P(x) is a polynomial function. If P(x2)=(ab+2)x32x2+(2a+b+7)x20 , what is P(a+b) ?

2 Answers
Jun 20, 2016

P(x) cannot be a polynomial because P(x2) would certainly be an even function.

Explanation:

If P(x)=ni=0aixi then

P(x2)=ni=0ai(x2)i=ni=0aix2i

The proposition is not feasible once defined P(x) as a polynomial.

Jun 20, 2016

P(a+b)=12

Explanation:

P(x2)=(ab+2)x32x2+(2a+b+7)x20

Since P(x) is a polynomial function, any powers of x in P(x2) must be even, not odd.

So we require (ab+2)=0 and (2a+b+7)=0

Adding these two equations together, we get: 3a+9=0, hence a=3 and b=1

P(x2)=2x220

So:

P(x)=2x20

Hence:

P(a+b)

=P((3)+(1))

=P(4)

=2(4)20

=820

=12