Question

if the polynomialp(x)=x3-kx2+3+2 is exactly divisible by (x+1) then the value of k is​

Answer 1

Answer:

The polynomial p(x) is exactly divisible by x+1.

so,

\begin{gathered}x + 1 = 0 \\ x = - 1\end{gathered}

x+1=0

x=−1

putting the value of x in given polynomial.

\begin{gathered}

p(x) = {x}^{3} - k {x}^{2} + 3x + 2 \\ p( - 1) = { - 1}^{3} - k( { - 1})^{2} + 3( - 1) + 2 = 0 \\ - 1 - k - 3 + 2 = 0 \\ - 1 - 3 + 2 - k = 0 \\ - 4 + 2 - k = 0 \\ - k = 2 \\ k = - 2\end{gathered}

p(x)=x

3

−kx

2

+3x+2

p(−1)=−1

3

−k(−1)

2

+3(−1)+2=0

−1−k−3+2=0

−1−3+2−k=0

−4+2−k=0

−k=2

k=−2

FINAL ANSWER :

k = - 2k=−2

Answer 2

Answer:

hope it help you.

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