how to factor polynomials?

Question

f(x)=7x^2-2x+3

Answer 1

Given polinomial is 7x^2-2x+3

Compare it to quadratic form is ax^2+bx+c

a = 7, b = -2, c = 3

Roots are x = [-b+√(b^2-4ac)]/2a   and       x = [-b-√(b^2-4ac)]/2a

x = [2+√(4-4*7*3)]/2*7                   and    x = [2-√(4-4*7*3)]/2*7

x = [2+√(4-84)]/14                        and     x = [2-√(4-84)]/14

x = [2+√-80]/14                            and     x = [2-√-80]/14

x = [2+2√-20]/14                          and     x = [2-2√-20]/14

x = 2(1+√-20]/14                          and     x = 2(1-√-20]/14

x = [1+2√-5]/7                             and     x = [1-2√-5]/7

Given polynomial has imagiinary roots.

x = [1+2(2.23i)]/7                         and     x = [1-2(2.23i)]/7

x = (1+4.46i)/7                            and      x = (1-4.46i)/7

Factoring of given trinomial  is [7x-(1+4.46i)][7x-(1-4.46i)]