To factor a polynomial by grouping, we first rewrite it in a way that allows us to identify common factors in pairs of terms. Let's use an example to demonstrate the process.

Example Polynomial:

Factor the polynomial $2x^3 + 4x^2 + 3x + 6$.

---

Step 1: Group the terms into two pairs.

$(2x^3 + 4x^2) + (3x + 6)$

---

Step 2: Factor out the greatest common factor (GCF) from each group.

$2x^2(x + 2) + 3(x + 2)$

---

Step 3: Factor out the common binomial factor.

Both groups contain $(x + 2)$, so factor it out: $(2x^2 + 3)(x + 2)$

---

Final Factored Form:

$(2x^2 + 3)(x + 2)$

This is the completely factored form of the polynomial.

---

If you have a specific polynomial in mind, feel free to share it, and I’ll solve it step by step! 😊

Would you like more details or have any questions?

---

Here are 5 related questions:

1. What is factoring by grouping, and why is it useful?
2. How do you identify the GCF in a polynomial?
3. Can all polynomials be factored by grouping? Why or why not?
4. What is the relationship between factoring and solving equations?
5. How do you check if your factored form is correct?

---

Tip: After factoring a polynomial, always verify by expanding the factored form to confirm it matches the original.