# 1) if x+2 and x+3 are factor of the polynomial xpower 4+ 5xcube +15x +18 find the other factor 2) find the value of a and b such that the polynomials xcube +10xsquare +ax+b is exactly divisible by x-1 and x+2 .

2
by saluja2001

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

i think there will be some mistake in the first question

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.
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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