Question

2. 3x3 - 4x2 + 9x - 12

Answer 1

Polynomial Factoring

Factor the following polynomial:

`p\mleft(x\mright)=3x^3-4x^2+9x-12`

Let's group the first two and the last two terms:

`p(x)=(3x^3-4x^2)+(9x-12)`

Factoring out x^2 from the first two terms and 3 from the last two terms

`p(x)=x^2(3x-4)+3(3x-4)`

Note the expression 3x-4 is common to both groups. Factoring it out:

`p(x)=\mleft(3x-4\mright)(x^2+3)`

The second factor is a sum of squares, so it cannot be factored further. The final factorization is:

`p(x)=\mleft(3x-4\mright)(x^2+3)`