Question

Factor the following trinomial5x^2+39x-8what are the factors

Answer 1

You have the following trinomial:

`5x^2+39x-8`

The general form of a trinomial is:

`ax^2+bx+c`

In order to find the factors you use the quadratic formula, which is given by:

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

By comparing the given trinomial with the general form you have;

a = 5

b = 39

c = -8

You replace the previous values into the quadratic formula:

`\begin{gathered} x=\frac{-39\pm\sqrt[]{(39)^2-4(5)(-8)}}{2(5)} \\ x=\frac{-39\pm\sqrt[]{1521+160}}{10} \\ x=\frac{-39\pm\sqrt[]{1681}}{10}=(-39\pm41)/(10) \end{gathered}`

Then, you have the following two solutions:

`\begin{gathered} x_1=(-39+41)/(10)=(2)/(10)=(1)/(5) \\ x_2=(-39-41)/(10)=(-80)/(10)=-8 \end{gathered}`

The factor of the trinomial are of the form:

`(x-x_1)(x-x_2)`

Finally, by replacing you obtain:

`5x^2+39x-8=(x-(1)/(5))(x-(-8))=(x-(1)/(5))(x+8)`

Hence, the factors are (x - 1/5)( x + 8)