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# Adding and subtracting polynomials

## Video transcript

Simplify 16x plus 14 minus
this entire quantity 3x squared plus x minus 9. So let me just rewrite it and
I'll get rid of some of the parentheses if we can. So we have this 16x
right here. 16x plus 14. we don't have to have those
parentheses, it doesn't change the order of operations. And then we can subtract
from that. Well, we can just distribute
this negative sign. So instead of having a positive
3x squared, if we multiply it times
this negative 1, it is minus 3x squared. That's that term right
over there. And then you have this
x over here. It's a positive x, but it's
being multiplied by this negative 1 out here. So it is minus x. And then finally, you have this
negative 9 out here, but it's being multiplied by a
negative 1 out in front of the parentheses, so a
negative times a negative is a positive. So plus 9. And so now we can just combine
terms that have the same degree of x in them. And I'll start with the
highest degree term. The highest degree
term right here. And the degree just
means x raised to the highest exponent. The highest degree term here
is negative 3x squared. It's the second degree term. x is being raised to
the second power. So I'll just write here,
negative 3x squared. It's the only when we have. Then we have the x terms.
We have 16x minus x. So if you have 16 of something
and you subtract 1 away from it, you're going to have 15x. So plus 15x. And then finally, you have your
constant terms. 14 and then you have plus 9. So 14 plus 9 is 23. Plus 23. And we are all done. We've simplified
the polynomial.