The polynomial function \(B(x)=x^3-21x+20\) has a known factor of \((x-4)\). Rewrite \(B(x)\) as a product of linear factors.

Let the function \(P\) be defined by \(P(x) = x^3 + 7x^2 - 26x - 72\) where \((x+9)\) is a factor. To rewrite the function as the product of two factors, long division was used but an error was made:

\(\displaystyle \require{enclose} \begin{array}{r}  x^2+16x+118\phantom{000} \\ x+9 \enclose{longdiv}{x^3+7x^2-26x-72} \phantom{000}\\    \underline{-x^3+9x^2} \phantom{-26x-720000} \\  16x^2-26x \phantom{-720000}\\ \underline{-16x^2+144x} \phantom{-20000} \\ 118x-72 \phantom{00} \\ \underline{-118x+1062} \\ 990 \end{array}\)

How can we tell by looking at the remainder that an error was made somewhere?

For the polynomial function \(A(x)=x^4-2x^3-21x^2+22x+40\) we know \((x-5)\) is a factor. Select all the other linear factors of \(A(x)\).