Question

Factor the trinomial.

3x4y5 - 108x3y6 + 972x²y7
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. 3x4y5-108x3y6 + 972x²y? = (Factor completely.)
B. The trinomial is prime.

Answer 1

To factor the trinomial 3x^4y^5 - 108x^3y^6 + 972x²y^7, first factor out the common factor of 3xy^5. Then, factor the trinomial inside the parentheses by finding two numbers that multiply to give the constant term and add to give the coefficient of the middle term. Finally, factor out the common factors in each set of parentheses.

Step-by-step explanation:

To factor the trinomial 3x4y5 - 108x3y6 + 972x²y7, we can first notice that each term has a common factor of 3xy5. So we can factor out 3xy5 from each term:

3x4y5 - 108x3y6 + 972x²y7 = 3xy5(x3 - 36xy - 324y2)

Next, we can factor the trinomial inside the parentheses. It is a quadratic trinomial, so we can look for two numbers that multiply to give the constant term (-324) and add to give the coefficient of the middle term (-36). The numbers -18 and 18 fit this criteria, so we can rewrite the trinomial:

3xy5(x3 - 18xy - 18xy - 324y2) = 3xy5((x3 - 18xy) - (18xy + 324y2))

Now, we can factor out the common factors in each set of parentheses:

3xy5((x - 18)(x2 + 18y))

So the factored form of the trinomial is 3xy5((x - 18)(x2 + 18y)).