If (x+1) is a factor of 2x^3+21x^2+54x+35, fully factorise 2x^3+21x^2+54x+35
In order to find the other factors, we need to do polynomial division. We can do this by method of long division. We start by finding what we must times the x in (x+1) by to get the largest term of the polynomial. E.g x*2x2 =2x3 ( 2x2 goes onto of the division line) we then must then multiply (x+1) by this number, giving 2x3+2x2 . We then subtract this from our original polynomial, to give a new polynomial of 19x2+54x+35. We then repeat the process, finding what we must multiply x by to get 19x2. The process continues until we get a polynomial of 0. The resulting polynomial on top of the division line is another factor. As the original polynomial is a cubic, this polynomial will be a quadratic. As a result it may be able to be factorised further. We can do this final factorisation by GCSE methods. This then answers the question, and gives the 3 factors of the polynomial.
