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

Answer:

Option (A) and (C).

Step-by-step explanation:

Prime polynomial can't be written as a product of lower degree polynomials.

(A)

$8x^2-10x-3$

=8x²-6x-4x-3

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

Here we can't write the polynomial as a product of lower degree.

Therefore it is a prime polynomial.

(B)

8x²+2x-3

=8x²+6x-4x-3

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

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

Therefore it is not a prime polynomial.

(C)

8x²-6x-3

Therefore it is a prime polynomial.

(D)

8x²+23x-3

=8x²+24x-x-3

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

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

Therefore it is not a prime polynomial.

Answer 2

Answer: C. 8x^2-6x-3