Ask AI: factor 7a²+53a+28

To factor the quadratic expression \(7a^2 + 53a + 28\), we need to find two binomials whose product gives us the original quadratic expression: \[7a^2 + 53a + 28\] Let's start by using the factoring method, where we look for two numbers that multiply to the product of the leading coefficient (7) and the constant term (28), and add up to the middle coefficient (53). First, compute the product of the leading coefficient and the constant term: \[7 \times 28 = 196\] Now, we need to find two numbers that multiply to 196 and add up to 53. Considering the factor pairs of 196, we find that: \[4 \times 49 = 196\] \[4 + 49 = 53\] So, the numbers we need are 4 and 49. Now, rewrite the middle term using these numbers: \[7a^2 + 4a + 49a + 28\] Next, group the terms to factor by grouping: \[(7a^2 + 4a) + (49a + 28)\] Factor out the greatest common factor (GCF) from each group: \[a(7a + 4) + 7(7a + 4)\] Notice that both terms contain a common binomial factor \((7a + 4)\). So we can factor that out: \[(a + 7)(7a + 4)\] Thus, the factored form of \(7a^2 + 53a + 28\) is: \[(a + 7)(7a + 4)\]