Add/Subtract polynomials
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1. The document provides examples of adding and subtracting polynomials by grouping like terms and using column form. 2. Students are asked to perform operations like adding (9y - 7x + 15a) + (-3y + 8x - 8a) and subtracting (4x^2 - 2xy + 3y^2) - (-3x^2 - xy + 2y^2). 3. The objectives are for students to learn how to add and subtract polynomials.
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Adding and subtracting polynomials
Adding and subtracting polynomials involves combining like terms. Like terms are terms that have the same variables and the same exponents. To add polynomials, terms are grouped by their like terms and the coefficients are combined by adding them. To subtract polynomials, the process is the same as adding the opposite of the second polynomial. The opposite of each term is found by changing its sign. Then the like terms are combined in the same way as when adding.
Slope of a Line
This document contains a lesson on slope of a line from a mathematics course. It includes examples of calculating slope given two points on a line, identifying whether graphs represent constant or variable rates of change, and word problems applying slope to real-world contexts like cost of fruit and gas. The key points are that slope is defined as the ratio of rise over run, or change in y over change in x, and represents the constant rate of change for linear equations and functions.
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To solve this rational equation, we first find the LCD of the fractions, which is x^2(x-5)(x-6). Then we multiply both sides of the equation by the LCD:
x^2(x-5)(x-6) = x^2(x-5)(x-6)
Canceling the common factors, we obtain:
x^2 = x^2
Since this holds for all real values of x, the solution is all real numbers. Therefore, the solution is x ∈ R.
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The document describes three methods for multiplying polynomials:
1) The distributive property, which involves multiplying each term of one polynomial with each term of the other.
2) FOIL (First, Outer, Inner, Last), which is a mnemonic for multiplying binomials by multiplying corresponding terms.
3) The box method, which involves drawing a box and writing one polynomial above and beside the box, then multiplying corresponding terms. Examples are provided to demonstrate each method.
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This document defines polynomials and describes how to perform operations on them such as addition and subtraction. It provides examples of adding and subtracting monomials and polynomials. Monomials are terms with variables and coefficients, and polynomials are the sum of monomials. Like terms refer to monomials with the same variables and exponents that can be combined. To add polynomials, like terms are lined up and their coefficients are summed. To subtract polynomials, the operation is changed to addition by using the keep-change-change method and then like terms are combined.
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Adding and subtracting polynomials
Adding and subtracting polynomials involves combining like terms. Like terms are terms that have the same variables and the same exponents. To add polynomials, terms are grouped by their like terms and the coefficients are combined by adding them. To subtract polynomials, the process is the same as adding the opposite of the second polynomial. The opposite of each term is found by changing its sign. Then the like terms are combined in the same way as when adding.
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This document contains a lesson on slope of a line from a mathematics course. It includes examples of calculating slope given two points on a line, identifying whether graphs represent constant or variable rates of change, and word problems applying slope to real-world contexts like cost of fruit and gas. The key points are that slope is defined as the ratio of rise over run, or change in y over change in x, and represents the constant rate of change for linear equations and functions.
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To solve this rational equation, we first find the LCD of the fractions, which is x^2(x-5)(x-6). Then we multiply both sides of the equation by the LCD:
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Canceling the common factors, we obtain:
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1) It explains how to factor polynomials by finding the greatest common factor (GCF).
2) It describes how to factor trinomials of the form x2 + bx + c by finding two numbers whose sum is b and product is c.
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This document provides steps for solving radical equations:
1) Isolate the radical on one side of the equation by performing inverse operations
2) Raise both sides of the equation to a power equal to the index of the radical to eliminate the radical
3) Solve the remaining polynomial equation
It includes examples of solving simpler radical equations as well as more complex equations involving fractions and multiple radicals. Checking solutions is emphasized as extraneous solutions may occasionally occur. Graphing calculators can also help visualize and find solutions to radical equations.
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- Polynomials are sums of terms involving variables raised to whole number exponents, with no variables in denominators.
- Types of polynomials include monomials (1 term), binomials (2 terms), and trinomials (3 terms). Degree is the largest exponent of any term.
- Operations on polynomials include adding/subtracting like terms, multiplying using distribution and FOIL, dividing using long division, and special products like (a+b)2 and (a+b)(a
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Using rules for fractions, rational expressions can be added and subtracted by finding common denominators. To find the common denominator, we find the least common multiple (LCM) of the denominators. With polynomials, the LCM will contain all factors of each denominator. We can then convert the fractions to equivalent forms using the LCM as the new denominator before combining like terms to evaluate the expression. Special cases may involve fractions with understood denominators of 1 or similar but non-equal denominators that can be made equal through factoring.
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This document provides instructions on factoring polynomials of various forms:
1) It explains how to factor polynomials by finding the greatest common factor (GCF).
