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1 May, 22:14

Find the complex factors of the quadratic trinomial x^2+8x+17

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  1. 1 May, 22:26
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    [x + (4-i) ][x + (4+i) ]

    Step-by-step explanation:

    Complete the square then regroup the first two terms. Add and subtract: (b/2) ^2 = (8/2) ^2=16

    x^2+8x+17 = (x^2+8x) + 17

    = (x^2+8x+16) + 17-16

    = (x+4) ^2+1 create a difference of squares using i^2 = - 1

    = (x+4) ^2 - (-1)

    = (x+4) ^2 - i^2 use the difference of two squares identity

    =[ (x+4) - i][ (x+4) + i]

    =[x + (4-i) ][x + (4+i) ]
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