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### Course: College Algebra > Unit 10

Lesson 2: Adding and subtracting polynomials# Subtracting polynomials

Master the art of adding and subtracting polynomials! Learn how to distribute negative signs across terms, combine like terms, and simplify expressions. This skill is key to understanding algebra and making math easier. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- at0:20why are we adding negative 1 times 3x(11 votes)
- because you are going to have to distribute the negative one to all of the 3x square + x - 9(4 votes)

- why it is multiplyed by -1?(7 votes)
- Because negative sign is equal to -1 and he is distributing it.(17 votes)

- I know Sal Khan doesn't mention this, but how would we go about solving for x in
*(16x+14) - (3x² + x - 9)*?(4 votes)- What you've written is just an expression, not an equation. You can't solve for x because there's nothing to solve.

You can simplify the expression, but it will still have different values for different values of x.(8 votes)

- why do we have to include the negative 1 in this problem, but not in others where you subtract polynomials.(4 votes)
- I believe the -1 is simply to emphasize the fact that you need to distribute the negative sign throughout the polynomial.

Either way, at the end (when done correctly), putting a negative 1 or a negative sign can be used interchangably.(6 votes)

- Is this really Algebra 2? At school I did this in Algebra 1. Is this a review/preview or something?(5 votes)
- Same I'm homeschooled and I did this last year I feel like 9th grade and 10th grade re the same I'm learning the same stuff I might just skip 10th or better yet get my G.E.D(1 vote)

- using division algorithm divide 6x^3+13x^2+x-2 by 2x+1 and find the quotient and remainder(4 votes)
- Just divide! The quotient would be 3x^2 + 5x - 2 and there is no remainder.

Hope this helps! If you have any questions or need help, please ask! :)(0 votes)

- where did you get the -1.(3 votes)
- Remember X and 1X are the same thing. Thus -X and -1X are the same thing. The "-" in front of the parentheses is just like the "-" in front of "-x". It can be changed to -1, which is what Sal did in the video.

Hope this helps.(5 votes)

- What is the Foil Method?(3 votes)
- AKA First Outside Inside Last(2 votes)

- why is this so hard bro(3 votes)
- Simplifying expressions can sometimes involve multiple steps and require careful attention to detail. It's important to identify like terms and combine them correctly.(4 votes)

- I thought the answer would be 15x+23-3x^2. Am I still correct?(2 votes)

## 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 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.