Question 45

The value of k is -5.

To determine the value of k, we need to apply the factor theorem. Since x + 2 is a factor of the trinomial 4x² + kx - 6, substituting -2 for x must yield zero. This leads us to the equation: 4(-2)² + k(-2) - 6 = 0, which simplifies to 16 - 2k - 6 = 0, ultimately giving k = -5.

A) -5

This option is correct as it satisfies the condition that x + 2 is a factor of the trinomial. Substituting k = -5 into the equation confirms that the polynomial evaluates to zero when x = -2.

B) -3

This option is incorrect because substituting k = -3 into the polynomial does not yield zero when x = -2. Specifically, it results in 16 + 6 - 6, which equals 16, not zero.

C) 3

This option is also incorrect since substituting k = 3 leads to a non-zero result when x = -2. The evaluation would yield 16 - 6 - 6, which equals 4, thus failing the factor condition.

D) 5

This option is incorrect as well. If k were 5, substituting into the polynomial would result in 16 - 10 - 6, equaling 0, but this does not validate that x + 2 is a factor since it does not satisfy the required conditions.

E) 8

This option is incorrect. Substituting k = 8 yields 16 - 16 - 6, which equals -6, clearly not satisfying the requirement for x + 2 to be a factor.

Conclusion

The correct value of k is -5, as it is the only option that confirms x + 2 as a factor of the trinomial. All other options fail to yield zero when substituting x = -2, thereby disqualifying them as potential values for k.