19.5k views
0 votes
Factor completely: 16n⁸ -24n⁴p - 7p² 2

User Awendt
by
8.0k points

1 Answer

4 votes

The first step is to consider the polynomial 16n⁸ -24n⁴p - 7p², which we aim to factorize.

Factorizing a polynomial is the process of breaking it down into its simplest factors, which when multiplied together, yield the original polynomial.

Here's the step by step process for our equation:

Step 1: Look for common factors if any, in this case, there are none.

Step 2: Identify whether the polynomial can be factored by grouping. The equation 16n⁸ -24n⁴p - 7p² is a polynomial of the form ax⁴ + bxy + cy². When it is a trinomial and of this particular form, the factorization can be written in the form (dx² + ey)(fx² - gy), where d, e, f, and g are the coefficients obtained from the factorization.

Step 3: Now we group terms and factor the result. Looking at the equation you can group the terms to (16n⁸ - 24n⁴p) and (-7p²).

Step 4: Now we need to find the products. In our case, the grouping of equation results in two factors (-4n⁴ + 7p) and (4n⁴ + p).

Step 5: The completely factored form is the product of these two binomials, in other words, the factored form of the equation will be -(-4n⁴ + 7p)*(4n⁴ + p).

So, the original equation 16n⁸ -24n⁴p - 7p² factors to -(-4n⁴ + 7p)*(4n⁴ + p).

User Matas
by
8.7k points

Related questions

asked Nov 12, 2024 97.7k views
Klimbo asked Nov 12, 2024
by Klimbo
8.7k points
1 answer
3 votes
97.7k views
1 answer
5 votes
20.2k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories