Question

Write a polynomial function of least degree with integral coefficients that has the given zeros. -2, -8, -7

Answer 1

A zero is a solution to a given function when f(x) = 0.

First, let's factor in our zeros.
\[f(x) = 0 = \left( x + 2 \right)\left( x + 7 \right)\left( x + 8 \right)\]
\[f(x) = (x ^{2} + 9x + 14)\left( x + 8 \right)\]
\[f(x) = x ^{3} + 17x ^{2} + 86x + 112\]
And there you have it.

Answer 2

Further clarification: in this case, zeros are used in this format
\[-2 = x \rightarrow \left( x + 2 \right) = 0\]
\[-8 = x \rightarrow \left( x + 8 \right) = 0\]
\[-7 = x \rightarrow \left( x + 7 \right) = 0\]
is it easier to see how, 'zeros' are basically solutions to a function when it equates to zero?