Question

Factorise each of the following polynomials.

Answer 1

\(2x^{3}-3x^{2}+1\)

Answer 2

I got the answer correct but not sure whether my working is right...

Answer 3

Here is my working:
Let P(x)=\(2x^{3}-3x^{2}+1\)
The constant term for P(x)=\(2x^{2}-3x^{2}+1\) is 1.
Hence,if (x-a) were to be a factor of 1,a=\(\pm1\)
If x=1,P(1)=\(2(1)^{3}-3(1)^{2}+1=0\)
Hence,(x-1) is a factor of P(x).
If x=-1,P(-1)=\(2(-1)^{3}-3(-1)^{2}+1=-4\neq0\)
Hence,(x+1) is not a factor of P(x).
Hence,by factor theorem,(x-1) is a factor of P(x).

Answer 4

Using the long division method,the quotient i got is \(2x^{2}-x-1\)

Answer 5

Therefore,P(x)=\(2x^{2}-3x^{2}+1\)
=\((x-1)(2x^{2}-x-1)\)
=\((x-1)(x-1)(2x+1)\)
=\((x-1)^{2}(2x+1)\)

Answer 6

@Zepdrix

Answer 7

Hmm I've never heard of the factor theorem before,
but your work looks good! :)

`If the coefficients add up to zero,`
`then x=1 is a root of the polynomial,`
`and x-1 must be a factor.`

And then from there you applied long division?
Yayyy good job

Answer 8

Yes,i tried applying long division since i don't hv any other methods to factorise it completely.

Answer 9

Thank you! @Zepdrix