Prove that the polynomial `x^2 + x + 1` can not be written as a product of first degree polynomials.

Prove that the polynomial. x^2+4 x+5 cannot be written as a product of first degree polynomials.

Prove that x^2+2x+2 cannot be written as the product of first degree polynomials.

What is the maximum value of 'k', for which the polynomial x^2-x+k can be written as a product of two first degree polynomials?

What is the smallest natural number k for which the polynomial 2 x^2+k x+6 can be written as a product of two first degree polynomials? Write down the polynomial using 'k' and express it as the product of two first degree polynomials.

Write 2x^2+5x+3 as a product of two first degree polynomials.

Prove that none of the polynomials below can be factored into a product of first degree polynomials:- x^2+x+1 .

Prove that none of the polynomials below can be factored into a product of first degree polynomials:- x^2-x+1 .

Prove that none of the polynomials below can be factored into a product of first degree polynomials:- x^2+2x + 2 .

Prove that none of the polynomials below can be factored into a product of first degree polynomials:- x^2+4x +5 .

Write 2 x^2-7 x+6 as the product of two first degree polynomials.