Let f(x) be a polynomial. When f(x) is divided by x-1, the quotient is 6x^2+17x-2. It is given that f(1)=4.
(a) Find f(-3).
(b) Factorize f(x).

Thanks a lot!

Question

Let f(x) be a polynomial. When f(x) is divided by x-1, the quotient is 6x^2+17x-2. It is given that f(1)=4.
(a) Find f(-3).
(b) Factorize f(x).

Thanks a lot!

kc_kennylau · Answer

From f(1)=4, what can we say about the remainder?

kc_kennylau · Answer

Then use the division algorithm

anonymous · Answer

i forgot the theorm lol

kc_kennylau · Answer

REMAINDER THEOREM:
If f(a)=r, then the remainder of f(x) divided by (x-a) is r.

anonymous · Answer

then reminder is 4?

kc_kennylau · Answer

yep

kc_kennylau · Answer

Now, realize that when f(x) is divided by (x-1), the quotient is (6x^2+17x-2) and the remainder is 4.

anonymous · Answer

yes

anonymous · Answer

f(-3)=0??

kc_kennylau · Answer

Yes

anonymous · Answer

and i dont know what part b said

kc_kennylau · Answer

Well, since f(-3)=0, we can know that (x+3) is a factor of f(x)

anonymous · Answer

umm...then the quotient multiply by (x+3)?

kc_kennylau · Answer

well, the quotient was generated by x-1, so we shouldn't use the quotient

anonymous · Answer

ohh...

kc_kennylau · Answer

Just expand f(x)=(x-1)(6x^2+17x-2)+4 and then divide that by x+3

anonymous · Answer

ohh i see! thanks a lot

kc_kennylau · Answer

then factorize the quotient you generate too

anonymous · Answer

ok i understand now;) thanks

kc_kennylau · Answer

no problem