SOLUTION: What are the number of possible values of b so that 4x² + bx - 9 can be factored as the product of two integral first degree polynomials?
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Question 1171716: What are the number of possible values of b so that 4x² + bx - 9 can be factored as the product of two integral first degree polynomials?
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
If the polynomial \ =\ 4x^2\,+\,bx\,-\,9)
can be factored into integral first degree polynomials, then
(4)(-9)}}{4}\,=\,\frac{-b\,\pm\,\sqrt{b^2\,+\,144}}{4}\,\in\ \mathbb{Q})
For that to be true, the radicand must be a perfect square and then both the sum and difference of 
and the radical must be evenly divisible by 4. Hence, the allowable values of 
are:
\,\text{mod} \,4 \,= \, 0\})
The only number I can find that fits into that set is 16.
John
My calculator said it, I believe it, that settles it
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