Determine if Prime 10x^3-15x^2+8x-12

$10 x^{3} - 15 x^{2} + 8 x - 12$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(10 x^{3} - 15 x^{2}) + 8 x - 12$

Factor out the greatest common factor (GCF) from each group.

$5 x^{2} (2 x - 3) + 4 (2 x - 3)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $2 x - 3$ .

$(2 x - 3) (5 x^{2} + 4)$

Step 3

Since the polynomial can be factored, it is not prime.

Not prime