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:

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