Question

\[Express f(x)=x^{3}-x+6 \in the form (x+2)(x ^{2}+bx+c, where b & c are integers.\]

Answer 1

one way of doing this is to multiply out the expression they have given you and then compare the coefficients of each power of x. i.e.\[(x+2)(x^2+bx+c)=x^3+bx^2+cx+2x^2+2bx+2c\]\[=x^3+(b+2)x^2+(c+2b)x+2c\]
now compare this to the original expression and we will get:\[f(x)=x^3-x+6\]\[=x^3+(b+2)x^2+(c+2b)x+2c\]
comparing coefficients, we get:\[b+2=0\]\[c+2b=-1\]\[2c=6\]you then just need to solve these equations to get the values for "b" and "c".

Answer 2

Many thanks, asnaseer

Answer 3

no problem - always glad to help :-)