This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey Blessings — ready when you are. To factorize the quadratic expression 3f^2 - 13f + 4, we will use the method of splitting the middle term. Step 1: Identify the coefficients. The expression is in the form af^2 + bf + c, where a=3, b=-13, and c=4. Step 2: Find two numbers that multiply to ac and add up to b. We need two numbers that multiply to a × c = 3 × 4 = 12 and add up to b = -13. The two numbers are -1 and -12, because (-1) × (-12) = 12 and (-1) + (-12) = -13. Step 3: Rewrite the middle term using these two numbers. 3f^2 - 13f + 4 = 3f^2 - f - 12f + 4 Step 4: Factor by grouping. Group the terms and factor out the common factors from each pair. (3f^2 - f) + (-12f + 4) Factor f from the first group and -4 from the second group. f(3f - 1) - 4(3f - 1) Step 5: Factor out the common binomial. Now, (3f - 1) is a common factor. (3f - 1)(f - 4) The factored form of the expression is: (3f - 1)(f - 4) Send me the next one 📸