Question

3x-5+6x²+x³-x⁴and 6-5x-2x³+2x²+2x⁴​

Answer 1

Step-by-step explanation:

Solution:

A prime polynomial is a polynomial which cannot be further factorised.

Solving each polynomial one by one.

a) x3 + 3x2 - 2x - 6,

x²(x + 3) -2(x + 3)

(x² - 2)(x + 3)

(x² - 2)(x + 3) are the factors ,

therefore x3 + 3x2 - 2x - 6 is not a prime polynomial.

b) x3 - 2x2 + 3x - 6

x²(x - 2) + 3(x - 2)

(x² + 3)(x - 2)

(x² + 3)(x - 2) are the factors,

therefore x3 - 2x2 + 3x - 6 in not a prime polynomial.

c) 4x4 + 4x3 - 2x - 2

4x³ (x + 1) - 2(x + 1)

(4x³ - 2)(x + 1)

(4x³ - 2)(x + 1) are the factors,

therefore 4x4 + 4x3 - 2x - 2 is not a prime polynomial.

d) 2x4 + x3 - x + 2

This polynomial cannot be further factorised ,therefore it is a prime polynomial.