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

#3**+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**+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

CPhill
Feb 8, 2016

#3**+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