(x^2-4x+16)(x+4)-x(x+1)(x+2)+3x^2=0

Jasonbradley

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Jun 17, 2024

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Solving the Polynomial Equation: (x^2-4x+16)(x+4)-x(x+1)(x+2)+3x^2=0

This article will guide you through the process of solving the polynomial equation:

(x^2-4x+16)(x+4)-x(x+1)(x+2)+3x^2=0

Step 1: Expand the Equation

First, we need to expand the equation by multiplying out the brackets:

• (x^2-4x+16)(x+4):
  • x^3 - 4x^2 + 16x + 4x^2 - 16x + 64 = x^3 + 64
• -x(x+1)(x+2):
  • -x(x^2 + 3x + 2) = -x^3 - 3x^2 - 2x

Now, our equation becomes:

x^3 + 64 - x^3 - 3x^2 - 2x + 3x^2 = 0

Step 2: Simplify the Equation

We can simplify the equation by combining like terms:

-2x + 64 = 0

Step 3: Solve for x

Now, we can solve for x by isolating it:

• -2x = -64
• x = -64 / -2
• x = 32

Solution

Therefore, the solution to the polynomial equation (x^2-4x+16)(x+4)-x(x+1)(x+2)+3x^2=0 is x = 32.