Question 9337
To factor {{{x^2 - 12x + 35 }}}, you need to find two numbers whose product is +35 and whose sum is -12.  The fact that the product of the numbers is positive, means that the numbers must be the same sign, and the fact that they must add up to a negative 12 means that they must both be negative.  So the answer is (x-7)(x-5).  


See my explanations in my lesson plans entitled Products of Binomials by F OI L  and also my lesson plan about Factoring Trinomials.  The first of these is also listed on my own website, as well as the lesson plan on algebra.com under "Math in Living Color."


For the second problem, you probably meant {{{x^2 +3x - 10 = 0}}}.  As an extra reference on this see my lesson plan on algebra.com on Solving Quadratic Equations, also on my own website as well.


{{{x^2 + 3x - 10 = 0}}}  The first step is to factor:


{{{ (x+5)(x-2) = 0}}}


Set each factor equal to zero:
x+ 5 = 0   
x= -5


x-2 = 0
x= 2


However, it is best to NOT use parentheses, since this means a LOT of other things of which this is NOT one of them.   (-5,2) is NOT correct notation.


R^2 at SCC