12:13 5G 12 siyavula.com Siya \( \sqrt{4} / 2 \) The other factor of \( x^{2}+b x+24 \) is: \( x+6 \) \( x-6 \) \( (x+b)+24 \) Impossible to find Exactly right. High five! Show the full solution 2. Consider the same equation: \[ x^{2}+b x+24=0 \] Use your answers to Question 1 to determine: 1. The other solution to the equation. 2. The value of \( b \). 95

We start with the quadratic:   x² + bx + 24 = 0 Suppose that in Question 1 you found one of the factors to be (x + 4). (This is consistent with the fact that factors of 24 that add up to give b in the factored form are 4 and 6.) To factor the quadratic completely, we need to find the other factor, say (x + c), such that   (x + 4)(x + c) = x² + bx + 24. Step 1. Expand the product:   (x + 4)(x + c) = x² + (4 + c)x + 4c. Step 2. Compare coefficients with x² + bx + 24:   • The constant term: 4c = 24 ⟹ c = 6.   • The coefficient of x: 4 + c = 4 + 6 = 10, so b = 10. Thus, the factorization is:   x² + 10x + 24 = (x + 4)(x + 6). Step 3. Find the solutions: Set each factor equal to zero.   x + 4 = 0 ⟹ x = –4,   x + 6 = 0 ⟹ x = –6. Since you already had one solution (x = –4), the other solution is x = –6. Summary of Answers: 1. The other solution of the equation is x = –6. 2. The value of b is 10.