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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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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..
You can equate to zero because its a factor of P(x), then -5/2 as value for x
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P(-5/2) = k(-5/2)^3+125/4 =0 P(-5/2) = k(-5/2)^3 = -125/4
There's something wrong with your calculations, k should be 2
i know, but i don't know where i wrong
i know, it should be 75..
\[-\frac{125}{8}k-\frac{225}{4}+\frac{75}{2}+50=0\] Multiply by 8, \[-125k-450+300+400=0 \\ \\ -125k+250=0 \\ \\ k=2\]
i got it

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