


Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
POLYNOMIAL OPERATIONS. ADDITION AND SUBTRACTION: Adding and subtracting polynomials is the same as the procedure used in combining like terms.
Typology: Study notes
1 / 4
This page cannot be seen from the preview
Don't miss anything!
Adding and subtracting polynomials is the same as the procedure used in combining like terms. When adding polynomials, simply drop the parenthesis and combine like terms. When subtracting polynomials, distribute the negative first, then combine like terms.
Examples:
Addition:
䙦2ᡶ⡰^ ㎗ 3ᡶ ㎘ 7䙧 ㎗ 䙦3ᡶ⡰^ ㎘ 4ᡶ ㎘ 10䙧 㐄 2ᡶ⡰^ ㎗ 3ᡶ⡰^ ㎗ 3ᡶ ㎘ 4ᡶ ㎘ 7 ㎘ 10 㐄 5ᡶ⡰^ ㎘ ᡶ ㎘ 17
Subtraction:
䙦5ᡶ⡰^ ㎘ 12ᡶ ㎗ 1䙧 ㎘ 䙦2ᡶ⡰^ ㎗ 3ᡶ ㎘ 7䙧 㐄 5ᡶ⡰^ ㎘ 12ᡶ ㎗ 1 ㎘ 2ᡶ⡰^ ㎘ 3ᡶ ㎗ 7 㐄 3ᡶ⡰^ ㎘ 15ᡶ ㎗ 8
MULTIPLICATION:
Example: 䙦㎘2ᡶ⡰ᡷ䙧䙦5ᡶᡷ⡵䙧 㐄 ㎘2 · 5ᡶ⡰^ · ᡶ · ᡷ · ᡷ⡵^ 㐄 ㎘10ᡶ⡱ᡷ⡶
Examples:
a. ㎘2ᡶ䙦ᡶ⡰^ ㎗ 3ᡶ ㎘ 8䙧 㐄 ㎘2ᡶ䙦ᡶ⡰䙧 ㎘ 2ᡶ䙦3ᡶ䙧 ㎘ 2ᡶ䙦㎘8䙧 㐄 ㎘2ᡶ⡱^ ㎗ 6ᡶ⡰^ ㎗ 16ᡶ b. 5ᡶ⡰䙦㎘2ᡶ⡲^ ㎗ 3ᡷ ㎘ 6䙧 㐄 5ᡶ⡰䙦㎘2ᡶ⡲䙧 ㎗ 5ᡶ⡰䙦3ᡷ䙧 ㎗ 5ᡶ⡰䙦㎘6䙧 㐄 ㎘10ᡶ⡴^ ㎗ 15ᡶ⡰ᡷ ㎘ 30ᡶ⡰
Example:
䙦ᡶ ㎗ 2䙧䙦ᡶ ㎘ 3䙧 㐄 ᡶ䙦ᡶ䙧 ㎗ ᡶ䙦㎘3䙧 ㎗ 2䙦ᡶ䙧 ㎗ 2䙦㎘3䙧 㐄 ᡶ⡰^ ㎘ 3ᡶ ㎗ 2ᡶ ㎘ 6 㐄 ᡶ⡰^ ㎘ ᡶ ㎘ 6
Special Products: The following formulas may be used in these special cases as a short cut to the FOIL method.
