How do you divide #(15x^2 + 22x + 8)/( 5x + 4)#?

1 Answer
Dec 27, 2015

#3x+2#

There is a slight problem with this. Look at the footnote in the explanation.

Explanation:

Method 1: See if you can factorise the numerator such that it cancels out part of the denominator

Method 2: Long division.

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#color(blue)("Trying method 1 first")#

Factors of 15 -> {1,15} ; {3,5}
Factors of 8 -> {1,8} ; {2,4}

Attempt No 1: For this to work we need #(5x+4)#

#=> (5x+4)(?_1 x+?_2) =15x^2+22x+8#

Using our list of factors this would give us:

#(5x+4)(3x+2) = 15x^2+10x+12x+8#
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This works so we have:

#((5x+4)(3x+2))/((5x+4))#

#(5x+4)/(5x+4) xx (3x+2)#

But #(5x+4)/(5x+4)=1# giving

#3x+2 # as the answer.

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However, you have to be mindful of the fact that division by 0 is 'not allowed' in mathematics (Undefined). Thus there is a value of x where #(5x+4)=0# so division by #(5x+4)# at that point gives you a bit of a problem!