Determine the value of k if 2x+1 is a factor of kx^3+7x^2+kx-3
Here's a bit more detail, though it's not really necessary
(2x+1)(x-a)(x-b) = 2x^3 + (1-2a-2b)x^2 + (2ab-a-b)x + ab
Now, we want that to be identical to 2x^3 + 7x^2 + 2x - 3 so all the coefficients have to match. That is, since the leading coefficient is k, k=2.
clearly k=2, since the factors would be
(2x+1)(x-a)(x-b)
You don't even have to find a and b, since the only factors of 2 are 2,1,1
But, just to check,
2x^3 + 7x^2 + 2x - 3 = (2x+1)(x+1)(x+3)
K(-1/8)+7/4-k/2-3=0
-k/8+7/4-k/2-3=0
-k/8-k/2=3-7/4
-k/2(1/4+1)=5/4
-k/2(5/4)=5/4
-k/2=1
K=-2
Look what am getting I don't know how you got k=2
ðŸ˜ðŸ˜ðŸ˜
Wow okay I think I have to write this down in paper
But what would you say about my calculation above why didn't I get k=2
Like you do???
I initially took
2x+1=0
x=-1/2
Which I evaluated in the expression
And how where you able to know it is (x-a) why not (x+a)? And (x+b)
So am guessing your initial thought is if x=a and if x=b??