Question

You are given that f(x) = x^3 - 19x + 30

1.) Calculate f(0) and f(3). Hence write down a factor of f(x).


Thanks.

Answer 1

@amistre64 @Hero

Answer 2

can u evaluate f(0) and f(3) ?

Answer 3

What does evaluate mean?

Answer 4

calculate-compute-

Answer 5

Hmmm hang on. Do you mean put them into the f(X)= thing?

Answer 6

Evaluate means to do this:
f(x) = x^3 - 19x + 30
f(0) = (0)^3 - 19(0) + 30 = ?
f(3) = (3)^3 - 19(3) + 30 = ?

Answer 7

Yes ok Ill have a go at that and tell you what I got thanks.

Answer 8

Right for f(0) I got 30 and the next one 0

Answer 9

f(3) = 0

Are you sure?

Answer 10

Ill do it again

Answer 11

Did it again and got 0 again.

Answer 12

f(3) = (3)^3 - 19(3) + 30
= 27 - 57 + 30
= 30 + 27 - 57
= 57 - 57
= 0

OK

Answer 13

Yes!! So now I have two more questions. Are you up for helping?

Answer 14

Wait what is the 'hence write down the factor of f(x)' bit?

Answer 15

@nincompoop

Answer 16

@estudier

Answer 17

If you calculated f(3) = 0, then (x-3) is a factor

Answer 18

:) I remeber that now. The 0 ones it is.

Answer 19

(ii) Find p and q such that f(x) = (x-2)(x^2 + px +q). How does one go about this?

Answer 20

@karatechopper @myininaya

Answer 21

@Coolsector

Answer 22

(x-2)(x^2 + px +q) = x^3 +px^2 +qx -2x^2 -2px -2q

= x^3 +(p-2)x^2 +(q-2p)x - 2q

and the orig is x^3 - 19x + 30
so we know that p-2 should be 0
and q-2p should be -19
and -2q should be 30
can you answer now ?

Answer 23

Wait....Where has that big line came from? ohhh you timesed out the brackets! Ok wait a min.

Answer 24

I get it up to when you start saying the so we know p-2=0 bit. I dont know how we know that.

Answer 25

ok you see we have a term (p-2)x^2
but in the general equation we dont have x^2 at all .. so we have to make it disappear ..
we do this by saying
p-2 = 0