SOLUTION
We want to factor the polynomial
3x² + 4x - 7
To do this, multiply the first term and the last term, we have
[tex]3x^2\times-7=-21x^2[/tex]Now,
[tex]\begin{gathered} look\text{ for two items with x, such that when you multiply, you get } \\ -21x^2,\text{ } \\ and\text{ when you add, you get } \\ 4x. \end{gathered}[/tex]These two items are 7x and -3x because
[tex]\begin{gathered} 7x\times-3x=-21x^2 \\ 7x-3x=4x \end{gathered}[/tex]Now, replace these items with the middle item, we have
[tex]\begin{gathered} 3x^2+4x-7 \\ 3x^2+7x-3x-7 \\ x(3x+7)-1(3x+7) \\ =(x-1)(3x+7) \end{gathered}[/tex]Hence the answer is
[tex](3x+7)(x-1)[/tex]