Explain how to solve this step by step, i know the answer, but need to explain it. 2n^4-10n^2-72

2(n + 3)(n - 3)(n² + 4)

Step-by-step explanation:

Your polynomial is: P =2n⁴ - 10n² - 72

1. Remove the common factor

2n⁴ - 10n² - 72 = 2(n⁴ - 5n² - 36)

2. Factor the quadratic

P is a quadratic in n².

(a) Find two numbers that multiply to give -36 and add to give -5.

List the positive factors of 36: 1, 2, 3, 4, 6, 9, 18, 36

One of the numbers must be negative. Start with the numbers near the middle of the list.

By trial and error, you will find that -9 and +4 work:

-9 × 4 = 36 and -9 +4 = -5

(b) Rewrite -5n² as -9n² + 4n²

n⁴ - 9n² + 4n² - 36

(c) Factor the first two and the last two terms

n²(n² - 9) + 4(n² - 9)

(d) Separate the common factor

(n² - 9)(n² + 4)

So, P = 2(n² - 9)(n² + 4)

(e) Factor n² - 9

n² - 9 is the difference of two squares.

n² - 9 = (n + 3)(n - 3)

P = 2(n + 3)(n - 3)(n² + 4)

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step-by-step explanation: