Question

How do you find 2p(a) + p(a-1) for the function `p(x)= x^2 - 5x + 8`?

Answer 1

`3a^2-17a+30`

Explanation:

If
`color(white)("XXX")p(color(red)(x))=color(red)(x)^2-5color(red)(x)+8`
then
`color(white)("XXX")p(color(red)(a))=color(red)(a)^2-5color(red)(a)+8`
and
`color(white)("XXX")2p(color(red)(a))=2color(red)(a)^2-10color(red)(a)+16`
and
`color(white)("XXX")p(color(red)(a-1))=color(red)(""(a-1))^2-5color(red)(""(a-1))+8`
`color(white)("XXXXXXX")=a^2-2a+1-5a+5+8`
`color(white)("XXXXXXX")=a^2-7a+14`

So
`2p(a)+p(a-1)`

`color(white)("XXX")=2a^2-10a+16`
`color(white)("XXXX")+underline(color(white)("x")a^2-7a+14)`
`color(white)("XXX")=3a^2-17a+30`