Thread: Integral values

Hey guys,

the task: For what integral values of k can 4x^2 + kx - 3 be factored?

My answer:

(4) (-3) = -12 Factors of 12= 1,12 2,6 and 3,4

So are the possible values for k = +11, +4 and +1 or all negative?

They should be positive right, because I am looking for k and the sign is positive in front of k.

You may either have:

or

or

or

I think it should be

(2x-1) (2x+3) or (2x+3)(2x-1)

or

(4x-1)(x+3) or (4x-3)(x+1)

because

(2x+1)(2x-3) = 4x^2 -4x-3 (in that case the value k would be negative) It should be 4x^2 + kx -3 (positive).

I missed a pair:

or

is just an arbitrary integer, it may either be positive or negative.

Okay, I got that.

So, for what integral values of k can 4x^2 + kx + 3 be factored? (note +3, not -3 like in task 1).
I would like to know your answer, because I got an example for 4x^2 + kx + 3 in my book. There is nothing about that k is just an arbitrary integer and it may be either positive or negative.

When it is said "for what integral values of " this implies that can be negative or positive, since the integers are {...-2,-1,0,1,2,...}.

The possibilities here are:

so

so

so

so

so

so

I hate thiss..

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Hello, ford2008!

For what integral values of can be factored?

My answer:

(4) (-3) = -12 . . Factors of 12: (1,12), (2,6) and (3,4).

So are the possible values are: .
This is correct!

My approach . . .

We have: .

Quadratic Formula: .

To be factorable, the discriminant must be a square:
. .

This occurs when: .