Question

Is (x - 10) a factor of x2 – 21x + 110?

Answer 1

No need to factor. Use the factor theorem.

Answer 2

If you need to check whether x - k is a factor, then see if f(k) = 0.

Answer 3

Here k = 10, right? Now find \(f(10)\) which will be \(10^2 - 21(10) + 110\)

Answer 4

\( \color{Black}{\Rightarrow 100 - 210 + 110}\)
\( \color{Black}{\Rightarrow 210 - 210}\)
\( \color{Black}{\Rightarrow 0}\)

We just showed that \(f(10) = 0\), therefore \(x - 10\) is a factor.