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
To prove that (x+2) is a factor of the polynomial P(x) = x^3 + 9x^2 + 26x + 24, we use the Factor Theorem. The Factor Theorem states that if (x-c) is a factor of a polynomial P(x), then P(c) = 0. In this case, c = -2. Step 1: Define the polynomial. Let P(x) = x^3 + 9x^2 + 26x + 24. Step 2: Substitute x = -2 into the polynomial. P(-2) = (-2)^3 + 9(-2)^2 + 26(-2) + 24 Step 3: Calculate the value of P(-2). P(-2) = -8 + 9(4) - 52 + 24 P(-2) = -8 + 36 - 52 + 24 P(-2) = 28 - 52 + 24 P(-2) = -24 + 24 P(-2) = 0 Step 4: Conclude based on the Factor Theorem. Since P(-2) = 0, by the Factor Theorem, (x+2) is a factor of x^3 + 9x^2 + 26x + 24. That's 2 down. 3 left today — send the next one.