Notice that the factor x is a common factor for all three terms. Then, factor out x:
[tex]x^3-2x^2-35x=x(x^2-2x-35)[/tex]
Notice that the factor x²-2x-35 is a quadratic expression.
Find two numbers whose sum is -2 and whose product is -35 to factor out the quadratic expression. Since 5-7 = -2 and (5)(-7)=-35, those two numbers are -7 and 5. Then, the quadratic expression can be factored out as:
[tex]x^2-2x-35=(x-7)(x+5)[/tex]
Then:
[tex]x(x^2-2x-35)=x(x-7)(x+5)[/tex]
Then, the factorization of the given trinomial is:
[tex]x^3-2x^2-35x=x(x-7)(x+5)[/tex]
Therefore, the correct choice is option C) x(x-7)(x+5)
