# Need help with Factoring and Solving Equations.

• Jan 10th 2011, 09:08 PM
donaldmax
Need help with Factoring and Solving Equations.
Hi! Ive been trying to do these problems for a while and Im stumped. I finished 13 problems and fully understand them , but I don't know how to do these problems. It would be nice if you could write each step out or the answer at the very least. Or hints or tips, like which theorem or something to use. Shortcuts.

1. P(x) = 5x + 2kx^4 + 4x^3 - 5k
P(x)/2x+4 has a remainder of 3, find k.

2. f(x) = -2x^4 + ix^3 - 2kx^2 - x + 3
Find k given that (x + 1 + i) is a factor

I dont even know how to do 1 and 2.

is there any short cuts? (Crying)

Thanks for answering my questions. I really don't understand these problems. I mean I do, but I want to know shorter ways since everything takes so long.
I dont know when to use synthetic division, factor theorem, etc.
I need help
(Crying)
• Jan 10th 2011, 09:16 PM
pickslides
Hi donaldmax, welcome to the forum.

Before your next post please review the forum rules as there is a number of them you have breached.

Quote:

Originally Posted by donaldmax

1. P(x) = 5x + 2kx^4 + 4x^3 - 5k
P(x)/2x+4 has a remainder of 3, find k.

\$\displaystyle \displaystyle 2x+4 = 0 \implies x=-2\$

Therefore \$\displaystyle \displaystyle P(-2) = 5(-2) + 2k(-2)^4 + 4(-2)^3 - 5k = 3\$

Finish him off, kind regards,
• Jan 10th 2011, 09:33 PM
donaldmax
number 1 and 2
for number 1
What does p(x)/2x+4 mean?
its like dividing the p(x)?
O_O
u told me to do that.
i found that k = 5/3. is that the answer? do i multiply anything else?
(Wondering)

and for number 2

do i plug in (1-i) and then solve it?
or is there more steps? like doing
(x+1+i)(x+i-i) then do that
then plug into
original equation
find roots/
and then plug roots into that?
(Crying)
• Jan 10th 2011, 09:43 PM
pickslides
Quote:

Originally Posted by donaldmax
u told me to do that.
i found that k = 5/3. is that the answer? do i multiply anything else?

No need for any further multipication.

Quote:

Originally Posted by donaldmax

and for number 2

do i plug in (1-i) and then solve it?
or is there more steps? like doing
(x+1+i)(x+i-i) then do that
then plug into
original equation
find roots/

Solve

\$\displaystyle \displaystyle f(-i-1) = -2(-i-1)^4 + i(-i-1)^3 - 2k(-i-1)^2 -(-i-1) + 3 = 0\$
• Jan 10th 2011, 09:47 PM
donaldmax
how did you get -i-1?
and this is factor theorem right?
• Jan 10th 2011, 09:49 PM
pickslides
Yep,

If \$\displaystyle P(a) = 0\$ then \$\displaystyle x-a\$ is a factor