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

User N Brouwer
by
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1 Answer

2 votes

Answer:

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

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)]


User KenavR
by
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