Factor the trinomial. t^3-4t^2-32t = t(t+4)(t-8)

can someone help me pleaseand check my answer.

you are correct

you can check you answer by expanding your result, obtaining the original expression

Thanks Reiny

To factor the trinomial t^3-4t^2-32t, you can use a method called factoring by grouping. Here's how you can do it:

1. Look for the greatest common factor (GCF) of all the terms. In this case, it is t as it appears in every term.
2. Factor out the GCF from the expression: t(t^2 - 4t - 32t)
This step is done by dividing each term by the GCF, in this case, t.

Now you have the expression t(t^2 - 4t - 32t). Next, you will need to factor the quadratic expression t^2 - 4t - 32t.

3. Look for two numbers whose product equals the product of the coefficient of the quadratic term (t^2) and the constant term (-32t), which is (-32t^3).
In this case, the two numbers are -4 and -8 because (-4) * (-8) = 32.

4. Rewrite the middle term (-4t) using these two numbers as coefficients, splitting the middle term:
t^2 - 4t - 32t = t^2 - 8t + 4t - 32t

5. Group the terms: (t^2 - 8t) + (4t - 32t)

6. Factor out the greatest common factor from each group.
t(t - 8) + 4t(t - 8)

7. Notice that both groups have the factor (t - 8) in common. Factor it out: (t - 8)(t + 4t)

Now you have the factored form: t(t - 8)(t + 4t)

To simplify the expression further, combine like terms: t(t - 8)(t + 5t) = t(t - 8)(t + 6t) = t(t - 8)(7t)

So, the factored form of the trinomial t^3 - 4t^2 - 32t is t(t - 8)(7t).

Your answer of t(t + 4)(t - 8) is not correct. The correct answer is t(t - 8)(7t).