Question

question 9 (4 points) write the simplest polynomial function in standard form with the given roots. you must upload your handwritten work to receive credit for your answer. roots: -5, 5, and -6

Explanation:

Step1: Form factor from roots

If $r$ is a root, $(x-r)$ is a factor. So the factors are $(x+5)$, $(x-5)$, $(x+6)$.
The polynomial is $f(x)=(x+5)(x-5)(x+6)$

Step2: Multiply first two factors

Use difference of squares: $(x+5)(x-5)=x^2-25$.
Now $f(x)=(x^2-25)(x+6)$

Step3: Distribute to expand fully

Multiply each term in $x^2-25$ by $x+6$:
$x^2(x+6) -25(x+6) = x^3+6x^2-25x-150$

Answer:

$x^3+6x^2-25x-150$