How do you factor completely the expression 4x^2 – 25x + 6 + 4x + 6 + 4x + 6x + 1 + 2x + 32x + 2 + 2x + 62x + 1?

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To factor the expression 4x² – 25x + 6 + 4x + 6 + 4x + 6x + 1 + 2x + 32x + 2 + 2x + 62x + 1 completely, we first need to simplify it by combining like terms.

Start by collecting all terms:

  • 4x²
  • – 25x + 4x + 6 + 4x + 6 + 6x + 2x + 32x + 2 + 2x + 62x + 1

Now, let’s combine the like terms:

  • 4x²
  • ((-25 + 4 + 4 + 6 + 6 + 2 + 32 + 2 + 2 + 62)x = (4 + (-25 + 4 + 4 + 6 + 6 + 2 + 32 + 2 + 2 + 62)) = 0

So it simplifies to:

  • 4x² + 0 = 4x²

Next, we can factor out the GCF (Greatest Common Factor), which is 4. This gives us:

  • 4(x²)

There’s no further factorization required here as x² is already in its simplest form. Thus, the fully factored form of the expression is:

4(x²)

In conclusion, the complete factor of the given expression is 4(x²).

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