Year 11 Quadratics - Factorisiation

[Jsy443]

Hey, can anyone help me with this question and show me how the factorisation is done for this equation?

-x^2 + 4x - 4

I forgot how to factorise this, and there are questions that are really similar following it. Just need someone to explain the method to factorise this. Thanks

[PolySquared]

Hey, can anyone help me with this question and show me how the factorisation is done for this equation?

-x^2 + 4x - 4

I forgot how to factorise this, and there are questions that are really similar following it. Just need someone to explain the method to factorise this. Thanks

Have you tried completing the square?

[Bell9565]

-x^2 + 4x - 4
Okay so factorise out -1
-1(x^2 - 4x + 4)
Then this takes a while to get the hang of but -2 multiplyed my -2 equals 4 and adds to -4 so place them in brackets as so
-(x-2)(x-2)
and this can be simplified to
-(x-2)^2
Sorry if that doesn't quite make sense haha 

[Sine]

Hey, can anyone help me with this question and show me how the factorisation is done for this equation?

-x^2 + 4x - 4

I forgot how to factorise this, and there are questions that are really similar following it. Just need someone to explain the method to factorise this. Thanks

Take out the negative, makes it a lot easier to work with when the x^2 has a invisible coefficient of 1

Think of what numbers multiply to 4 but add to -4. Which choose from the list that are the factors of 4 which are (1,4), (-1,-4), (2,2) and (-2,-2)
All of these multply to 4 but only (-2,-2) adds to -4 so we choose those as the factors.

[snowisawesome]

Hey, can anyone help me with this question and show me how the factorisation is done for this equation?

-x^2 + 4x - 4

I forgot how to factorise this, and there are questions that are really similar following it. Just need someone to explain the method to factorise this. Thanks

Hi
The numbers need to multiply to get 4 and add to get -4
So it looks like this
-(x^2-4x+4)
so x^2 - 4x + 4
= (x-2)(x-2)
so it becomes -(x-2)(x-2)
Hope this helps, and welcome to atar notes
Enjoy the ride onboard the forums

[VanillaRice]

Hey, can anyone help me with this question and show me how the factorisation is done for this equation?

-x^2 + 4x - 4

I forgot how to factorise this, and there are questions that are really similar following it. Just need someone to explain the method to factorise this. Thanks

In addition to the above, you can also identify this as a perfect square, and factorise by bypassing a few intermediary steps:

What you should notice is that the coefficient of x is double 2, and the (positive) constant is 2 squared (expanding the answer might make this clearer). You might ask "How can I tell when its a perfect square?". With practise, it'll become easier to identify them.

Hope this helps

[ExamPro]

Here is ExamPro's treatise on quadratics. It's part of our detailed solution to the first question of the book, but it is 6 pages of general quadratic solution theory before it dives into the specific problem asked, so you won't need to have a copy of the book with you.

Hopefully it will put to rest any issues you have with quadratics. Best of luck with your studies

[snowisawesome]

Here is ExamPro's treatise on quadratics. It's part of our detailed solution to the first question of the book, but it is 6 pages of general quadratic solution theory before it dives into the specific problem asked, so you won't need to have a copy of the book with you.

Hopefully it will put to rest any issues you have with quadratics. Best of luck with your studies

Would these skills help me with unit 3/4 methods this year?

[ExamPro]

Would these skills help me with unit 3/4 methods this year?

That excerpt is from the 3&4 book, but is directly relevant to 1&2 assumed knowledge.

Factorising quadratics is an essential skill in Methods 3&4! It's one of, if not the most relied-upon pieces of assumed knowledge from Units 1&2. So many questions on the Units 3&4 end-of-year Methods exams boil down to a quadratic at the end! Being extremely sharp and well-practised with them will score you a ton of marks in 3&4.