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.

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1. Review of Real Numbers2h 39m

Simplifying Fractions
30m

Evaluating Exponents
29m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
40m

2. Linear Equations and Inequalities3h 38m

The Addition and Subtraction Properties of Equality
41m

The Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Linear Inequalities in One Variable
1h 11m

3. Solving Word Problems2h 43m

Introduction to Problem Solving
37m

Formulas
21m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphing Linear Equations in Two Variables3h 17m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

5. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

6. Exponents and Polynomials3h 25m

The Product Rule
10m

The Quotient Rule
13m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

7. Factoring2h 42m

Factoring by Greatest Common Factor & Grouping
37m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
33m

Quadratic Equations & Applications
41m

8. Rational Expressions and Equations3h 13m

Simplifying Rational Expressions
39m

Multiplying and Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

9. Inequalities and Absolute Value2h 52m

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42m

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38m

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39m

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28m

Systems of Linear Inequalities
23m

10. Relations and Functions1h 10m

Introduction to Relations and Functions
25m

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15m

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5m

Composition of Functions
24m

11. Roots, Radicals, and Complex Numbers2h 33m

Introduction to Radical Expressions
11m

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27m

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19m

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23m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

12. Quadratic Equations and Functions1h 23m

The Square Root Property
25m

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26m

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31m

13. Inverse, Exponential, & Logarithmic Functions1h 5m

Introduction to Inverse Functions
25m

Exponential Functions
13m

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26m

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32m

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15m

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10m

15. Sequences, Series, and the Binomial Theorem1h 20m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Factorials
11m

6. Exponents and Polynomials

Adding and Subtracting Polynomials

Beginning & Intermediate Algebra

6. Exponents and Polynomials

Adding and Subtracting Polynomials

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Multiple Choice

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

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

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

$4 x^{2} + 3 x + 5$

$4 x^{2} + 15 x + 5$

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Verified step by step guidance

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

Remove the parentheses by distributing the subtraction sign to each term inside the second parentheses. This changes the signs of each term in $(-x^2 + 6x + 10)$, so rewrite the expression as \$3x^2 + 9x + 15 + x^2 - 6x - 10$.

Group like terms together: combine the $x^2$ terms, the $x$ terms, and the constant terms separately. This gives $(3x^2 + x^2) + (9x - 6x) + (15 - 10)$.

Add or subtract the coefficients of the like terms: add the coefficients of $x^2$, add the coefficients of $x$, and subtract the constants.

Write the simplified polynomial by combining the results from the previous step into the form $ax^2 + bx + c$.

7:43m

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Struggling with Beginning & Intermediate Algebra?

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

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