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2015-04-13T08:55:13+05:30
2)    a = 7 and b = -18

i think there will be some mistake in the first question

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2015-04-13T10:57:11+05:30

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The polynomial was incorrectly given.
       P(x) = x⁴ + 5 x³ + 15 x + 18
  x+2 and x+3 are roots.         P(-2 ) = 0      P(-3)  = 0
       + 16 - 40 -30 + 18 ≠ 0.  so  x+2 is not a factor of given polynomial.

  there is some thing wrong with the polynomial given.
===================================
2)
  P(x) =  x³ + 10 x² + a x + b
       divisible by x - 1 and x+2
   P(1) = 0  =>  1 + 10 + a + b = 0  => a + b = -11
  p(-2) = 0  =>  -8 + 40 -2 a + b = 0  =>  -2 a + b = -32
 
   solving the equations we get:        a = 7,  b = -18

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