SOLUTION: Find a value for k that will make {{{4x^2+12x+k}}} a perfect square. Describe the procedure that you used which requires algebra (this is not a trial and error).

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a value for k that will make {{{4x^2+12x+k}}} a perfect square. Describe the procedure that you used which requires algebra (this is not a trial and error).      Log On


   

Question 133599: Find a value for k that will make 4x%5E2%2B12x%2Bk a perfect square. Describe the procedure that you used which requires algebra (this is not a trial and error).
Answer by solver91311(24713) About Me  (Show Source):
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Step 1: Divide the entire polynomial by the coefficient on the x%5E2 term. x%5E2%2B3x%2Bk%2F4

Step 2: Divide the coefficient on the x term by 2: Result: 3%2F2

Step 3: Square the result of step 2: Result: 9%2F4

The result of step 3 is the value of the constant term required to make x%5E2%2B3x%2Bk%2F4 a perfect square, therefore k%2F4=9%2F4 => k=9

x%5E2%2B3x%2B9%2F4 can be multiplied by 4 to reverse the effects of step 1, resulting in 4x%5E2%2B12x%2B9 which then factors to %282x%2B3%29%282x%2B3%29=%282x%2B3%29%5E2