Question

The expression x³ - kx² + 5x + 3 leaves a remainder of 5 when divided by x - 2. Find the value of k.

Answer 1

Step-by-step explanation:

x

3

+2x

2

+kx+3

∴f(3)=21

3

3

+2.3

2

−3k−3=21

9+6+k+1=7

k=−9

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Answer 2

Given : the expression is $x^{3}-kx^{2} +5x+3$ leaves remainder 5 , when divided by $x-2$ .

To find : the value of K

Answer : we have $x-2$

By evaluating it with 0 ,

$x-2 = 0 \\x=2$

So f(2) = 5

$f(2)=x^{3}-kx^{2} +5x+3\\f(2)=(5)^{3}-k(5)^{2} +5(5)+3$

$=125-25k+25+3\\=150-25k+3\\=153-25k$

$5 = 153-25k\\153-5=25k\\148=25k\\k=148/25\\k = 5.92$\

Hence , the value of k is 5.92