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# Manu needs to determine whether x + 4 is a factor of f(x)=−x^4−6x^3+15x−72 .

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Manu needs to determine whether x + 4 is a factor of f(x)=−x^4−6x^3+15x−72 .

How can Manu use the factor theorem to determine whether x + 4 is a factor of f(x) ?

Drag a value, expression, or phrase into each underline to correctly complete the statements.

Manu evaluates  ________   and determines its value to be  _______ . Manu concludes that x + 4 ______ a factor of f(x)=−x^4−6x^3+15x−72 .

The options are f(-4) , -4 , f(0 ), f(4) ,-652 , -72 ,is , is not

I think it should be f(-4) ,-4 , and is not

Sep 12, 2019

#1
+2 (x+4) is not. Sep 12, 2019
#4
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thank you! jjennylove  Sep 12, 2019
#2
+1

Manu needs to determine whether x + 4 is a factor of f(x)=−x^4−6x^3+15x−72 .

How can Manu use the factor theorem to determine whether x + 4 is a factor of f(x) ?

If x + 4 is a factor, then x = -4  is a root.....use synthetic division....if we get a 0, then x + 4  is a factor....so

-4  [ -1       -6         0         15       -72  ]

4          8        -32        68

____________________________

-1      -2          8        -17        -4

We have a remainder of -4, so..  x = -4  is not a root and ..x + 4  is NOT a factor   Sep 12, 2019
#3
+1

Awesome, so I inputted it correct?

Manu evaluates  f(-4)  and determines its value to be  -4 . Manu concludes that x + 4 is not a factor of f(x)=−x^4−6x^3+15x−72 .

Like this ?

jjennylove  Sep 12, 2019
#5
+1

Exactly   ....!!!

If   f(a)   produces anything but a "0"....then "a"  is not a root  and  (x - a)  is not a factor....   CPhill  Sep 12, 2019