# Thread: How to solve this?

1. ## How to solve this?

Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ?
A. –6x2 + 25x + 6
B. 6x2 + 5x + 6
C. 6x2 – 5x + 6
D. 6x2 – 5x – 6
E. 6x2 – 13x – 6

How do I solve this?

For all [r is not equal to plus or minus 2], (r squared - 5r + 6) over (r squared - 4 = ?
A. (r - 3) over (r + 2)
B. (r - 2) over (r + 2)
C. (r - 2) over (r + 3)
D. (r + 3) over (r - 2)
E. (r + 3) over (r + 2)

How do I solve this one as well?

2. Originally Posted by Brazuca
Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ?
A. –6x2 + 25x + 6
B. 6x2 + 5x + 6
C. 6x2 – 5x + 6
D. 6x2 – 5x – 6
E. 6x2 – 13x – 6

How do I solve this?
Are you sure "solve" is the right word?

You've a quantity. It is called 'x'.

"Twice x" is 2x
"Three less than twice x" is 2x-3

"The quantity three times x" is 3x
"Two more than the quantity three times x" is 3x+2

(2x-3)(3x+2) = ???

Next, the constant term must be -6. Discard Choices B & C.

You tell me how to decide between D and E.

3. Thanks. The way it is worded out didn't make any sense to me...

I still need help with my second question.

4. Hullo !

For all [r is not equal to plus or minus 2], (r squared - 5r + 6) over (r squared - 4 = ?
A. (r - 3) over (r + 2)
B. (r - 2) over (r + 2)
C. (r - 2) over (r + 3)
D. (r + 3) over (r - 2)
E. (r + 3) over (r + 2)

How do I solve this one as well?
You can see something nice, it's that the denominator seems to have been reduced !

So try to factor r²-5r+6 and r²-4 !

r²-4=r²-2². And use identity (a²-b²)=(a+b)(a-b).

r²-5r+6 : factor this the way you know, completing the square, using discriminant, find an obvious root (1), etc... ^^

And observe, be concentrated, let the mathematics get into you... hmmm I've just given you the path, now you have to walk.

5. Thanks Moo after a few minutes I understood it that I had to cross out the (r-2)'s