Question

Use the Rational Root Test to write each polynomial as a product of irreducible polynomials in :

$\mathrm{\mathbb{Q}}\left(x\right)$

f)$6x^4-31x^3+25x^2+33x+7$

Short answer

The factorization is $6x^4-31x^3+25x^2+33x+7=\left(3x+1\right)\left(2x-7\right)\left(x^2-2x-1\right)$

Step-by-step solution

Rational root test 

Consider is a polynomial with integer coefficients. If and if the rational number is (in lowest terms), then it is a root of , also and .