Write the polynomial in factored form. Check by multiplication.
x^3-2x^2-35x
To factor the polynomial x^3 - 2x^2 - 35x, we first look for any common factors among the terms. In this case, there are no common factors, so we proceed to factor by grouping.
First, we can factor out an x from each term: x(x^2 - 2x - 35).
Next, we look for two numbers that multiply to give -35 and add to give -2. The numbers that satisfy this condition are -7 and 5. So we can rewrite the middle term -2x as -7x + 5x.
Now, we can group the terms and factor them separately:
x(x^2 - 7x + 5x - 35).
Factor the terms inside the parentheses:
x[(x^2 - 7x) + (5x - 35)].
Now factor out the common terms from each group:
x[x(x - 7) + 5(x - 7)].
Combine like terms within each group:
x[(x - 7)(x + 5)].
So the factored form of the polynomial x^3 - 2x^2 - 35x is x(x - 7)(x + 5).
To check if the factored form is correct, we can multiply the factors:
x(x - 7)(x + 5) = x(x^2 + 5x - 7x - 35)
= x(x^2 - 2x - 35).
This is equal to the original polynomial, so our factored form is correct.