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# What is the factored form of the function f(x)=x 3 +7x 2 +8x−16 ?

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1. What is the factored form of the function f(x)=x3+7x2+8x−16 ?

f(x)= (    )  (     )   (     )

2.

What is the polynomial function of least degree whose only zeros are −3 , −2 , and 4?

Drag a value to each parenthese to correctly state the function.

f(x)= x3(    )  x2  (     )     x (      )

the options are -24 ,-14,-9 ,-1, 1,9,14,24

i am unsure on both questions, can someone help me?

Aug 21, 2019
edited by jjennylove  Aug 21, 2019

#1
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are you graphing functions?

Aug 21, 2019
#2
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no just these 2 questions

jjennylove  Aug 21, 2019
#3
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(1)   x^3  + 7x^2 + 8x - 16

Note that   x  = 1   produces a zero....so....(x -1)  is a factor...and we can use synthetic division to find the remaining polynomial

1 [   1     7       8      - 16   ]

1       8        16

_____________________

1     8      16         0

The remainig polynomial is   x^2  + 8x + 16    which factors as  (x + 4) (x + 4)

So.....we have  (x - 1) (x + 4) ( x + 4)   Aug 21, 2019
#4
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What is the polynomial function of least degree whose only zeros are −3 , −2 , and 4?

We have

( x + 3)  ( x + 2) ( x - 4)  =

(x^2 + 5x + 6) ( x - 4)  =

x^3 + 5x^2 + 6x  - 4x^2 - 20x - 24  =

1x^3  +  1x^2  - 14x  - 24   Aug 21, 2019
edited by CPhill  Aug 21, 2019
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there only 3 boxes you included 4, im quite unsure. All the work makes sense but theres only 3 boxes to fill

f(x)= x3(    )  x2  (     )     x (      )

the options are -24 ,-14,-9 ,-1, 1,9,14,24

jjennylove  Aug 23, 2019
edited by Guest  Aug 23, 2019