SOLUTION: For the polynomial below, -3 is a zero. f(x)= x^3-x^2-10x+6 Express f(x) as a product of linear factors. f(x)=

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Question 960773: For the polynomial below, -3 is a zero.
f(x)= x^3-x^2-10x+6
Express f(x) as a product of linear factors.
f(x)=
Found 2 solutions by Edwin McCravy, lwsshak3:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%22f%28x%29%22=+1x%5E3-1x%5E2-10x%2B6   -3 is a zero.

-3 | 1  -1  -10   6
   |    -3   12  -6
     1  -4    2   0

So we have factored f(x) as

%22f%28x%29%22=+%28x%2B3%29%28x%5E2-4x%2B2%29

Now we must factor x%5E2-4x%2B2 into two linear factors.

We find its zeros by setting it equal to 0

x%5E2-4x%2B2=0

x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%282%29%29%29%2F%282%281%29%29+

x+=+%284+%2B-+sqrt%2816-8%29%29%2F2+

x+=+%284+%2B-+sqrt%288%29%29%2F2+

x+=+%284+%2B-+sqrt%284%2A2%29%29%2F2+

x+=+%284+%2B-+2sqrt%282%29%29%2F2+

x+=+%282%282+%2B-+sqrt%282%29%29%29%2F2+

x+=+%28cross%282%29%282+%2B-+sqrt%282%29%29%29%2Fcross%282%29+

x+=+2+%2B-+sqrt%282%29+

so the other two zeros are 2+%2B+sqrt%282%29+ and 2+-+sqrt%282%29+

So the remaining linear factors are %28x%5E%22%22+-%28+2+%2B+sqrt%282%29%29%29+ and %28x%5E%22%22+-%28+2+-+sqrt%282%29%29%29+



%22f%28x%29%22=+%28x%2B3%29%28x+-+2+-+sqrt%282%29%29%28x+-+2+%2B+sqrt%282%29%29%29+

Edwin

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
For the polynomial below, -3 is a zero.
f(x)= x^3-x^2-10x+6
Express f(x) as a product of linear factors.
f(x)=
***
By synthetic division:
....-3...|....1....-1....-10.....6........
....................-3......12.....-6.........
.............1.....-4.......2.......0
f(x)=(x+3)(x^2-4x+2)