How do you find 2p(a) + p(a-1) for the function p(x)= x^2 - 5x + 8p(x)=x2−5x+8?

1 Answer
Alan P.
Jun 1, 2016

3a^2-17a+303a2−17a+30

Explanation:

If
color(white)("XXX")p(color(red)(x))=color(red)(x)^2-5color(red)(x)+8XXXp(x)=x2−5x+8
then
color(white)("XXX")p(color(red)(a))=color(red)(a)^2-5color(red)(a)+8XXXp(a)=a2−5a+8
and
color(white)("XXX")2p(color(red)(a))=2color(red)(a)^2-10color(red)(a)+16XXX2p(a)=2a2−10a+16
and
color(white)("XXX")p(color(red)(a-1))=color(red)(""(a-1))^2-5color(red)(""(a-1))+8XXXp(a−1)=(a−1)2−5(a−1)+8
color(white)("XXXXXXX")=a^2-2a+1-5a+5+8XXXXXXX=a2−2a+1−5a+5+8
color(white)("XXXXXXX")=a^2-7a+14XXXXXXX=a2−7a+14

So
2p(a)+p(a-1)2p(a)+p(a−1)

color(white)("XXX")=2a^2-10a+16XXX=2a2−10a+16
color(white)("XXXX")+underline(color(white)("x")a^2-7a+14)
color(white)("XXX")=3a^2-17a+30

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