University:
Winston-Salem Forsyth County Schools
Course:
AP Calculus AB
Academic year:

2014
Views:

444

Pages:

2
Author:

Jesus Pugh

Notes: Polynomials (Adding/Subtracting) Like terms are defined as having the same _____________________ and the same ________________________. When adding and subtracting polynomials, you add and subtract the __________________________________. ADDING Polynomials: 1. Remove parentheses and rewrite each term. 2. Combine _____________ terms! **Note: Final answers should be in _____________________ form of polynomials! Example 1: Simplify. (a) (12m 2 + 4) + (8m 2 + 5) What about these: (b) ( 6 s 2 + 3 s + 7 ) + ( 2 s 3 + −6 s − 4) 5( 2 x 2 − 3 x + 10) + 3( 3 x 2 + 2 x − 10) 1. Distribute _________________ outside of the _________________________ FIRST! 2. Follow Steps Above Try it…… (c) 5(2 x 2 − 3 x + 10) + 3(3 x 2 + 2 x − 10) SUBTRACTING Polynomials: Subtraction is the same thing as adding the _________________________. 1. Remove the parentheses from the first expression and rewrite each term; ____ _____ change the signs. 2. When you remove the parentheses from the second expression, change each term to its _________________________ sign. 3. ______________________ like terms. Example 2: Simplify. (a) ( 2 x 3 + 4 x 2 − 6) − ( 5 x 3 + 2 x 2 − 2) What if it looks like this: 1. (b) (8c 4 + 2c + 3) − ( 3c 2 − c + 1) 5( 2 x 2 − 3 x + 10) − 3( 3 x 2 + 2 x − 10) Distribute the ______________ outside of the parenthesis to each _______________ FIRST! (Be Mindful of the MINUS!) 2. Multiply the __________________ 3. Combine ____________ terms. Try it…… (c) 5(2 x 2 − 3 x + 10) − 3(3 x 2 + 2 x − 10) Notes: Polynomials (Adding/Subtracting) Like terms are defined as having the same ______VARIABLE______ and the same _____DEGREE (EXPONENT)____. When adding and subtracting polynomials, you add and subtract the ______COEFFICIENTS_____________. ADDING Polynomials: 3. Remove parentheses and rewrite each term. 4. Combine ____LIKE____ terms! **Note: Final answers should be in ____SIMPLEST_______ form of polynomials! Example 1: Simplify. (a) (12m 2 + 4) + (8m 2 + 5) What about these: (b) ( 6 s 2 + 3 s + 7 ) + ( 2 s 3 + −6 s − 4) 5( 2 x 2 − 3 x + 10) + 3( 3 x 2 + 2 x − 10) 3. Distribute __NUMBER___ outside of the _____PARENTHESES_______ FIRST! 4. Follow Steps Above Try it…… (c) 5(2 x 2 − 3 x + 10) + 3(3 x 2 + 2 x − 10) SUBTRACTING Polynomials: Subtraction is the same thing as adding the _____OPPOSITE______. 4. Remove the parentheses from the first expression and rewrite each term; _DO_ _NOT_ change the signs. 5. When you remove the parentheses from the second expression, change each term to its ___OPPOSITE_____ sign. 6. ___COMBINE___ like terms. Example 2: Simplify. (a) ( 2 x 3 + 4 x 2 − 6) − ( 5 x 3 + 2 x 2 − 2) What if it looks like this: (b) (8c 4 + 2c + 3) − ( 3c 2 − c + 1) 5( 2 x 2 − 3 x + 10) − 3( 3 x 2 + 2 x − 10) 4. Distribute the ___NUMBER___ outside of the parenthesis to each __COEFFICIENT__ FIRST! (Be Mindful of the MINUS!) 5. Multiply the __COEFFICIENTS___ 6. Combine __LIKE____ terms. Try it…… (c) 5(2 x 2 − 3 x + 10) − 3(3 x 2 + 2 x − 10)