Question

Sort the polynomials according to whether they are prime or non-prime.

Prime Polynomials
6x−5x^2+2x−14
Non-Prime Polynomials128−18x^2.88−12
128−18x^2.88−12
6.9x^2.10x+15
122−3x+4x+7

Answer 1

To determine whether a polynomial is prime or non-prime, we need to factorize the polynomial completely. If it can be factored into two or more smaller polynomials, then it is non-prime. If it cannot be further factored, then it is prime.

Step-by-step explanation:

To determine whether a polynomial is prime or non-prime, we need to factorize the polynomial completely. If it can be factored into two or more smaller polynomials, then it is non-prime. If it cannot be further factored, then it is prime. Let's analyze each polynomial from the given list:

6x-5x^2+2x-14 = -5x^2+8x-14 = -5(x^2-8/5x+14/5)

128-18x^2 = 2(64-9x^2) = 2(8+3x)(8-3x)

6.9x^2.10x+15 = 6.9x^2+60x+15 = 3(2.3x^2+20x+5) = 3(6.x+1)^2

122-3x+4x+7 = 125+x = 5(25+x)

From the analysis, the prime polynomials are: 6x-5x^2+2x-14 and 122-3x+4x+7, while the non-prime polynomials are: 128-18x^2 and 6.9x^2.10x+15.