Add or subtract the polynomials.(3x2+9x+15)−(−x2+6x+10)(3x^2+9x+15)-(-x^2+6x+10)

4 x 2 + 3 x + 5 4x^2+3x+5 4 x 2 + 3 x + 5

Add or subtract the polynomials. ( 3 x 2 + 9 x + 15 ) − ( − x 2 + 6 x + 10 ) (3x^2+9x+15)-(-x^2+6x+10)

Alright, folks. So, let's get started with our first practice problem in the set. So, here we are going to add or subtract the following polynomials. Our first one is three x squared plus nine x plus 15 minuteus the second polynomial, which is negative x squared plus six x plus 10. Now, there's a couple things that we learned in our video. When we add or subtract polynomials, we combine like terms. These are terms with the same variable with the same exponents. And then we also learned that when we have distribute, when we have minus signs, we have to distribute those in the parentheses before we can drop them and start dealing with the like terms. So, let's go ahead and tackle this problem over here. First, what I want to do is kind of look through my problems and figure out what the like terms are. So, I've got three x squared in the first term, and I've got a negative x squared in the second term as well. Here, what I've got is a nine x, so that is only just one power of x. In the second polynomial, I also have a six x, so those are going to be like terms. And then, I've got a 15 and then I've got a 10, so I've got constants in both of them as well. Now, I'm not going to do anything just yet because first I have to deal with the minus sign. What we learned is that you have to distribute this minus sign inside of everything in the parentheses before you can drop the parentheses. With addition, when we're adding polynomials, this usually doesn't happen here, but with subtraction we have to do this first. What I can do here is for this first term, I actually don't change anything because there's no minus signs, right? So, I've just got three x squared plus nine x plus 15, so so I could just go ahead and rewrite that without any parentheses. Now, what I want to do is I want to be able to drop the parentheses on the second term, but have to distribute this negative sign to everything that's inside of it. So what happens? I've got a minus sign that distributes into a negative x squared. So, what happens here is this becomes a positive the negative cancels out. Then, we've got a minus that's going into a positive six x that becomes negative six x and then a minus sign into a positive 10 which becomes minus 10. Now that I've done this, I can go ahead and just drop the parentheses, and now I can start again combining my like terms. So, again, I'm just gonna go through, I've got a three x squared and an x squared, I've got a plus nine x and a negative six x, and I've got a plus 15 and a minus 10. Alright? So, you go ahead and start rearranging these, what you can do is you can put them together. Three x squared plus x squared, you have to keep the sign that's in front of that term. Then we've got a you've got a plus nine x minus 6x, and then we've got a plus 15 minus 10. All right, so again I've got the, these terms that all are like or similar to each other, same variable, same exponents that are together, and now I can just start to combine them. So, what is three x squared plus x squared? That just becomes four x squared. What about the nine x minus six x? Well, nine minus six becomes three x over here. And then what about 15 minus 10? So, plus 15 minus 10 just turns into plus five. Oh, I'm sorry. This is gonna be a positive three x. I don't know if you caught that. So, nine x minus three x is positive three x, and then 15 minus 10 is positive five. So, we're left with just positive for everything. And notice how we can't really combine anything else, right, because we only have one of each type of term, one with the x squared, one with the x, and one with the constants. So, this is all we can do. Alright? So, let me know if you have any questions. Thanks for watching, and let's get to the next one.

Add or subtract the polynomials. ( 3 x 2 + 9 x + 15 ) − ( − x 2 + 6 x + 10 ) (3x^2+9x+15)-(-x^2+6x+10)

4 x 2 + 3 x + 5 4x^2+3x+5 4 x 2 + 3 x + 5

4 x 2 + 15 x + 5 4x^2+15x+5 4 x 2 + 15 x + 5

6. Exponents, Polynomials, and Polynomial Functions

Adding and Subtracting Polynomials

Intermediate Algebra

6. Exponents, Polynomials, and Polynomial Functions

Adding and Subtracting Polynomials

Struggling with Intermediate Algebra?

Join thousands of students who trust us to help them ace their exams!

Multiple Choice

Add or subtract the polynomials.
$(3 x^{2} + 9 x + 15) - (- x^{2} + 6 x + 10)$

$4 x^{2} + 3 x + 25$

$3 x^{2} + 3 x + 5$

$4x^2+3x+5$

$4x^2+15x+5$

Verified step by step guidance

Identify the given expression: $(3x^2 + 9x + 15) - (-x^2 + 6x + 10)$.

Remove the parentheses carefully, remembering to distribute the minus sign to each term inside the second parentheses: \$3x^2 + 9x + 15 - (-x^2) - 6x - 10$.

Simplify the expression by changing the signs inside the second parentheses: \$3x^2 + 9x + 15 + x^2 - 6x - 10$.

Combine like terms by grouping the $x^2$ terms, the $x$ terms, and the constant terms separately: $(3x^2 + x^2) + (9x - 6x) + (15 - 10)$.

Write the simplified polynomial by adding the coefficients of like terms: \$4x^2 + 3x + 5$.

7:43m

Watch next

Master Adding and Subtracting Polynomials with a bite sized video explanation from Patrick Ford