If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

# Subtracting polynomials

CCSS.Math:

## Video transcript

simplify 16x plus 14 minus the entire expression 3x squared plus X minus 9 so when you subtract an entire expression this is the exact same thing as having 16x plus 14 and then you're adding the opposite of this whole thing or you're adding negative 1 you're adding negative 1 times 3x squared plus X minus 9 or another way to think about is you can distribute this negative sign along all of those terms that's essentially what we're about to do here we're just adding the negative of this entire thing we're adding the opposite of it so this first part I'm not going to change it that's still just 16x plus 14 but now I'm going to distribute the negative sign here so negative 1 times 3x squared is negative 3x squared negative 1 times positive x is negative x because that's a positive 1 X negative 1 times negative 9 remember you have to consider this negative right over there that is part of the term negative 1 times negative 9 is positive 9 negative times a negative is a positive so then we have positive 9 and now we just have to combine like terms so what's our highest degree term here I like to write in that order if we have only one x squared term second degree term we only have one of those let me write it over here negative 3x squared and then what do we have in terms of first degree terms of just an X X to the first power well we have a 16x and then from that we're going to subtract an X subtract 1 X so 16x minus One X is 15 X if you have 16 or something and you subtract one of them away you're going to have 15 of that something and then finally you have 14 you could view that as 14 times X to the 0 or just 14 14 plus 9 they're both constant terms or they're both being multiplied by X to the 0 14 plus 9 is 23 23 and we're done negative 3x squared plus 15 X plus 23