Factoring Polynomials I Score: 3/8 Answered: 3/8 Question Factor completely: 5x^2+22x+8 square

To factor the polynomial \(5x^2 + 22x + 8\) completely, we need to find two binomials whose product gives us the original polynomial. Here are the steps:<br /><br />1. **Multiply the leading coefficient (5) by the constant term (8):**<br /> \[<br /> 5 \times 8 = 40<br /> \]<br /><br />2. **Find two numbers that multiply to 40 and add up to the middle coefficient (22):**<br /> The numbers are 20 and 2 because:<br /> \[<br /> 20 \times 2 = 40 \quad \text{and} \quad 20 + 2 = 22<br /> \]<br /><br />3. **Rewrite the middle term (22x) using the two numbers found:**<br /> \[<br /> 5x^2 + 22x + 8 = 5x^2 + 20x + 2x + 8<br /> \]<br /><br />4. **Factor by grouping:**<br /> Group the terms in pairs and factor out the common factor from each pair:<br /> \[<br /> 5x^2 + 20x + 2x + 8 = 5x(x + 4) + 2(x + 4)<br /> \]<br /><br />5. **Factor out the common binomial factor \((x + 4)\):**<br /> \[<br /> 5x(x + 4) + 2(x + 4) = (5x + 2)(x + 4)<br /> \]<br /><br />So, the completely factored form of the polynomial \(5x^2 + 22x + 8\) is:<br />\[<br />(5x + 2)(x + 4)<br />\]