find the value of p such that (x-4) is a factor of 5x cube - 7x square - px - 28
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Step-by-step explanation:
Solution:
Let p(x) = x⁴+7x³+7x²+px+q
g(x) = x²+7x+12
It is given that, p(x) is exactly
divisible by g(x)
g(x)|x⁴+7x³+7x²+px+q|x²-5
****x⁴+7x³+12x²
_____________________
********** -5x²+px+q
********** -5x²-35x-60
_______________________
Remainder [(p+35)x+(q+60)]
According to the problem given,
p(x) is exactly divisible by g(x),
Remainder = 0
=> p+35 = 0 and q+60 = 0
=> p = -35 and q = -60
Therefore,
p = -35 , q = -60
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