What does it mean when it says Roots (order) for a function eg. -x^3-2x^2+15x+36

Question

What i mean is how do you the answer.

Answer 1

the highest exponent is the order...and the number of roots

a root is a value that makes the function equal to zero

you can test values for roots
... 4 works here

divide the function by (x - 4) to factor out the known root
... this leaves a quadratic
... use the quadratic formula for the last two roots

Answer 2

so if i found that the roots are -3 and 4 how would i write that?

-3(order 2), 4

because at -3 the function acts like a quadratic but at 4 it acts linear.

Answer 3

-3 is not a root

the roots are ... -3±i

4, -3+i, -3-i

Answer 4

the highest exponent is the degree
the order of a root is the number of times it appears.

So, you have three roots of degree 1.

Any polynomial of degree n has exactly n roots, though all may not be unique (order 1).