Hi can someone please help me figure this out?
WHen a polynomial is divided by (2x + 1)(x - 3), the remainder is 3x - 1. What is the remainder when the polynomial is divided by 2x +1?
Thanks !
Hello ipokeyouThe remainder when any polynomial in is divided by a quadratic in will be a linear expression in : (where either or both of and may be zero); in other words the remainder will be of degree at most 1.
When it is divided by a linear expression, the remainder will be a constant term (which, again, may be zero).
So let's suppose that the polynomial is and that the quotient when it is divided by is . Then, since we know that the remainder is , we can write:which we can write as:Now when this expression is divided by the quotient will be the polynomial , and the remainder will be . So there's your answer: .
Grandad