If (x + 3) is a factor of x³ + kx² - 8x + 48, find k.

2. Hello,

Originally Posted by tim_mannire
If (x + 3) is a factor of x³ + kx² - 8x + 48, find k.
Let $\displaystyle f(x)=x^3+kx^2-8x+48$.

If (x+3) is a factor, then -3 is a root.

Which means that $\displaystyle f(-3)=0$.

Can you continue ?

3. Originally Posted by Moo
Hello,

Let $\displaystyle f(x)=x^3+kx^2-8x+48$.

If (x+3) is a factor, then -3 is a root.

Which means that $\displaystyle f(-3)=0$.

Can you continue ?
yes I have done that, however, my peers have a few different answers to me. Do you know what K would would equal in this situation?

4. Originally Posted by tim_mannire
If (x + 3) is a factor of x³ + kx² - 8x + 48, find k.
when f(x) is divided by x-a, we have
f(x) = (x-a)Q(x)+Remainder
-> f(x) = (x-a)Q(x)+f(a)
IF f(a) = 0, the remainder is 0.
then f(x) = (x-a)Q(x)

f(x) = x³ + kx² - 8x + 48
f(-3) = (-3)
³+k(-3)²-8(-3)+48 = 0
-27+9k+24+48 = 0
9k = -45
k = -5

5. ## Check it out

U should use factor theorem
if x+3 is i factor of x^3+kx^2-8x+48 then on substituting x=-3 the value of polynomial will become equal to 0(u may ask why is that so in another thread or u may post it in the reply)
therfor (-3)^3+k(-3)^2-8(-3)+48=0 or -27+9k+24+48=0
or 9k=-45 therefor k=-5.

6. Originally Posted by nikhil
U should use factor theorem
if x+3 is i factor of x^3+kx^2-8x+48 then on substituting x=-3 the value of polynomial will become equal to 0(u may ask why is that so in another thread or u may post it in the reply)
therfor (-3)^3+k(-3)^2-8(-3)+48=0 or -27+9k+24+48=0
or 9k=45 therefor k=5.
Please do not use U for ewe, or you or, .. Ewe will just confuse everyone otherwise.

Also it is against the rules here to use l33t or text abreviations and if ewe do it habitualy ewe will start to collect infractions.

RonL

7. ## Sooooo...... Sorry

Originally Posted by CaptainBlack
Please do not use U for ewe, or you or, .. Ewe will just confuse everyone otherwise.

Also it is against the rules here to use l33t or text abreviations and if ewe do it habitualy ewe will start to collect infractions.

RonL
sorry sir,next time this point will be kept in mind.