For which value of b can the expression x2 + bx + 18 be factored?

A. 17

B. - 19

C. 7

D. 3

B. - 19

Step-by-step explanation:

A second degree polynomial can be factored if the discriminant is greater of equal to zero.

For a polynomial of the type: ax2 + bx + c, the discriminant is given by:

b^2 - 4ac.

In this case, a=1, b=b and c=18. Therefore:

b^2 - 4ac = b^2 - 72.

Option C and D are automatically discarded, given that if b equals 7 or 3 the discriminant will be negative, and the polynomial will have no real roots.

Now, if b equals 17 or - 19 the polynomial can be factored. But, if b=17 the solution will be a decimal number. Therefore, the correct answer is B.

Substituting the value of B, we have:

x2 - 19x + 18 = 0

(x-1) (x-18) = 0