Mathematics, 05.07.2019 08:30 amyeaglin2003
Factor the expression completely over the complex numbers. x3+5x2+9x+45
Answers: 1
![x^3+5x^2+9x+45=x^2(x+5)+9(x+5)=(x+5)(x^2+9)=(*)\\\\x^2+9=x^2+3^2=x^2-(-1)(3^2)=x^2-(i^2)(3^2)=x^2-(3i)^2\\\\i=\sqrt{-1}\to i^2=-1\\\\(*)=(x+5)[x^2-(3i)^2]=(x+5)(x-3i)(x+3i)\\\\Used:\ a^2-b^2=(a-b)(a+b)\\\\\ x^3+5x^2+9x+45=(x+5)(x-3i)(x+3i)](/tpl/images/0053/4218/e1d1c.png)
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Factor the expression completely over the complex numbers. x3+5x2+9x+45...
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