Adding & subtracting polynomials
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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 times 3x squared plus x minus 9. Or another way to think about it 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 positive 1x. 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 it in that order. We have only one x squared term, second-degree term. We only have one of those. So 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 1x. So 16x minus 1x is 15x. If you have 16 of something and you subtract 1 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. And we're done. Negative 3x squared plus 15x plus 23.