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The student will learn to:
1. Add and subtract polynomials by grouping like terms.
2. Use column form to add and subtract polynomials with three terms.
3. Simplify polynomial expressions involving addition and subtraction.
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The student will be able to:
1. Add and subtract polynomials.
The document provides examples of adding and subtracting polynomials by combining like terms. It includes adding and subtracting polynomials using column form. There are also practice problems for students to find the sum or difference of polynomials.
ADDITION, SUBTRACTION OF POLYNOMIALS.ppt
1. Add the polynomials (9y - 7x + 15a) and (-3y + 8x - 8a) by grouping like terms to get 12y - 15x + 23a.
2. Subtract the polynomials (7a - 10b) and (3a + 4b) by rewriting subtraction as addition of opposites and grouping like terms to get 4a - 14b.
3. Add or subtract polynomials in column form by lining up like terms and adding or subtracting the coefficients.
adding polynomials .pptx
1. Add the polynomials (9y - 7x + 15a) and (-3y + 8x - 8a) by grouping like terms to get 12y - 15x + 23a.
2. Subtract the polynomials (7a - 10b) and (3a + 4b) by rewriting subtraction as addition of opposites and grouping like terms to get 4a - 14b.
3. Add or subtract polynomials in column form by lining up like terms and adding or subtracting the coefficients.
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The student will learn how to:
1. Add and subtract polynomials by grouping like terms. This includes combining terms with the same variables but different coefficients, as well as using column form to align terms.
2. Solve polynomial addition and subtraction problems by lining up and combining like terms. This involves changing subtraction of a term to addition of the opposite term.
3. Simplify sums and differences of polynomials through grouping like terms and finding the final algebraic expression.
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This document provides instruction on adding, subtracting, and finding the degree of polynomials. It includes examples of combining like terms, arranging polynomials in ascending and descending order, finding the degree of monomials and polynomials, and solving problems involving adding and subtracting polynomials. The objectives are for students to be able to find the degree of a polynomial, arrange terms in ascending or descending order, and add and subtract polynomials.
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The student simplified 6a3 - a3 and incorrectly obtained a6 as the result. The student's error was due to not combining like terms - the a3 terms which have the same coefficient. When combining like terms, terms with the same variables but different coefficients are collected.
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To add and subtract polynomials:
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1. The ac-method is used to factor 3x^2 - 4x - 20 by finding two numbers whose product is ac and sum is b.
2. Checking if b^2 - 4ac is a perfect square to determine if a trinomial is factorable.
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The document provides definitions and explanations of key concepts in algebra including:
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- 1. Objectives The student will be able to: 1. add and subtract polynomials. 14-2 Page 493
- 2. 1. Add the following polynomials: (9y - 7x + 15a) + (-3y + 8x - 8a) Group your like terms. 9y - 3y - 7x + 8x + 15a - 8a 6y + x + 7a
- 3. 2. Add the following polynomials: (3a2 + 3ab - b2) + (4ab + 6b2) Combine your like terms. 3a2 + 3ab + 4ab - b2 + 6b2 3a2 + 7ab + 5b2
- 4. Add the polynomials. + X2 X X Y Y X XY 1 1 Y Y Y Y 1 1 Y 1 1 1 1 1. x2 + 3x + 7y + xy + 8 2. x2 + 4y + 2x + 3 3. 3x + 7y + 8 4. x2 + 11xy + 8
- 5. 3. Add the following polynomials using column form: (4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2) Line up your like terms. 4x2 - 2xy + 3y2 + -3x2 - xy + 2y2 _________________________ x2 - 3xy + 5y2
- 6. 4. Subtract the following polynomials: (9y - 7x + 15a) - (-3y + 8x - 8a) Rewrite subtraction as adding the opposite. (9y - 7x + 15a) + (+ 3y - 8x + 8a) Group the like terms. 9y + 3y - 7x - 8x + 15a + 8a 12y - 15x + 23a
- 7. 5. Subtract the following polynomials: (7a - 10b) - (3a + 4b) Rewrite subtraction as adding the opposite. (7a - 10b) + (- 3a - 4b) Group the like terms. 7a - 3a - 10b - 4b 4a - 14b
- 8. 6. Subtract the following polynomials using column form: (4x2 - 2xy + 3y2) - (-3x2 - xy + 2y2) Line up your like terms and add the opposite. 4x2 - 2xy + 3y2 + (+ 3x2 + xy - 2y2) -------------------------------------- 7x2 - xy + y2
- 9. Find the sum or difference. (5a – 3b) + (2a + 6b) 1. 3a – 9b 2. 3a + 3b 3. 7a + 3b 4. 7a – 3b
- 10. Find the sum or difference. (5a – 3b) – (2a + 6b) 1. 3a – 9b 2. 3a + 3b 3. 7a + 3b 4. 7a – 9b