[tex](x + 3)(x + 4)[/tex] is the completely factorized form of [tex]x^2 + 7x + 12[/tex]. The solutions to the equation [tex]x^2 + 7x + 12 = 0[/tex] are x = -3 and x = -4.
Thus, finding two binomial factors that multiply to generate the quadratic formula [tex]x^2 + 7x + 12[/tex] is necessary to fully factorize it. The quadratic equation may be factored to determine the factors: [tex]x^2 + 7x + 12 = (x + 3)(x + 4)[/tex].
We may use the factored form obtained in step a to solve the quadratic problem [tex]x^2 + 7x + 12 = 0[/tex]. We solve for x by setting each component to zero: [tex]x + 3 = 0 -- > x = -3 x + 4 = 0 -- > x = -4[/tex]. So, x = -3 and x = -4 are the answers to the equation [tex]x^2 + 7x + 12 = 0[/tex].
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