Factor the polynomial x^2+(a+b)x+ab=(x+a)(x+b) using the pattern x^2+9x+8

hello : here is a general - method

x²  + 9x + 8  = x²+(a+b)x+ab

you have the system :  a + b = 9 (1)

                                        ab = 8   (2)

solve this system :    by  (1)   : b = 9 - a

subsct in (2) : a(9 - a ) = 8

9a - a² = 8

a² - 9a +8 = 0

calculate Δ = (-9)² - 4(1)(8) = 81 -  32 = 49 =  7²

a1 = ( 9-7)/2 = 2/2 =1       a2 = (9+7)/2 = 16/2 = 8

if : a = 1       b = 9-1 = 8             if : a = 8     b = 9-8 = 1

factor the polynomial  x²+9x+8 = (x+1)(x+8)

the fist one is not equalvalent but i think th second one isand the third isnt definetly or the last one is i think. hope this !

step-by-step explanation:

b.an increase in a causes b to decrease