Question

Write this trinomial in factored form. 5a² - 30 - 14

Answer 1

`5x^2-3x-14`

replace x with a for this exercise

we use this formula to factor

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

where a=5, b=-3 and c=-14

`x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(5)(-14)}}{2(5)}`
`\begin{gathered} x=\frac{3\pm\sqrt[]{9+280}}{10} \\ \\ x=\frac{3\pm\sqrt[]{289}}{10} \\ \\ x=(3\pm17)/(10) \end{gathered}`

we have two roots

`\begin{gathered} x=(3+17)/(10) \\ x=2 \end{gathered}`

and

`\begin{gathered} x=(3-17)/(10) \\ \\ x=-(7)/(5) \end{gathered}`

so the simplified equation is

`(x-2)(x+(7)/(5))`

now replace x for a

`(a-2)(a+(7)/(5))`