Problem solving exercise with polynomial.
Initially posted in the Facebook group 'Math Help'. I first 'solved' it after misreading the details. However, still useful practice and explanation.
How to find the polynomial?
Setup:
We have a polynomial with 2 roots: -5, and 3/2 (assumed to both be multiplicity 1).
- This means we have a quadratic as our model (ax^2 + bx + c) and if we substitute the two values above into this, we get zero. This gives us two equations.
We also know there is a remainder of -7 when it is divided by (x - 2).
- This means we perform long division of the above cubic expression by (x - 2). This will give us one more equation for the remainder of -7.
We also know that we can express the polynomial as a product of it's roots:
- y = k.(x - 3/2).(x + 5). If we then divide this by (x - 2) as above, we get a fourth equation also for the remainder of -7.
This gives us four equations in three unknowns (more than we need) which we can now solve.
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