Question

80 points

Factor 360 t + 10 t3 - 120 t2 .

10t(t - 6) 2
-10t(t - 6)(t + 6)
10t(t - 6)(t + 6)

Answer 1

To factor the expression 360t + 10t^3 - 120t^2, we can begin by factoring out the greatest common factor, which is 10t:

10t(36 + t^2 - 12t)

We can then factor the trinomial inside the parentheses using the quadratic formula, or by completing the square. However, we notice that the trinomial can be rewritten as (t - 6)^2 - 36:

10t((t - 6)^2 - 36)

We can then apply the difference of squares formula to further factor the expression:

10t(t - 6 + 6)(t - 6 - 6)

Simplifying, we get:

10t(t - 6)(t + 6)

Therefore, the fully factored form of the expression 360t + 10t^3 - 120t^2 is 10t(t - 6)(t + 6).

Answer 2

The factorization of 360t + 10t^3 - 120t^2 is 10t(t - 6)(t + 6).

Explanation:

The factorization of 360t + 10t^3 - 120t^2 is 10t(t - 6)(t + 6).