How do you divide #(x^2 - 5x + 4)/( x-2)#?

Question

Julia Adams · Accepted Answer

#x-3-2/(x-2)# #"one way is to use the divisor as a factor in the numerator"# #"consider the numerator"# #color(red)(x)(x-2)color(magenta)(+2x)-5x+4# #=color(red)(x)(x-2)color(red)(-3)(x-2)color(magenta)(-6)+4# #=color(red)(x)(x-2)color(red)(-3)(x-2)-2# #"quotient " =color(red)(x-3)," remainder "= -2# #rArr(x^2-5x+4)/(x-2)=x-3-2/(x-2)#

Genesis Allen · Answer

undefined To divide (x^2 - 5x + 4) by (x-2), you can use long division or synthetic division. Here is the solution using long division:

x - 3
    ---------------
x - 2 | x^2 - 5x + 4
        - (x^2 - 2x)
        -------------
                 -3x + 4
                 - (-3x + 6)
                 ------------
                          2

Therefore, (x^2 - 5x + 4)/(x-2) simplifies to x - 3 with a remainder of 2.

Eva Adamson · Answer

undefined To divide (x^2 - 5x + 4) by (x - 2), you can use polynomial long division or synthetic division. Polynomial long division involves dividing the terms of the dividend by the divisor, similar to long division with numbers. Synthetic division is a quicker method that can only be used when the divisor is of the form (x - c), where c is a constant. You choose c = 2, as it is the root of the divisor. Both methods will yield the same quotient, which is x - 3.