Which expression is a factor of 12x2 + 29x – 8?x – 82x – 13x + 84x + 1
Accepted Solution
A:
Answer:3x + 8Step-by-step explanation:Please use the symbol " ^ " to indicate exponentiation: 12x^2 + 29x – 8.To answer this question, try dividing this 12x^2 + 29x – 8 by each of the given possible factors, one by one. If the end result is a zero remainder, that indicates that the particular factor is in fact a factor of 12x^2 + 29x – 8.Alternatively, use synthetic division; if the end result is zero, then you have identified a root of 12x^2 + 29x – 8, as well as a factor.Let's focus on x - 8: Is this a factor? Is 8 a root? Set up synthetic division as follows:8 ) 12 29 -8 96 1000 ----------------- 12 125 992 The non-zero remainder (992) indicates that 8 is not a root of 12x^2 + 29x – 8, and that x - 8 is not a factor.Continuing onto the next given possible factor, 2x - 1, we set this = to 0 and solve for x, obtaining x = 1/2. Use synthetic division again:1/2 ) 12 29 -8 6 35/2 ------------------------ 12 35 19/2 No, 1/2 is not a root and 2x - 1 is not a factor of 12x^2 + 29x – 8.Try possible root x = -8/3:-8/3 ) 12 29 -8 -32 8 ---------------------------- 12 -3 0This zero remainder tells us that 3x + 8 is a factor of 12x^2 + 29x – 8.