+0

0
92
3

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Nov 15, 2019
edited by Guest  Nov 15, 2019

#1
+109563
+1

We are testing to see if  x  = 4  is a root....so

4  [    1       2        -13        -14        24    ]

4         24         44     120

____________________________

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

Nov 15, 2019
#2
+109563
+1

2)

1 [   1    2      -13    - 14       24   ]

1         3     - 10    -24

__________________________

1      3     -  10   -24        0

The remainder is  0....so   ( x - 1)  is a factor ofthe given polynomial

Nov 15, 2019
#3
+109563
0

3)   If x + 2   is a factor, then  x   =  -2   is a root

-2  [ 1     3      -10     -24  ]

-2       -2       24

____________________

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

Nov 15, 2019