Find the value of k, if x-3 is a factor of 5x3 -3x2 2x-k.?

Question

Find the value of k, if x-3 is a factor of 5x3 -3x2   2x-k.?

Answer

Explanation:

Factor Theorem

The Factor Theorem states that if a polynomial f(x) is divided by (x-a) and leaves a remainder of 0, then (x-a) is a factor of f(x).

Given

We are given that x-3 is a factor of 5x³ - 3x² + 2x - k.

Using Factor Theorem

Using the Factor Theorem, we know that if x-3 is a factor of the polynomial, then when we substitute x=3, the polynomial should equal 0.

So we have:

5(3)³ - 3(3)² + 2(3) - k = 0

135 - 27 + 6 - k = 0

114 - k = 0

k = 114

Conclusion

Thus, we have found that the value of k is 114.

Answer

P(x) = x-3
x-3 = 0
x=3

x-3 is a factor so
5x3-3x2*2x -k = 0
put p(3) = 5*3*3-3*3*2*2*3-k = 0
45-108-k = 0
-63-k = 0
-k = 63
k = -63