You are Here: Home >< Maths

# Factorising Quadratic when a does not = 1 Watch

1. So I get most of it, there's just one step that I don't understand. For example:

-7x2+14x-22

= -7(x2-2x)-22
=-7(x2-2x+1-1)-22

The next bit I don't get. You're supposed to factorise the bit in brackets, excluding the -1, i.e. you're supposed to factorise x2-2x+1 aren't you? But the video I'm watching says it should be (x-1)2, but I don't understand why... Can anyone explain why? Thanks!
2. can you post the video please brother?
3. when 'a' does not equal 1, you find two numbers that multiply to give 'a x c' and add to give 'b' then rewrite the original equations but instead of 'b' you'll write those two values.
4. (Original post by Prokaryotic_crap)
can you post the video please brother?
5. from the:

=

=
bracketing the +1 with x^2 and -2x

=

=

EDITED)
6. (Original post by Hasufel)
from the:

=

=
bracketing the +1 with x^2 and -2x

=

=

Okay, so how did the x^2 -2x +1 become (x-2)^2?
7. at the top, you said (x-1)^2

if video says (x-2)^2 that`s balls!
8. (Original post by Qaiys)
Okay, so how did the x^2 -2x +1 become (x-2)^2?
It doesn't - it should be (x-1)^2
9. (Original post by davros)
It doesn't - it should be (x-1)^2
So how does it become that? :P
10. (Original post by Qaiys)
So I get most of it, there's just one step that I don't understand. For example:

-7x2+14x-22

= -7(x2-2x)-22
=-7(x2-2x+1-1)-22

The next bit I don't get. You're supposed to factorise the bit in brackets, excluding the -1, i.e. you're supposed to factorise x2-2x+1 aren't you? But the video I'm watching says it should be (x-1)2, but I don't understand why... Can anyone explain why? Thanks!
If thats what you need factoring..

ax2 - bx + c = x2 - 2x + 1 = (x-1)2

When factoring, remember that if it follows the standard form quadratic equation (ax2 + bx + c = 0), then to make things easier for yourself begin with two empty brackets.

1. ( )( ) We see at this point, upon examining your equation that we have x2 - 2x + 1. As we know, this means simply that x is multiplying by itself. So it follows that:

2. (x )(x ). To establish what we need next, we should consider the "c" in the standard form, and find what C equals in our equation. In this instance, the number we are looking for is = x2 - 2x + 1. So we take 1, and consider its its factors.. (just 1 lol.) Usually we would examine which pair of factors would combine together to give us "b". (x2- 2x + 1). However in this case, as 1 only has a factor of 1, we neednt bother with that step. So we proceed to fill in the brackets.

3. (x 1)(x 1). Be sure to leave a space between x and 1 (or whatever future number you insert here). As mentioned earlier, we have to consider that since we know the factors of c (1 in this case) combine to make bx, we know that in some way, somehow, 1 and 1 combine to make -2 (x2- 2x + 1) So we examine in what way our pair of factors combine to make -2, in this case, it's -1 and -1.

4. (x - 1)(x - 1). So we simply added the - sign between the x and the 1. Had b = +2 in x2+ 2x + 1, then we wouldve used + signs in the brackets instead.

5 (x - 1)2 . Because (x-1) multiplied by (x-1) is the same as (x-1)2

At the risk of this post getting marked at a dissertation we'll quickly prove how (x-1)2 = x2 - 2x + 1. We'll use the FOIL method... because it's fresher than tupperware. First Outer Inner Last.

(x - 1)(x - 1) = x2 First (x times x is x2)
(x - 1)(x - 1) = x2-1x Outer (x times -1 = -1x)
(x - 1)(x - 1) = x2 -1x -1x Inner (x times -1 = -1x)
(x - 1)(x - 1) = x2 -1x -1x +1 Last (-1 times -1 = +1.)

So would you agree, that by simplifying the above , we get:
(x - 1)2 = x2 -2x +1

If so, GOOD JOB MOTHER ****ER CAUSE WE JUST WENT QUADRATIC UP IN THIS *****
11. (Original post by Hasufel)
from the:

=

=
bracketing the +1 with x^2 and -2x

=

=

oops

I think you meant (x-1)
12. (Original post by Qaiys)
So I get most of it, there's just one step that I don't understand. For example:

-7x2+14x-22

= -7(x2-2x)-22
=-7(x2-2x+1-1)-22

The next bit I don't get. You're supposed to factorise the bit in brackets, excluding the -1, i.e. you're supposed to factorise x2-2x+1 aren't you? But the video I'm watching says it should be (x-1)2, but I don't understand why... Can anyone explain why? Thanks!
You appear to be completing the square rather than factorising - what does your question ask?
13. (Original post by Reece Sure)
If thats what you need factoring..

ax2 - bx + c = x2 - 2x + 1 = (x-1)2

When factoring, remember that if it follows the standard form quadratic equation (ax2 + bx + c = 0), then to make things easier for yourself begin with two empty brackets.

1. ( )( ) We see at this point, upon examining your equation that we have x2 - 2x + 1. As we know, this means simply that x is multiplying by itself. So it follows that:

2. (x )(x ). To establish what we need next, we should consider the "c" in the standard form, and find what C equals in our equation. In this instance, the number we are looking for is = x2 - 2x + 1. So we take 1, and consider its its factors.. (just 1 lol.) Usually we would examine which pair of factors would combine together to give us "b". (x2- 2x + 1). However in this case, as 1 only has a factor of 1, we neednt bother with that step. So we proceed to fill in the brackets.

3. (x 1)(x 1). Be sure to leave a space between x and 1 (or whatever future number you insert here). As mentioned earlier, we have to consider that since we know the factors of c (1 in this case) combine to make bx, we know that in some way, somehow, 1 and 1 combine to make -2 (x2- 2x + 1) So we examine in what way our pair of factors combine to make -2, in this case, it's -1 and -1.

4. (x - 1)(x - 1). So we simply added the - sign between the x and the 1. Had b = +2 in x2+ 2x + 1, then we wouldve used + signs in the brackets instead.

5 (x - 1)2 . Because (x-1) multiplied by (x-1) is the same as (x-1)2

At the risk of this post getting marked at a dissertation we'll quickly prove how (x-1)2 = x2 - 2x + 1. We'll use the FOIL method... because it's fresher than tupperware. First Outer Inner Last.

(x - 1)(x - 1) = x2 First (x times x is x2)
(x - 1)(x - 1) = x2-1x Outer (x times -1 = -1x)
(x - 1)(x - 1) = x2 -1x -1x Inner (x times -1 = -1x)
(x - 1)(x - 1) = x2 -1x -1x +1 Last (-1 times -1 = +1.)

So would you agree, that by simplifying the above , we get:
(x - 1)2 = x2 -2x +1

If so, GOOD JOB MOTHER ****ER CAUSE WE JUST WENT QUADRATIC UP IN THIS *****
Hahaa thanks a lot!!
14. (Original post by TenOfThem)
You appear to be completing the square rather than factorising - what does your question ask?
It was completing the square, I just got a bit confused on the way but I understand now
15. (Original post by TenOfThem)
oops

I think you meant (x-1)

Aaagh! to quote stewie: "*****...i just got jacked, *****!"

SORTED NOW, THOUGH
16. (Original post by Qaiys)
Hahaa thanks a lot!!
No problem. Hope that helped clear things up!

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: July 8, 2014
Today on TSR

### Oxford grad sues for £1m

Claims damages because he didn't get a first

### 'No evidence of shots fired' at Oxford Circus

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.