Question

using factor method divide the following polynomials by a binomials

Answer 1

$\text{Concept used:}$

$\textbf{Factor theorem:}$

$\textbf{(x-a) is a factor of f(x) iff f(a) =0}$

$\text{Let }P(z)=z^2-10z+16$

$\text{put z=2 in P(z), we get}$

$P(2)=2^2-10(2)+16$

$P(2)=4-20+16=0$

$\therefore\textbf{(z-2) is a factor of P(z)}$

$\text{put z=8 in P(z), we get}$

$P(8)=8^2-10(8)+16$

$P(8)=64-80+16=0$

$\therefore\textbf{(z-8) is a factor of P(z)}$

$\implies\boxed{\bf\,z^2-10z+16=(z-2)(z-8)}$

Answer 2

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