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WHAT IS X2-16X+5

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3 Answers

HI Rayanna;
 
X2-16X+5
 
It is not factorable.  As far as I know, there is only way to resolve this.
First, let's do FOIL.  I do not know if you are familiar with this.
FIRST
INNER
OUTER
LAST
 
(x-   )(x+  )
or
(x+  )(x+  )
or
(x-   )(x-   )
 
FIRST...x2
 
INNER & OUTER will be
?x-?x=-16x
 
LAST...
? times ?=+5
 
Obviously
+1 times +5 =5
or
-1 times -5 =5
There is no other option.
So...
(x-5)(x-1)
x2-5x-1x+5
x2-6x+5
 
I believe there was a typographical error in the equation.  Please re-check it.  If there is not, then this must be the factoring result...
((x-5)(x-1))-10x
 
I hope this helps.  Please let me know if you need anything else.
x^2-16x+5 is the equation
it is in the form ax^2+bx+c where a=1 and c=5
1 can only be factored into 1*1 or (-1)(-1) and 5 can only be factored into 1*5 or (-1)(-5)
you are limited to 1*1 and 1*5 which gives 1 and 5 as products, which do not add or subtract to give you 16
(disregarding signs for the moment)
if you use -1*1 and -1*5 you get -1 and -5 and these numbers don't add or subtract to get 16
therefore you cannot factor this polynomial into the product of two binomials with integer coefficients
you could use the quadratic formula to arrive at a solution
 
When all else fails, try the quadratic formula.    x = (-b + sqrt(b^2 - 4 ac) )/2a.
For your problem this yields  x = 8 + sqrt(59)   and x = 8 - sqrt(59)   So
 
x^2 - 16 x + 5 = (x- 8-sqrt(59))  (x - 8 + sqrt(59))
 
This method always works, but overkill for simpler factoring problems.