Mathematics, 06.01.2022 14:00 he0gaubong
The solutions to a polynomial equation include 1-12i, (-8-i), and 6. Write the factors of these solutions.
Answers: 2
![\begin{cases} x = 6\implies &x-6=0\\ x=1-12i\implies &x-1+12i=0\\ x=1+12i\implies &x-1-12i=0\\ x=-8-i\implies &x+8+i=0\\ x-8+i\implies &x+8-i=0 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ x-6=0\implies \stackrel{factor}{(x-6)} \\\\[-0.35em] ~\dotfill\\\\ (x-1+12i)(x-1-12i)=0\implies \underset{\textit{difference of squaeres}}{[(x-1)+12i][(x-1)-12i]=0}](/tpl/images/2611/5283/a5992.png)
![[(x-1)^2-(12i)^2]=0\implies [(x^2-2x+1)-(12^2i^2)]=0 \\\\\\ (x^2-2x+1)-(144(-1))=0\implies x^2-2x+1+144=0 \\\\\\ x^2-2x+145=0\implies \stackrel{factor}{(x^2-2x+145)} \\\\[-0.35em] ~\dotfill\\\\ (x+8+i)(x+8-i)=0\implies \underset{\textit{difference of squares}}{[(x+8)+i][(x+8)-i]=0} \\\\\\\ [(x+8)^2-(i)^2]=0\implies (x^2+16x+64)-(i^2)=0 \\\\\\ x^2+16x+64-(-1)=0\implies \implies x^2+16x+65=0\implies \stackrel{factor}{x^2+16x+65}](/tpl/images/2611/5283/6d972.png)
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The solutions to a polynomial equation include 1-12i, (-8-i), and 6. Write the factors of these solu...
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