answer 32

2x = (3 - 1)x

Answer 33

2 = 3 - 1

Answer 34

All I did was replace 2 with 3 - 1

The x and -1 were already there

Answer 35

\[3x^2 + \color\red{2x} - 1\]

\[3x^2 + \color\red{(3 - 1)x} - 1\]

Answer 36

Or if you can't see it that way then

\(3x^2 + \color\green{2}x - 1\)
\(3x^2 + \color\green{(3 - 1)}x - 1\)