The factored form of 2(x - 2)^2 - (x - 2) - 1 is...? Please! I need help!?

Question

These are the last few questions that I need help with to help my Grandson. Thankyou so much! Best answer will get the points!

The factored form of 2(x - 2)^2 - (x - 2) - 1 is?

Answer 1

let u = (x-2).

then you need to factor this first:

2u^2 -u -1
=(2u +1)(u -1).

Then back substitute for x:

=(2(x-2)+1)((x-2)-1)

=(2x -4 +1)(x -2 -1)

=(2x -3)(x -3)

Answer 2

2(x-2)^2-(x-2)-1=

2(x^2-4x+4)-(x-2)-1= (start by multiplying (x-2) times itself in step 1)

2x^2-8x+8-x+2-1= (next, distribute)

2x^2-9x+9= (then combine like terms)

Now to factor: 2x^2 can only be factored into two terms: 2x and x.

9 is easily factored into 3 times 3.

Since the middle term is negative, the signs between terms are negative. So the factored form of 2x^2-9x+9 is (2x-3)(x-3).

Answer 3

Replace the value (x-2) with y and then factor the equation 2y^2 -y -1. Once you get the factors replace y with (x-2) to get the answer in terms of x.

This is factorable but you or your Grandson should do the work to learn how to do it.

Answer 4

First you need to combine like terms.

2(x - 2)^2 - (x - 2) - 1
2[(x-2)(x-2)]- (x-2)-1
2(x^2-4x+4)-(x-2)-1
2x^2-8x+8-x+2-1
=2x^2-9x+9
Then this can be factored further..

(2x-3)(x-3)

Hope this helps :-)

Answer 5

2(x - 2)^2 - (x - 2) - 1
=2a^2 -a -1 if you let a=x-2
=(2a+1)(a-1)
Now resubstitute
=(2(x-2)+1)((x-2)-1)
=(2x-3)(x-3)

Answer 6

replace "(x-2)" as "A".

2A^2-A-1
Factor:
(A-1)(2A+1)
Substitute "A" with "(x-2)"
(x-2-1)[2(x-2)+1]
(x-3)(2x-4+1)
Answer:
(x-3)(2x-3)

Answer 7

yes