Answer :
[tex]\begin{gathered} f(x)=25x^3+150x^2\text{ + 131x + 30 } \\ g(x)\text{ = 5x + 3} \end{gathered}[/tex]
if g(x) = 5x + 3,
[tex]k\text{ =}\frac{-3}{5}[/tex]Using synthetic division, we have:
It implies that (5x + 3) is a factor of f(x)
Now we're left with the expression
[tex]25x^2\text{ + 135x + 50 }[/tex]By factorizing:
[tex]\begin{gathered} 25x^2\text{ + 125x + 10x + 50 } \\ 25x(x^{}\text{ + 5) + 10(x + 5)} \\ (25x\text{ + 10)(x + 5)} \\ \end{gathered}[/tex]Hence, the zeros of f(x) are : (5x + 3)(25x + 10)(x + 5)
