Factor the polynomial completely.%0D%0A%0D%0Ax3−4x2−21x
To factor the polynomial completely, we first look for any common factors. In this case, there are no common factors among the terms.
Next, we try to factor the polynomial by grouping. We can rewrite the polynomial as follows:
x^3 - 4x^2 - 21x
= x(x^2 - 4x - 21)
Now, we look for factors of -21 that add up to -4. The factors that satisfy this condition are -7 and 3. We can rewrite the middle term as -7x + 3x:
= x(x^2 - 7x + 3x - 21)
Now, we group the terms:
= x((x^2 - 7x) + (3x - 21))
= x(x(x - 7) + 3(x - 7))
We can see that (x - 7) is a common factor in both terms. Factoring it out, we get:
= x(x - 7)(x + 3)
Therefore, the polynomial x^3 - 4x^2 - 21x factors completely as x(x - 7)(x + 3).