If the polynomial 6x³+16x²+px-5 is exactly divisible by 3x+5 , then find the value of p
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Hey Mate
your answer is --
Given, p(x) = 6x³+16x²+px-5
Now, 3x+5 =0 => x = -5/3
since, p(x) is exactly divide by 3x+5
therefore, p(-5/3) =0
=> 6×(-5/3)^3 + 16×(-5/3)^2+p×(-6/3)-5=0
=> 6×(-125/27)+16×(25/9)-6p/3-5=0
=> -750/27 + 400/9 - 6p/3 -5 = 0
=> -750/27 + 400/9 -6p/3 = 5
=> (-750+1200-54p) = 135
=> 450 - 54p = 135
=> 54p = 450 - 135
=> p = 315/54
Hope it helps you
your answer is --
Given, p(x) = 6x³+16x²+px-5
Now, 3x+5 =0 => x = -5/3
since, p(x) is exactly divide by 3x+5
therefore, p(-5/3) =0
=> 6×(-5/3)^3 + 16×(-5/3)^2+p×(-6/3)-5=0
=> 6×(-125/27)+16×(25/9)-6p/3-5=0
=> -750/27 + 400/9 - 6p/3 -5 = 0
=> -750/27 + 400/9 -6p/3 = 5
=> (-750+1200-54p) = 135
=> 450 - 54p = 135
=> 54p = 450 - 135
=> p = 315/54
Hope it helps you
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