The value of k for which x – 1 is a factor of the polynomial 4x3+ 3x2 – 4x + k is :-a.3b.0c.1d.- 3
Question
The value of k for which x – 1 is a factor of the polynomial 4x³ + 3x² – 4x + k is :
- a. 3
- b. 0
- c. 1
- d. -3
Solution
To find the value of k for which x – 1 is a factor of the polynomial 4x^3 + 3x^2 – 4x + k, we use the Factor Theorem. The Factor Theorem states that a polynomial f(x) has a factor (x - c) if and only if f(c) = 0.
Here, x - 1 is the factor, so we let x = 1.
Substitute x = 1 into the polynomial:
4(1)^3 + 3(1)^2 - 4(1) + k = 0 4 + 3 - 4 + k = 0 3 + k = 0
Solving for k, we get k = -3.
So, the value of k for which x – 1 is a factor of the polynomial 4x^3 + 3x^2 – 4x + k is -3 (option d).
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