Question 124326
Given the following expression to factor:
.
{{{5x^2 - 26x + 5}}}
.
The 5 that is the multiplier of the {{{x^2}}} has only two factors ... namely 5 and 1. So
the {{{5x^2 }}} can only factor to 5x times 1x (or just 5x times x). This means the pair of
factors must be of the form:
.
(5x +_____)*(x + _____)
.
The constant in the expression is also +5. It can factor into either +5 and +1 or into -5 and -1
because in either case the product is +5. However, in the original expression, the middle term is
negative. Therefore, we need to introduce a negative sign. This means that the factors of the
+5 constant must be the pair -5 and -1. This means that our factors have two possibilities. They
are either:
.
{{{(5x -5)*(x - 1)}}}
.
or:
.
{{{(5x - 1)*(x - 5)}}}
.
If you multiply out the first set of factors the result is:
.
{{{5x*x + 5x(-1) + (-5)(x) + (-5)(-1) = 5x^2 - 5x -5x + 5 = 5x^2 -10x + 5}}}
.
That didn't work. So multiply out the second set of factors:
.
{{{(5x - 1)*(x - 5) = 5x*x + (5x)(-5) + (-1)(x) + (-1)(-5) = 5x^2 - 25x -x + 5 = 5x^2 - 26x +5}}}
.
and that does work because the product is the same as the original expression you were given
to factor.
.
So the answer to this problem is that the factored form of the original expression is:
.
{{{(5x - 1)*(x - 5)}}}
.
Hope this helps you to understand the problem a little better.
.