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## College Algebra

# Subtracting polynomials

CCSS.Math: ,

Sal simplifies (16x+14) - (3x² + x - 9). 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(9 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?(5 votes)
- Because negative sign is equal to -1 and he is distributing it.(13 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.(6 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)

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

- I thought the answer would be 15x+23-3x^2. Am I still correct?(2 votes)
- what do you do if the same variable has different exponents? for example: D^2 - D^3(3 votes)
- The same variables with different exponents can just be thought of as separate terms. D²-D³ does not simplify further, and it is
*not*equal to D⁻¹.(3 votes)

- How does Sal make people understand so quickly(4 votes)
- Why is he adding! @1:40(3 votes)
- Once the minus is distributed across the polynomial to subtract, you just need to combine like terms. You add/subtract based upon the signs on each like term.

Hope this helps.(3 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.