Final answer:
Factorisation of the cubic polynomial 2x³+9x²+7x-6 using the remainder theorem involves finding the roots by testing potential factors of the constant term and then simplifying the polynomial using appropriate methods of factoring and algebraic simplification.
Step-by-step explanation:
The question pertains to factorising a cubic polynomial using the remainder theorem. In order to factorise 2x³+9x²+7x-6, we need to find the zeroes of the polynomial by testing potential factors of the constant term, which is -6 in this case. These potential factors are ±1, ±2, ±3, and ±6.
Once a zero is found, the remainder theorem states that (x - zero) is a factor. We can then divide the polynomial by this factor to reduce it to a quadratic. The quadratic factor thus obtained can be further factored, if possible, by using methods such as factoring by grouping, completing the square, or using the quadratic formula.
Throughout the process, we need to eliminate terms wherever possible to simplify the algebra and check the answer to see if it is reasonable. This ensures that we have factored the polynomial correctly.