Final answer:
To find the other factor of the polynomial 8x^2 - 2x - 3 given that (4x - 3) is one factor, we can attempt to factor by polynomial division or grouping.
Step-by-step explanation:
The student has asked to find the other factor of the quadratic polynomial 8x^2 - 2x - 3 given that (4x - 3) is one of its factors. To find the other factor, we must perform polynomial division or use a method such as factoring by grouping. However, the sample information provided does not directly help in solving this particular problem because it does not relate to the quadratic polynomial in question.
Instead, we can solve the quadratic equation by factoring it. Since we are given that (4x - 3) is one factor, the other factor must multiply with (4x - 3) to give the original polynomial 8x^2 - 2x - 3. Hence, we must find a binomial factor such that:
(4x - 3)(Ax + B) = 8x^2 - 2x - 3
We can expand the left-hand side and compare coefficients with the right-hand side to find the values of A and B. After finding A and B, the expression Ax + B will give us the other factor. Remember to eliminate terms wherever possible to simplify the algebra and check the answer to see if it is reasonable. If the binomial (4x - 3) is indeed a factor, we should expect the factors that result from this process to correctly multiply back to the original quadratic polynomial.