Question

3x^2+x-4factor each polynomial completely. if a polynomial is prime, state this.

Answer 1

(3x + 4)(x-1)

Explanation:$3x^2\text{ + x - 4}$

Factors of of the produnct whose sum gives 1:

product = 3(-4) = -12

factors of -12 whose sum gives 1: +4 and -3

$\begin{gathered} 3x^2\text{ + 4x - 3x - 4} \\ \end{gathered}$$\begin{gathered} 3x^2\text{ - 3x + 4x - 4} \\ 3x(x\text{ - 1) + 4(x - 1)} \\ (3x\text{ + 4) (x-1)} \end{gathered}$

A polynoial is prime if it is an irreducible polynomial- if it cannot be factorised.

Since, the above polynomial was factorsed, it not a prime polynomial.

The factored form:

(3x + 4)(x-1)