Question

f (x) = 10 – 3x – 22*This can be factored using the quadratic formula

Answer 1

You have to factor the following function

$f(x)=10-3x-x^2$

The coefficients of the function are:

a=-1

b=-3

c=10

Using the quadratic formula you have to calculate the roots of the function

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

Replace the formula with the values of the coefficients of the function

$\begin{gathered} x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(-1)10}}{2(-1)} \\ x=\frac{3\pm\sqrt[]{9+40}}{-2} \\ x=\frac{3\pm\sqrt[]{49}}{-2} \\ x=\frac{3\pm7}{-2} \end{gathered}$

Positive calculation:

$\begin{gathered} x=\frac{3+7}{-2} \\ x=\frac{-10}{-2} \\ x=-5 \end{gathered}$

Negative calculation

$\begin{gathered} x=\frac{3-7}{-2} \\ x=\frac{-4}{-2} \\ x=2 \end{gathered}$

The roots of the function are x=-5 and x=2

The factorized function is

$f(x)=(x+5)(x-2)$

Note that the roots have to have the inverse sign when you write the factorized function.

The final step is to multiply the function by -1, to make it point downwards just like the original one.

$f(x)=-(x+5)(x-2)$