How do you divide 15x2+22x+85x+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.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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)(?1x+?2)=15x2+22x+8

Using our list of factors this would give us:

(5x+4)(3x+2)=15x2+10x+12x+8
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This works so we have:

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

5x+45x+4×(3x+2)

But 5x+45x+4=1 giving

3x+2 as the answer.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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!