Write the polynomial in factored form. x3−4x2−21x
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To factor the polynomial x^3 - 4x^2 - 21x, we first identify any common factors among the terms. In this case, there is no common factor among all the terms.
Next, we look for any common factor among some of the terms. In this case, we can factor out x. Factoring out x from each term gives us:
x(x^2 - 4x - 21)
Now, we can proceed to factor the quadratic expression x^2 - 4x - 21. To do this, we look for two numbers that multiply to give -21 and add up to -4. After trying different pairs of factors, we find that -7 and 3 satisfy these conditions.
Therefore, the quadratic expression can be factored as:
x(x - 7)(x + 3)
Putting it all together, the polynomial x^3 - 4x^2 - 21x in factored form is:
x(x - 7)(x + 3)