factor 9-6x-3x^2

The expression x^2-8x+k cannot be factored if k has the value
A.)7
B.)0
C)-7
D)-9
Please show me how to do these questions step by step so that I can understand & learn

2 answers

9-6x-3x^2
notice the common factor of -3
= -3(x^2 + 2x - 3)
= -3(x + 3)(x - 1)

x^2 - 8x + k

If we have 1x^2 at the front, then the sum of the roots equal the coefficients of the middle term, and the product of the constants.
so x^2 - 8x +7 ??
two numbers that have a sum of -8 and a product of -7 are -1 and -7 , so it will factor
x^2 - 8x + 0 = x(x-8) , also works
x^2 - 8x - 7 ??
mmmh, can't thing of two numbers that add to -8 and multiply to get -7

x^2 - 8x - 9 = (x-9)(x+1)
So, what's the verdict ?
Oh I get it! It's -7! OMG thank u so much I really appreciate it :)
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