Factorise (x -1)^2 + 4 (x-1) + 3?

Question

Could you explain it as you are doing it, thanks?

Is expanding the way to go about it?

Answer 1

Let y=x-1

So we get

y^2+4y+3

Which factors to

(y+3)(y+1)

Now replace y with (x-1)

((x-1)+3)((x-1)+1)

Now add like terms (in the first parenthesis its -1+3=2 in the 2nd its -1+1=0)

So we get:

(x+2)(x)

Did that make sense? If not ask further.

Answer 2

We do a sneaky transformation, work with the transformation, and then translate back to the starting variable. Step 1. Let u = (x-1). Then we have u^2 + 4u +3. This factors nicely to (u+3)(u+1). Now, we replace u with x-1 to get (x+2)(x).

Answer 3

look at it as thought the polynomial was:
y^2+4y+3
this factors into:
(y+1)*(y+3)
plug the x-1 back in and it's:
x*(x+2)
expanding works too:
(x-1)^2=x^2-2x+1 so
x^2-2x+1+4x-4+3 = x^2+2x = x*(x+2)

Answer 4

let's break this up
(x-1)^2 means this
square the first term: x^2
multiply the two terms and then double it: -1x *2 = -2x
lastly square the last term: 1
now put it all together
x^2 - 2x + 1

4(x-1) simplifies to 4x -4 (you multiplied the four by the x and the -1)

Now put everything together and you get:
x^2 - 2x + 1 + 4x - 4 + 3

Collect like terms
-2x + 4x = 2x
1 - 4 + 3 = 0

x^2 + 2x + 0

Answer 5

(x -1)^2 + 4 (x-1) + 3
= (x-1+3)(x-1+1)
= (x-2)(x)
---------
You don't need to expand it. Just treat (x-1) as a whole.

Answer 6

x^2+2x=0
x(x+2)=o