+0  
 
0
496
3
avatar

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+91001 
+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
Sort: 

2+0 Answers

 #2
avatar+78618 
+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+91001 
+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

12 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details