+128408 We are testing to see if x = 4 is a root....so
4 [ 1 2 -13 -14 24 ]
4 24 44 120
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1 6 11 30 144
We get a remainder of 144.......f x = 4 is a root we should get a remainder of 0
So
x - 4 is not a factor of the given polynomial
+128408 2)
1 [ 1 2 -13 - 14 24 ]
1 3 - 10 -24
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1 3 - 10 -24 0
The remainder is 0....so ( x - 1) is a factor ofthe given polynomial
+128408 3) If x + 2 is a factor, then x = -2 is a root
-2 [ 1 3 -10 -24 ]
-2 -2 24
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1 1 -12 0
4) the remaining ploynomilal is x^2 + x -12
This factors as ( x + 4) ( x - 3)
So x = - 4 is a root and so is x = 3
5 ) The complet factoriztion of the original polynomial is
( x + 4) ( x + 2) (x - 1) ( x - 3)
The zeroes are x = -4 x = -2 x = 1 and x = 3
Here's the graph : https://www.desmos.com/calculator/njts63vjnn
