Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor.\newlineu2+13u+22u^2 + 13u + 22

Full solution

Q. Factor.\newlineu2+13u+22u^2 + 13u + 22
  1. Identify Coefficients: Identify the coefficients for u2u^2, uu, and the constant term.\newlineThe quadratic expression is u2+13u+22u^2 + 13u + 22. Here, the coefficient of u2u^2 (aa) is 11, the coefficient of uu (bb) is 1313, and the constant term (cc) is uu00.
  2. Find Multiplying Numbers: Find two numbers that multiply to give the constant term c=22c = 22 and add up to the coefficient of uu b=13b = 13. We need to find two numbers mm and nn such that m×n=22m \times n = 22 and m+n=13m + n = 13.
  3. List Factors and Sum: List the factors of 2222 and determine which pair adds up to 1313. The factors of 2222 are 11 and 2222, 22 and 1111. The pair that adds up to 1313 is 22 and 1111 because 131300.
  4. Write Factored Form: Write the factored form using the two numbers found in the previous step.\newlineThe factored form of the quadratic expression is (u+2)(u+11)(u + 2)(u + 11) because these two binomials multiply to give the original quadratic expression.