Quick question on factor theorem

use the factor theorem to factorise the following cubics as far as possible:
f(x) = x^3 -7x-6

As there is no x^2 in the cubic do i need to first do algebraic division?

Reply 1

steve2005

17

Original post by dippers

use the factor theorem to factorise the following cubics as far as possible:
f(x) = x^3 -7x-6

As there is no x^2 in the cubic do i need to first do algebraic division?

See what the values of f(1) f(-1) etc You are looking for the value to be zero. This gives you your first factor.

Reply 2

bijesh12

13

If f(a) =0, then the algebraic expression has the factor (x-a). That's the factor theorem. Experiment with values of 1,-1,2,-2 etc to see what the factor is. Once you find this factor you can use algebraic division to find the others.

Reply 3

dippers

OP

12

Original post by steve2005

See what the values of f(1) f(-1) etc You are looking for the value to be zero. This gives you your first factor.

I did that then I did algrebraic division and got x^2-x-6, is this right? Then I'm not sure how to factorise it. I know you use (x+1) for the first bracket and i'm unsure how to do the rest.

Reply 4

steve2005

17

Original post by dippers

I did that then I did algrebraic division and got x^2-x-6, is this right? Then I'm not sure how to factorise it. I know you use (x+1) for the first bracket and i'm unsure how to do the rest.

You could do long division OR synthetic division.

Reply 5

dippers

OP

12

I'm having problems with this question
Find a and b given that (x-1) and (2x+3) are factors of f(x)= ax^3+3x^2+bx-3.
I know I input 1 and -3/2 into the equation and then solve by doing simulataneous equations but I keep getting the wrong answer.

Reply 6

TenOfThem

18

Original post by dippers

I'm having problems with this question
Find a and b given that (x-1) and (2x+3) are factors of f(x)= ax^3+3x^2+bx-3.
I know I input 1 and -3/2 into the equation and then solve by doing simulataneous equations but I keep getting the wrong answer.