Weegy: (6x^(2)-31x+5)/(x-5)
For a polynomial of the form ax^(2)+bx+c, find two factors of a*c (30) that add up to b (-31).In this problem -(1)/(6)*-5=(5)/(6) (which is (c)/(a)) and -(1)/(6)-5=-(31)/(6) (which is (b)/(a)) , [ so insert -(1)/(6) as the right hand term of one factor and -5 as the right-hand term of the other factor.
((x-(1)/(6))(x-5))/(x-5)
Remove the fraction by multiplying the first term of the factor by the denominator of the second term.
((6x-1)(x-5))/(x-5)
Reduce the expression by canceling out the common factor of (x-5) from the numerator and denominator.
((6x-1) (x-5) )/( (x-5) )
Reduce the expression by canceling out the common factor of (x-5) from the numerator and denominator.
(6x-1)
Find the derivative of the expression.
(d)/(dx) (6x-1)
Remove the parentheses around the expression 6x-1.
6x-1
To find the derivative of 6x, multiply the base (x) by the exponent (1), then subtract 1 from the exponent (1-1=0). Since the exponent is now 0, x is eliminated from the term.
(d)/(dx) 6x-1=6+(d)/(dx) -1
Since -1 does not contain x, the derivative of -1 is 0.
(d)/(dx) 6x-1=6+0
Add 0 to 6 to get 6.
(d)/(dx) 6x-1=6
The derivative of ((6x^(2)-31x+5))/((x-5)) is 6.
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