Difference of Squares: 䙦ᡓ ㎗ ᡔ䙧䙦ᡓ ㎘ ᡔ䙧 㐄 ᡓ⡰^ ㎘ ᡔ⡰
Example: 䙦3ᡶ ㎗ 4䙧䙦3ᡶ ㎘ 4䙧 㐄 9ᡶ⡰^ ㎘ 16 Perfect Squares: 䙦ᡓ ㎗ ᡔ䙧⡰^ 㐄 ᡓ⡰^ ㎗ 2ᡓᡔ ㎗ ᡔ⡰
Example: 䙦ᡶ ㎗ 4䙧⡰^ 㐄 ᡶ⡰^ ㎗ 2䙦ᡶ䙧䙦4䙧 ㎗ 4⡰^ 㐄 ᡶ⡰^ ㎗ 8ᡶ ㎗ 16
Example: 䙦ᡶ ㎘ 3䙧⡰^ 㐄 ᡶ⡰^ ㎘ 2䙦ᡶ䙧䙦3䙧 ㎗ 3⡰^ 㐄 ᡶ⡰^ ㎘ 6ᡶ ㎗ 9
Examples:
a. 䙦ᡶ⡰^ ㎗ 3ᡶ ㎘ 4䙧䙦ᡶ⡰^ ㎘ 6ᡶ ㎗ 5䙧 㐄 ᡶ⡰䙦ᡶ⡰䙧 ㎗ ᡶ⡰䙦㎘6ᡶ䙧 ㎗ ᡶ⡰䙦5䙧 ㎗ 3ᡶ䙦ᡶ⡰䙧 ㎗ 3ᡶ䙦㎘6ᡶ䙧 ㎗ 3ᡶ䙦5䙧 ㎘ 4䙦ᡶ⡰䙧 ㎘ 4䙦㎘6ᡶ䙧 ㎘ 4䙦5䙧 㐄 ᡶ⡲^ ㎘ 6ᡶ⡱^ ㎗ 5ᡶ⡰^ ㎗ 3ᡶ⡱^ ㎘ 18ᡶ⡰^ ㎗ 15ᡶ ㎘ 4ᡶ⡰^ ㎗ 24ᡶ ㎘ 20 㐄 ᡶ⡲^ ㎘ 3ᡶ⡱^ ㎘ 17ᡶ⡰^ ㎗ 39ᡶ ㎘ 20 b. 䙦2ᡶ ㎘ 3䙧䙦4ᡶ⡰^ ㎘ 5ᡶ ㎗ 1䙧 㐄 2ᡶ䙦4ᡶ⡰䙧 ㎗ 2ᡶ䙦㎘5ᡶ䙧 ㎗ 2ᡶ䙦1䙧 ㎘ 3䙦4ᡶ⡰䙧 ㎘ 3䙦㎘5ᡶ䙧 ㎘ 3䙦1䙧 㐄 8ᡶ⡱^ ㎘ 10ᡶ⡰^ ㎗ 2ᡶ ㎘ 12ᡶ⡰^ ㎗ 15ᡶ ㎘ 3 㐄 8ᡶ⡱^ ㎗ 22ᡶ⡰^ ㎗ 17ᡶ ㎘ 3 DIVISION:
Examples:
a. ⡱け
ㄘ⡹⡷け⡸⡩⡲ ⡱け 㐄^
⡱けㄘ ⡱け ㎘^
⡷け ⡱け ㎗^
⡩⡲ ⡱け 㐄 ᡶ ㎘ 3 ㎗^
⡩⡲ ⡱け
b. ⡩⡨げ
ㄘ⡹⡰⡳げ⡸⡰⡨ ⡹⡳げ 㐄^
⡩⡨げㄘ ⡹⡳げ ㎘^
⡰⡳げ ⡹⡳げ ㎗^
⡰⡨ ⡹⡳げ 㐄 ㎘2ᡷ ㎗ 5 ㎘^
⡲ げ
Use the long division format as follows:
Examples:
a. 䙦ᡶ^2 ㎘ 2ᡶ ㎘ 15䙧 㐂 䙦ᡶ ㎗ 3䙧 㐄 ᡶ ㎘ 5
x x x x
b. ⡷け
ㄙ⡹け⡸⡱ ⡱け⡹⡰ 㐄 3ᡶ
⡱け⡹⡰
2 3 2
x x ㎘䙦ᡶ⡰^ ㎗ 3 ᡶ䙧 x x x x ㎘ 5 ᡶ ㎘ 15 ㎘䙦㎘ 5 ᡶ ㎘ 15 䙧 0
㎘䙦 9 ᡶ⡱^ ㎘ 6 ᡶ⡰䙧 6 ᡶ⡰^ ㎘ ᡶ ㎘䙦6ᡶ⡰^ ㎘ 4ᡶ䙧 3ᡶ ㎗ 3 ㎘䙦 3 ᡶ ㎘ 2 䙧 5
ㄣ ⡲ ㎘ 5ᡶ
⡰
ㄠ ⡰ ㎘ 5ᡶ
⡱