kryton1212
Let P(x)=kx^(3)9x^(2)15x+50.
(a) If 2x+5 is a factor of P(x), find the value of k.
(b) Factorize P(x) completely.



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.Sam.
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If 2x+5 is a factor of P(x)
Then P(5/2) = k(5/2)^(3)9(5/2)^(2)15(5/2)+50 =0
Find k..

.Sam.
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You can equate to zero because its a factor of P(x), then 5/2 as value for x

kryton1212
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dw:1362193274349:dw
dw:1362193313133:dw

.Sam.
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P(5/2) = k(5/2)^3+125/4 =0
P(5/2) = k(5/2)^3 = 125/4

kryton1212
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dw:1362193409011:dw

.Sam.
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There's something wrong with your calculations, k should be 2

kryton1212
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i know, but i don't know where i wrong

kryton1212
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i know, it should be 75..

.Sam.
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\[\frac{125}{8}k\frac{225}{4}+\frac{75}{2}+50=0\]
Multiply by 8,
\[125k450+300+400=0 \\ \\ 125k+250=0 \\ \\ k=2\]

kryton1212
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i got it

kryton1212
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thanks