find value of constant C such that the clause can be canceled in some manner. What will be the canceled form of the clause.
-presumably C is a constant, and also an integer.
-polynomial factorization will be attempted
-cancelling of rational numbers keeps the value the same. In cancelling, you divide numerator and denominator by the same number (other number than 1 or 0).
The Attempt at a Solution
we know initially that we have to have something like
this is because there will be no further factorization for the divisor. For the clause to be cancellable, I think the (x+5) must be one of the factors in the upstairs of the division line.
and from an educated guess point of view, I think we have to get the 3x^2 term finished somehow. So, that 3x^2 is the product of something.
if the other integer is an unknown one. maybe it can be represented by letter r
(x+5)(3x+r) should equal what we originally had upstairs (3x^2 +x +C) and we know C will be an integer also
At this point I was honestly a little bit stumped and I had to review some older Khan academy problems about factoring. I'm still alittle bit unsure why the so-called analytical method of finding the factorization works...
I was fiddling around with the clause (x+5)*(3x+r)
and if you multiply it out, it comes out such as
Well... looking at that clause in that form it looks like xr +15x=1x must be a true equation.
Because this would allow you to choose the r so that the factors are correct for the original clause's terms for x^1 terms
So, I suppose firstly r= 1-15
C= 5*(-14) = -70
[(x+5)(3x-14)]= 3x^2 -14x +15x -70