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By factor theorem, if (x - a) is a factor of a polynomial P(x) in x, then P(a) = reminder of P(x) when divided by (x - a) = 0.

P(1)=1+10+p+q

11+p+q=0-----(1)

P(-2)=-8+10(4)+(-2)p+q

-8+40-2p+q=0

32-2p+q=0..........(2)

Adding eq:1 and 2,

11+p+q=0

32-2p+q=0

- + -

-21+3p=0

3p=21

P=7

Substitute p value in equation 1

11+p+q=0

11+7+q=0

18+q=0

q=-18

P=7 and q=-18