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Q: Divide. Check your answers for exercises (6x^2 – 31x + 5) / (x – 5)
A: (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. 6 ]
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Asked 9/3/2012 5:36:01 PM
Updated 7/22/2014 4:25:58 PM
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(6x^2 – 31x + 5) / (x – 5)
= (6x^2/x-5) - (31x/x-5) + (5/x-5)
= 6x - 1

(6x - 1)(x - 5)
= 6x^2 - 30x - x + 5
= 6x^2 - 31x + 5
Added 7/22/2014 4:25:58 PM
This answer has been confirmed as correct and helpful.
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