Factor Theorem Help Please!

Hi,

Can someone help me with the following question...

The cubic polynomial f(x) is given by

f(x) = x^3 + ax + b

where a and b are constants. It is given that (x+1) is a factor of f(x) and that the remainder when f(x) is divided by (x-3) is 16

a) Find the values of a and b

b) Hence verify that f(2)=0, and factorise f(x) completely

Cheers,

Sarg

Reply 1

hey_its_nay

2

if x+1 is a factor then if u sub in -1 it will = 0
(-1)^3 +a(-1)+b=0..........-1-a+b=0

if u sub in 3 then it will = 16
(3)^3 +(3)a + b ..............27+3a +b=16.........3a+b=-11
you now hav a set of simultaneous equations u can use to find a and b
3a+b=-11(1)
b-a=1 (2)
(1)-(2) gives 4a=-12...a=-3
therefore b=-2

Reply 2

Clarity Incognito

11

Sarg92

Hi,

Can someone help me with the following question...

The cubic polynomial f(x) is given by

f(x) = x^3 + ax + b

where a and b are constants. It is given that (x+1) is a factor of f(x) and that the remainder when f(x) is divided by (x-3) is 16

a) Find the values of a and b

b) Hence verify that f(2)=0, and factorise f(x) completely

Cheers,

Sarg

What does the factor theorem say? How can you use the information they have given above in f(x)? By inputting the information into f(x) separately will get you simultaneous equations in a and b, which you can then solve.