Question

prove that none of the polynomial below can be factored into a product first degree polynomial. (a) x²+ x+1 (b) x²+2x+2​

Answer 1

In the same way as you could factor trinomials on the form of

x2+bx+c

You can factor polynomials on the form of

ax2+bx+c

If a is positive then you just proceed in the same way as you did previously except now

ax2+bx+c=(x+m)(ax+n)

wherec=mn,ac=pqandb=p+q=am+n