6. Factor the following COMPLETE LY. 28x^2+16x-80

To factor the quadratic expression \(28x^2 + 16x - 80\) completely, we can follow these steps:<br /><br />1. **Factor out the greatest common factor (GCF):**<br /> The GCF of \(28x^2\), \(16x\), and \(-80\) is 4. So, we first factor out 4:<br /> \[<br /> 28x^2 + 16x - 80 = 4(7x^2 + 4x - 20)<br /> \]<br /><br />2. **Factor the quadratic expression inside the parentheses:**<br /> We need to factor \(7x^2 + 4x - 20\). To do this, we look for two numbers that multiply to \(7 \times (-20) = -140\) and add up to \(4\).<br /><br /> The pair of numbers that satisfy these conditions are \(14\) and \(-10\):<br /> \[<br /> 14 \times (-10) = -140 \quad \text{and} \quad 14 + (-10) = 4<br /> \]<br /><br />3. **Rewrite the middle term using these numbers:**<br /> \[<br /> 7x^2 + 14x - 10x - 20<br /> \]<br /><br />4. **Group the terms and factor by grouping:**<br /> \[<br /> (7x^2 + 14x) + (-10x - 20)<br /> \]<br /> Factor out the common factors from each group:<br /> \[<br /> 7x(x + 2) - 10(x + 2)<br /> \]<br /><br />5. **Factor out the common binomial factor \((x + 2)\):**<br /> \[<br /> (7x - 10)(x + 2)<br /> \]<br /><br />6. **Combine with the GCF factored out initially:**<br /> \[<br /> 4(7x - 10)(x + 2)<br /> \]<br /><br />So, the completely factored form of \(28x^2 + 16x - 80\) is:<br />\[<br />\boxed{4(7x - 10)(x + 2)}<br />\]