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f(x) = x^5 + x^4 + 5x^3 + 5x^2 - 36x - 36 has factors of (x-2), (x+2) and (x+1) Find...

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kristenmarieb... | Student, Grade 10 | (Level 1) Valedictorian

Posted August 3, 2013 at 7:11 AM via web

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f(x) = x^5 + x^4 + 5x^3 + 5x^2 - 36x - 36 has factors of (x-2), (x+2) and (x+1)

Find the remaining factors.

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aruv | High School Teacher | (Level 2) Valedictorian

Posted August 3, 2013 at 8:33 AM (Answer #1)

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`f(x) = x^5 + x^4 + 5x^3 + 5x^2 - 36x - 36 `

since (x+2) is factor of f(x) ,so

`f(x)=x^5+2x^4-x^4-2x^3+7x^3+14x^2-9x^2-18x-18x-36`

`=(x+2)(x^4-x^3+7x^2-9x-18)`

since (x-2) is also factor so

`f(x)=(x+2)(x^4-2x^3+x^3-2x^2+9x^2-18x+9x-18)`

`=(x+2)(x-2)(x^3+x^2+9x+9)`

`=(x+2)(x-2)(x+1)(x^2+9)`

`=(x-2)(x+2)(x+1)(x^2-(3i)^2)`

`=(x-2)(x+2)(x+1)(x-2i)(x+2i)`

Thus other factors are (x-2i) and (x+2i).

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