Question

Х²+5х-14 ________ х²-6х+8

Answer 1

(x²+5х-14)/(х²-6х+8)=(x-2)(x+7) /  (x-4)(x-2) =(x-7)/(x-4)

Answer 2

Х2+5х-14=0
D=b2-4ac
D=5(2)-4×1×(-14)=25+56=81
х= -b+-√D ÷2a
х= -5+-√81÷2×1= -5+-9÷2
х(1)= -5-9÷2= -14÷2= -7
х(2)= -5+9÷2= 4÷2= 2

х2-6х+8=0
D= 6(2)-4×1×8=36-32=4
х= 6+-√4÷2×1= 6+-2÷2
х(1)= 6-2÷2=2
х(2)= 6+2÷2=4

Answer 3

To simplify the expression, let's divide the numerator by the denominator using polynomial long division:

scssCopy code
            x + 11
    _____________________
x² - 6x + 8 | x² + 5x - 14
    - (x² - 6x + 8)
    ______________
              11x - 22
           - (11x - 66)
           ____________
                    52

The simplified expression is x + 11 with a remainder of 52 over the denominator x² - 6x + 8.