Question

25x^3+150x^2+131x+30 ;5x+3factor using synthetic division and list All zeros

Answer 1

$\begin{gathered} f(x)=25x^3+150x^2\text{ + 131x + 30 } \\ g(x)\text{ = 5x + 3} \end{gathered}$

if g(x) = 5x + 3,

$k\text{ =}\frac{-3}{5}$

Using synthetic division, we have:

It implies that (5x + 3) is a factor of f(x)

Now we're left with the expression

$25x^2\text{ + 135x + 50 }$

By factorizing:

$\begin{gathered} 25x^2\text{ + 125x + 10x + 50 } \\ 25x(x^{}\text{ + 5) + 10(x + 5)} \\ (25x\text{ + 10)(x + 5)} \\ \end{gathered}$

Hence, the zeros of f(x) are : (5x + 3)(25x + 10)(x + 5)