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 !

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- Nov 23rd 2009, 10:46 PMipokeyoumore polynomials
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 ! - Nov 24th 2009, 07:10 AMGrandad
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:

Grandad