Question

Find whether the first polynomial is a factor of the second.

 4 − z, 3z² − 13z + 4

Answer 1

\[ \frac{{3z}^2 -13z+4}{4-z}\]
\[ = \frac{{3z}^2 -12z-z+4}{4-z}\]
\[ = \frac{3z(z-4)-1(z-4)}{4-z}\]
\[ = \frac{(z-4)(3z-1)}{4-z}\]
\[ = \frac{(4-z)(1-3z)}{4-z}\]
\[ =1-3z \]
\[ \because \text{Remainder = 0}\]
\[ \therefore \text{(4-z) is a factor of}\ {3z}^2 -13z+4.\]