SOLUTION: 1. Explain why a^2 + b^2 cannot be factored. 2. Find a value for k that will make 4x^2 + 6.4x + k a perfect square. Describe the procedure that was used that was not trial and

Question 149831: 1. Explain why a^2 + b^2 cannot be factored.
2. Find a value for k that will make 4x^2 + 6.4x + k a perfect square. Describe the procedure that was used that was not trial and error.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. Explain why a^2 + b^2 cannot be factored.
There is no common factor.
It is not a "difference of squares".
It is not a trinomial.
If it was the product of two binomials the factor form would be:
(a + b)(a+b)
But (a+b)^2 = a^2 + 2ab + b^2.
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It is factorable in the complex number system.
a^2 + b^2 = (a+bi)(a-bi)
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Find a value for k that will make 4x^2 + 6.4x + k a perfect square. Describe the procedure that was used that was not trial and error.
4x^2 + 6.4x + k
sqrt(4x^2) = 2x
sqrt(k)
2(2x)sqrt(k) = 6.4x
4xsqrt(k) = 6.4x
sqrt(k) = 1.6
k = 2.56
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Cheers,
Stan H.
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