Factor 4x^2+484 (Factor 4x Squared Plus 484) - Factorization

Factor 4x^2+484 On this page, we will show you how to factor 4x squared plus 484 (4x^2+484) using the sum of squares formula. In addition to factoring 4x^2+484, we will also verify that our answer is correct by calculating the product of the factors we found. Before we begin, note that 4 and 484 are both perfect squares. Adding one perfect square to another is called sum of squares or sum of two squares. Furthermore, you cannot factor sum of squares with real numbers. However, you can solve 4x^2+484 with a complex or imaginary number. We will make our imaginary number (i) equal to -1. The sum of squares formula we will use to factor 4x^2+484 with our imaginary number is as follows: a2 + b2 = (a + bi) • (a − bi) We start by setting up our problem in mathematical terms like this: 4x2 + 484 The greatest common factor of 4 and 484 is 4, which means that we can factor out 4 like this: 4 • (x2 + 121) To make our problem fit into the formula, we have to convert our problem to match the left side like so: 4 • (x2 + 112) Now that it matches, we can simply plug in x for a and 11 for b into the formula to get the factors of 4x^2+484: 4 • (x + 11i) • (x − 11i) To verify that our answer is correct, we can calculate the product of the factors to see if it equals 4x^2+484. And it does, as illustrated below: = 4 • (x + 11i) • (x − 11i) = 4 • (x(x - 11i) + 11i(x - 11i)) = 4 • (x2 - 11xi + 11xi - 121i2) - 11xi + 11xi evens out and -i2 equals -1, so now we get this: = 4 • (x2 - (121)(-1)) = 4 • (x2 + 121) = 4x2 + 484 Factoring Sum of Squares Do you need to factor another polynomial using the sum of squares formula? If so, enter it below, but remember that both numbers must be perfect squares. x2 + Factor 4x^2+529 We hope this step-by-step tutorial to teach you how to factor 4x squared plus 484 was helpful. Do you want to learn more? Go here for the next tutorial on our list. Copyright | Privacy Policy | Disclaimer | Contact