Question

Please help me with these problems, I am completely stumped : /

Answer 1

X² - d = (x + 9) (x + c)
c and d are integers.

Integers are whole numbers found in the number line. These can be positive integers or negative integers.

x² - d ⇒ this means that there is no middle term. The sum of the middle term is 0.

(x + 9)(x - 9) = x(x - 9) + 9(x - 9) = x² - 9x + 9x - 81 = x² - 81

c = -9
d = 81

x² + Mx + 18 = (x + g)(x + h)

if M = -11
x² - 11m + 18 ⇒ (x-9)(x-2) ⇒ x(x-2) -9(x-2) 
x² - 2x - 9x + 18 ⇒ x² - 11x + 18

if M = 7
x² + 7m + 18 ⇒ (x + 9)(x-2) ⇒ x(x-2) + 9(x-2) 
x² - 2x + 9x - 18 ⇒ x² + 7x - 18

Only Pat is correct.
M = -11
g = 9
h = 2