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Find b: (x+2) is a factor of b^2x^4 + 5mx^3 + x^2 - 7x -2Show all work

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foxwit | Student, Undergraduate | (Level 1) Salutatorian

Posted August 19, 2012 at 11:17 PM via web

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Find b:

(x+2) is a factor of b^2x^4 + 5mx^3 + x^2 - 7x -2

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lfryerda | High School Teacher | (Level 2) Educator

Posted August 20, 2012 at 12:13 AM (Answer #1)

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If `x+2` is a factor of `f(x)=b^2x^4+5mx^3+x^2-7x-2` , then by the factor theorem, `f(-2)=0` .  This will give us an equation in b that can be solved.

`b^2(-2)^4+5m(-2)^3+(-2)^2-7(-2)-2=0`

`16b^2-40m+4+14-2=0`

`16b^2=40m-16`

`b^2=5/2m-1`

`b=+-sqrt{5/2m-1}`

Since x+2 is a factor, `b=+-sqrt{5/2m-1}` .

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