Polynomials and Factor Theorem

Study Notes

Factor theorem in polynomials
Factor: a term or number that completely divides another term
Polynomial: an algebraic expression with constant and variable terms
Polynomial powers cannot be fractions or negative terms
Examples of polynomials: ax² + bx + c, where a, b, c are numerical terms and x is the variable
Example of non-polynomial: 3x^-2 + 2x^(1/2)
Polynomial degree: highest power of the variable
Zero polynomial: no variable term present (e.g., 5x^0 = 5)
Linear polynomial: highest power of the variable is 1 (e.g., 2x + 3)
Quadratic polynomial: highest power of the variable is 2 (e.g., x² + 5x + 6)
Cubic polynomial: highest power of the variable is 3 (e.g., 2x³ + 3x² + 4x + 7)
Remainder theorem: if a polynomial is divided by a factor, the remainder should be zero
Example of applying remainder theorem to quadratic polynomial: x² + 5x + 6, factors are (x + 2) and (x + 3)
Division rule: dividend = (divisor * quotient) + remainder
Importance of practicing math regularly for better understanding and performance in exams- Chapter well-known and understood by the speaker
Confidence check by pausing and writing questions
Match your answer to the speaker's answer
Working together to finish math problems
Aim for 100 out of 100
Question involves finding the remainder
Use the divisor (x+3) to find the value of x
Polynomial of highest power called degree
Basic concepts to advanced topics covered in one chapter
Importance of understanding each topic
Polynomial has highest power of three, called cubic polynomial
Focus on understanding and practicing each question
Method of finding remainder without division
Factor theorem: If remainder is zero, the divisor is a factor
Remainder can be found by substituting variable value in the polynomial
Confidence, hard work, and patience required for mastering math
Engineering students need strong math foundation
Solve problems step by step
Remainder can be zero or nonzero
Factors can be found using division method
Practice silently and let your success make a big impact in the world

Description

Test your understanding of polynomials, factor theorem, and remainder theorem. Learn how to find the remainder and factors of a polynomial, and practice solving problems step by step. Improve your math skills and confidence with this quiz.