Question

Find all integers k such that the trinomial can be factored.

a) x^2 + kx + 8

A. k = 1
B. k = -7
C. k = -1
D. k = 7
b) x^2 + kx - 6

A. k = 5
B. k = -5
C. k = 1
D. k = -1

Answer 1

To factor the given trinomials, we need to find values of k that make the constant term, 8 and -6, respectively, factorable. The correct values of k for the first trinomial are k = 1 and k = -7, and for the second trinomial, the correct values of k are k = 5 and k = -5.

Step-by-step explanation:

To find the values of k such that the trinomial can be factored, we need to determine when the trinomial can be written as the product of two binomials. For the trinomial x^2 + kx + 8, we can factor it if the constant term (8) can be expressed as the product of the two coefficients in the binomials.

So, we need to find two numbers whose product is 8. The possible values for k are 1 and -7 since (1)(8) = 8 and (-7)(-1) = 8. Therefore, the correct answer is A. k = 1 and B. k = -7.

Similarly, for the trinomial x^2 + kx - 6, we need to find two numbers whose product is -6. The possible values for k are 5 and -5 since (5)(-6) = -30 and (-5)(6) = -30. Therefore, the correct answer is A. k = 5 and B. k = -5.