Question

Is p=-6 a zero of 3p^3+23p^2+28p-12?

Answer 1

We must check if p = -6 is a zero of the polynomial:

`f(p)=3p^3+23p^2+28p-12.`

By definition, the zero of a function is any replacement for the variable that will produce an answer of zero.

Replacing p = -6 in the equation above, we get:

`f(-6)=3\cdot(-6)^3+23\cdot(-6)^2+28\cdot(-6)-12=(-216)+23\cdot36-168-12=0\text{ }✓`

Answer

p = -6 is a zero of the polynomial because we have f(-6) = 0.