Question

Which polynomials are prime? Check all that apply.

Answer 1

The awnser is A,D,and E

Answer 2

Answer:

The prime polynomials are 1, 4 and 5

Step-by-step explanation:

Given some polynomials we have to classify the polynomials prime or not.

Prime polynomials are the polynomial with integer coefficients that cannot be factored into lower degree polynomials.

$15x^2 + 10x - 9x + 7$

⇒ $5(3x+2)-(9x-7)$

can't be factored into lower degree polynomial ∴ prime polynomial.

$20x^2 - 12x + 30x - 18$

⇒ $4x(5x-3)+6(5x-3)$

⇒ $(4x+6)(5x-3)$

hence, not a prime polynomial.

$6x^3 + 14x^2 - 12x - 28$

⇒ $2x^2(3x+7)-4(3x+7)$

⇒ $(2x^2-4)(3x+7)$

hence, not a prime polynomial.

$8x^3 + 20x^2 + 3x + 12$

⇒ $4x^2(2x+5)+(3x+20)$

can't be factored into lower degree polynomial ∴ prime polynomial.

$11x^4 + 4x^2 - 6x^2 - 16$

⇒ $x^2(11x^2+4)-2(3x^2+8)$

can't be factored into lower degree polynomial ∴ prime polynomial.

The prime polynomials are 1, 4 and 5