Question

Complete factorization f(x)=x^4-x^3-5x^2-x-6

Answer 1

The solution to the above  factorization problem is given as f′(x)=4x³−3x²−10x−1. See steps below.

What are the steps to the above answer?

Step 1 - Take the derivative of both sides

f′(x)=d/dx​​(x^4−x^3−5x^2−x−6)

Step 2 - Use differentiation rule d/dx​(f(x)±g(x))=d/dx​(f(x))±d/dx​(g(x))

f′(x)=d/dx​​(x4)−d/dx​​(x^3)−d/dx​​(5x^2)−d/dx​​(x)−d/dx​​(6)

f′(x)=4x^3−d/dx​​(x3)−d/dx​​(5x^2)−d/dx​​(x)−d/dx​​(6)

f′(x)=4x^3−3x2−d/dx​​(5x^2)−d/dx​​(x)−d/dx​​(6)

f′(x)=4x^3−3x^2−10x−d/dx​​(x)−d/dx​​(6)

f′(x)=4x^3−3x^2−10x−1−dxd​(6)

f′(x)=4x^3−3x^2−10x−1−0

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