Originally Posted by

**Jen1603** Use the remainder theorem to factorise :

1)

The rational roots theorem tells us if this has rational roots, they will be

Test each one using the remainder theorem to see which one(s) satisfy

I found , so is a factor.

To find the remaining factors, you could test the rest of the possible rational roots using the remainder theorem or use synthetic division with divisor **-2**to reduce the polynomal to a quadratic that you can factor.

Code:

-2 | 1 3 0 -4
-2 -2 4
------------
1 1 -2 0

The quadratic remaining after factoring is

That factors into

Originally Posted by

**Jen1603** 2)

Test these factors

There are no sign changes in this polynomial, so no need to check for positive zero because there aren't any (Descartes Rule of Signs)