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Algebra (all content)

Course: Algebra (all content)>Unit 10

Lesson 2: Adding & 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.

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• at why 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
(5 votes)
• why it is multiplyed by -1?
(7 votes)
• Because negative sign is equal to -1 and he is distributing it.
(16 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)
• I know Sal Khan doesn't mention this, but how would we go about solving for x in (16x+14) - (3x² + x - 9)?
(3 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)
• Is this really Algebra 2? At school I did this in Algebra 1. Is this a review/preview or something?
(5 votes)
• Algebra 2 is an extension of Algebra 1 so you will see some overlab.
(3 votes)
• another question, how can i apply this to a job (which jobs?) why odes the stupid government require this nonsense?
(3 votes)
• Any STEM field and even many social science fields involve the use of polynomials. Even if you aren’t interested in any jobs in those fields, mastering this skill develops problem solving and reasoning skills that you will use no matter what career you pursue.
(7 votes)
• 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)
• why is this so hard bro
(4 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.
(3 votes)
• What is the Foil Method?
(3 votes)
• AKA First Outside Inside Last
(2 votes)
• where did you get the -1.
(2 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.
(6 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.