Factor polynomials using the grouping method. 3. 21x^3+24x^2-14x-16

To factor the polynomial \(21x^3 + 24x^2 - 14x - 16\) using the grouping method, follow these steps:<br /><br />1. **Group the terms in pairs:**<br /> \[<br /> (21x^3 + 24x^2) + (-14x - 16)<br /> \]<br /><br />2. **Factor out the greatest common factor (GCF) from each pair:**<br /> \[<br /> 3x^2(7x + 8) - 2(7x + 8)<br /> \]<br /><br />3. **Factor out the common binomial factor:**<br /> \[<br /> (3x^2 - 2)(7x + 8)<br /> \]<br /><br />So, the factored form of the polynomial \(21x^3 + 24x^2 - 14x - 16\) is:<br />\[<br />(3x^2 - 2)(7x + 8)<br />\]