Answer:
3x + 8
Step-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 0
This zero remainder tells us that 3x + 8 is a factor of 12x^2 + 29x – 8.
