[tex]f(x)=7x^4-17x^2-12[/tex]
Factor f(x):
1- Rewrite -17x² as a difference:
[tex]=7x^4+4x^2-21x^2-12[/tex]
2- Factor x² as a common factor of the first two terms:
[tex]=x^2(7x^2+4)-21x^2-12[/tex]
3- Factor -3 as common factor in the last two terms:
[tex]=x^2(7x^2+4)-3(7x^2+4)[/tex]
4-Factor (7x²+4):
[tex]f(x)=(7x^2+4)(x^2-3)[/tex]
Make the equation equal to x:
[tex](7x^2+4)(x^2-3)=0[/tex]
If the product of two numbers is zero, then at least one of the factors is 0:
[tex]\begin{gathered} 7x^2+4=0 \\ \\ x^2-3=0 \end{gathered}[/tex]
