+0

# Factor the polynomial function over the complex number.

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861
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Factor the polynomial function over the complex number.

f(x) = x^4 + 9x^3 + 15x^2 + 9x + 14

Oct 27, 2017

### 3+0 Answers

#1
+96956
+4

Factor the polynomial function over the complex number.

f(x) = x^4 + 9x^3 + 15x^2 + 9x + 14

any roots must be factors of 14    and when they are substituted they must make the function =0

By substitution I found that x=-7 and x=-2 are both roots of this function.

So two of the factors are (x+7) and (x+2)

(x+7)(x+2)=x^2+9x+14

I divided f(x) by x^2+9x+14 and found the answer to be (x^2+1)

so

\(f(x) = x^4 + 9x^3 + 15x^2 + 9x + 14\\ f(x) = (x+7)(x+2)(x^2+1)\\ f(x) = (x+7)(x+2)(x+i))(x-i)\\\)

.
Oct 27, 2017
#2
+9912
+3

Factor the polynomial function over the complex number.

f(x) = x^4 + 9x^3 + 15x^2 + 9x + 14

Oct 27, 2017
#3
+95859
+2

x^4 + 9x^3 + 15x^2 + 9x + 14

Split  15x^2  into  14x^2  +  x^2

x^4 + 9x^3 + 14x^2 + x^2 + 9x + 14     factor as

x^2  [x^2 + 9x + 14 ]  +  1 [ x^2 + 9x + 14 ]   take out GCF

[ x^2 + 1 ] [ x^2 + 9x + 14 ]

[ x^2 + 1 ] [  x + 7 ] [ x + 2 ]

Oct 27, 2017

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