Find a value for k such that the following trinomial can be factored x^2-8x+k

16

Step-by-step explanation:

x^2-8x+k is a quadratic expression of the form ax^2 + bx + c.  Here a = 1, b = -8 and c = k.  Focus on x^2-8x and complete the square as follows:  Take half of the coefficient of x (that is, take half of -8) and square the result:

(-4)^2 = 16; if we now write x^2-8x+ 16, we'll have the square of (x - 4):  (x -4)^2.

Thus, k = 16 turns x^2-8x+k into a perfect square.

the first one, all those points on the line just make a strait line.