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When the polynomial P(x) = 3x^3 + kx^2 + 45x + 25 is divided by x + 5, the remainder is 0. Which of the following is also a factor of P(x)?

A.)3x-5

B.) x-1

C.) 3x+5

D.) 3x+1

Guest Feb 8, 2016

Best Answer 

 #3
avatar+94105 
+5

When the polynomial P(x) = 3x^3 + kx^2 + 45x + 25 is divided by x + 5, the remainder is 0. Which of the following is also a factor of P(x)?

 

Chris has used the factor theorem.

I will try and walk you through why it works :)

 

If the remainder is 0 when P(x) is divided by x+5 that must mean that   x+5 is a factor of  P(x)

 

so     P(x) = (x+5) (some other polynomial)

 

If this is true then  P(x) must equal zero when   x+5=0     and that happens when  x=-5

 

so  P(x) must =0  when  x=-5

 

that is       P(-5)=0

 

Now I am up to where Chris started.  :)

It will make life easier for you if you work out what I am saying.  The more things you understand the better it is for you :)

Melody  Feb 8, 2016
 #2
avatar+92673 
+5

If x + 5  is a factor, then -5 is a root.....so we can find the value  of "k"  as follows:

 

3(-5)^3 + k(-5)^2 + 45(-5) + 25  = 0

 

-375  + 25k - 225 + 25 = 0

 

25k = 375 + 225 - 25

 

25k = 575

 

k = 23

 

 

And using sythetic division, we have

 

-5   [ 3       23       45       25  ]

                -15      -40       25   

       -------------------------------

       3           8         5        0

 

So......the  remaining polynomial  is    3x^2 + 8x + 5

 

Setting this to 0 and factoring, we get :

 

(3x + 5) (x + 1)  = 0

 

(C)  is the answer

 

 

 

cool cool cool

CPhill  Feb 8, 2016
 #3
avatar+94105 
+5
Best Answer

When the polynomial P(x) = 3x^3 + kx^2 + 45x + 25 is divided by x + 5, the remainder is 0. Which of the following is also a factor of P(x)?

 

Chris has used the factor theorem.

I will try and walk you through why it works :)

 

If the remainder is 0 when P(x) is divided by x+5 that must mean that   x+5 is a factor of  P(x)

 

so     P(x) = (x+5) (some other polynomial)

 

If this is true then  P(x) must equal zero when   x+5=0     and that happens when  x=-5

 

so  P(x) must =0  when  x=-5

 

that is       P(-5)=0

 

Now I am up to where Chris started.  :)

It will make life easier for you if you work out what I am saying.  The more things you understand the better it is for you :)

Melody  Feb 8, 2016

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