SOLUTION: Consider the following. x3 − kx2 + 2kx − 18 Find the value of k such that x − 3 is a factor of the above.

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Question 1128287: Consider the following.
x3 − kx2 + 2kx − 18
Find the value of k such that x − 3 is a factor of the above.
Found 3 solutions by josgarithmetic, MathLover1, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Performing synthetic division for root or zero of 3, the remainder is , which must be .




Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

Find the value of such that is a factor of the above.
We should attempt synthetic division to find when
has a remainder of 0, which would signify that it is a factor of the polynomial.
The synthetic substitution would be set up as:
| .............

------------------------------------------------------|
Treating the synthetic division like any other synthetic division problem, we see that
| ................................
−----------.................
−−---------....................|

If the remainder equals , then we know that









Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Consider the following.
x3 − kx2 + 2kx − 18
Find the value of k such that x − 3 is a factor of the above.
Set the expression equal to 0, as follows: 

One factor: x - 3 signifies that 1 of its roots is 3.

All you have to do is substitute 3 for x, and you'll see that k = 3.

That's all! Nothing MORE, nothing LESS!! 

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