Question

Find the value of k so that the binomial x-1 is a factor of -3x^4+kx^3+6x^2-9x+3

Answer 1

replace \(x\) by 1, set the result equal to zero, solve for \(k\)

Answer 2

if \(x-1\) is a factor of \(f(x)=-3x^4+kx^3+6x^2-9x+3\) then \(f(1)=0\)
this is because if \(x-1\) is a factor then \(-3x^4+kx^3+6x^2-9x+3=(x-1)(something)\)
and so \(x=1\) gets you
\((1-1)(something )=0\)
therefore
\[-3+k+6-9+3=0\] and you can find
\(k\) from that equation

Answer 3

Thanks :)