Question

A prime polynomial cannot be written as a product of lower-degree polynomials. Which polynomial is prime? a)8x2 – 10x – 3 b)8x2 + 2x – 3 c)8x2 – 6x – 3 d)8x2 + 23x – 3

Answer 1

As already described above, the prime polynomial is that which can no longer be factored to yield a much simpler terms. From the given choices, that which cannot be factored is letter C. 

Answer 2

Answer:

The correct option is c.

Step-by-step explanation:

Option a,

$8x^2-10x-3$

$8x^2-12x+2x-3$

$4x(2x-3)+(2x-3)$

$(2x-3)(4x+1)$

A prime polynomial cannot be written as a product of lower-degree polynomials. Therefore option a is not prime.

Similarly find the factors of other expressions.

$8x^2+2x-3$

$8x^2-6x+4x-3$

$2x(4x-3)+(4x-3)$

$(2x+1)(4x-3)$

Therefore option b is not prime.

$8x^2-6x-3$

This polynomial factored further and cannot be written as a product of lower-degree polynomials.  Therefore it is prime and option c is correct.

$8x^2+23x-3$

$8x^2+24x-x-3$

$8x(x+3)-(x+3)$

$(8x-1)(x+3)$

Therefore option d is not prime.