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# ​ One of the zeros of the polynomial function is 2.

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One of the zeros of the polynomial function is 2.

Feb 8, 2018

#2
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Use synthetic division to find  (x4 - 3x3 - 23x2 + 75x - 50)  /  (x - 2) .

(x4 - 3x3 - 23x2 + 75x - 50)  /  (x - 2)   =  x3 - x2 - 25x + 25

So

x4 - 3x3 - 23x2 + 75x - 50   =   (x - 2)(x3 - x2 - 25x + 25)

Now we can factor   x3 - x2 - 25x + 25  .

x3 - x2 - 25x + 25   =   x2(x - 1) - 25(x - 1)   =   (x - 1)(x2 - 25)   =   (x - 1)(x - 5)(x + 5)

So

x4 - 3x3 - 23x2 + 75x - 50   =   (x - 2)(x - 1)(x - 5)(x + 5)

Feb 8, 2018
edited by hectictar  Feb 10, 2018

#2
+8146
+3

Use synthetic division to find  (x4 - 3x3 - 23x2 + 75x - 50)  /  (x - 2) .

(x4 - 3x3 - 23x2 + 75x - 50)  /  (x - 2)   =  x3 - x2 - 25x + 25

So

x4 - 3x3 - 23x2 + 75x - 50   =   (x - 2)(x3 - x2 - 25x + 25)

Now we can factor   x3 - x2 - 25x + 25  .

x3 - x2 - 25x + 25   =   x2(x - 1) - 25(x - 1)   =   (x - 1)(x2 - 25)   =   (x - 1)(x - 5)(x + 5)

So

x4 - 3x3 - 23x2 + 75x - 50   =   (x - 2)(x - 1)(x - 5)(x + 5)

hectictar Feb 8, 2018
edited by hectictar  Feb 10, 2018