Factor completely. 4x^3+7x^2+36x+63 Answer Attempt 1 out of 3

To factor the polynomial \(4x^3 + 7x^2 + 36x + 63\) completely, we can follow these steps:<br /><br />1. **Group the terms**: Group the polynomial into two pairs.<br /> \[<br /> (4x^3 + 7x^2) + (36x + 63)<br /> \]<br /><br />2. **Factor out the greatest common factor (GCF) from each group**:<br /> \[<br /> x^2(4x + 7) + 9(4x + 7)<br /> \]<br /><br />3. **Factor out the common binomial factor**:<br /> \[<br /> (4x + 7)(x^2 + 9)<br /> \]<br /><br />So, the completely factored form of the polynomial \(4x^3 + 7x^2 + 36x + 63\) is:<br />\[<br />(4x + 7)(x^2 + 9)<br />\]<br /><br />This is the final factored form.