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9. State how many linear factors each polynomial has.

1.   f(x) = x3 + 24x – 2x + 6 = 0

 

2.   f(x) = x16 + 72x6 + x = 0

 

 

3.   f(x) = (x + 2)

 Mar 25, 2019
 #1
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\(\text{a linear factor is of the form }(x-a)\)

 

\(f(x) = x^3 + 24x^2 - 2x + 6 \text{ (I'm assuming what was written was a typo)}\\ \text{This doesn't seem to have any linear factors} \)

 

\(f(x) = x^{16}+72x^6 + x = x(x^{15}+72x^5+1)\\ \text{This has one linear factor, }x\)

 

\(f(x)=(x+2)\text{ clearly has a single linear factor which is itself}\)

.
 Mar 25, 2019

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