Polynomials — Concept Maps
Madhya Pradesh Board · Class 9 · Mathematics
4 concept maps of Polynomials for Madhya Pradesh Board Class 9 Mathematics, each also written out as a text outline.
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How to Identify if an Expression is a Polynomial
The map in words
- Start: Is it a polynomial?
- Does it have a variable?
- No: Constant Polynomial\nExample: 7 or -3
- Yes: Are ALL exponents\nWHOLE NUMBERS?
- No: NOT a Polynomial\nExamples: sqrt x or 1 divided by x
- Yes: Are ALL coefficients\nreal numbers?
- No: NOT a Polynomial
- Yes: Finite number\nof terms?
- No: NOT a Polynomial
- Yes: YES it is a POLYNOMIAL
- Find the degree
- Highest exponent of variable
- Degree 1 = Linear\nDegree 2 = Quadratic\nDegree 3 = Cubic
- Highest exponent of variable
- Find the degree
- Does it have a variable?
Polynomials Chapter Overview
The map in words
- Polynomials
- Types by Terms
- Monomial
- One term
- Binomial
- Two terms
- Trinomial
- Three terms
- Monomial
- Types by Degree
- Constant
- Degree 0
- Linear
- Degree 1
- Quadratic
- Degree 2
- Cubic
- Degree 3
- Constant
- Zeroes
- Set p of x equal to 0
- Solve for x
- Linear has one zero
- Theorems
- Remainder Theorem
- Remainder equals p of a
- Factor Theorem
- p of a equals 0 means factor
- Remainder Theorem
- Identities
- Sum of squares identity
- Cube identities
- Sum of cubes
- Difference of cubes
- Types by Terms
Polynomials – Complete Chapter Overview
The map in words
- Polynomials
- Definition
- Variable with whole number exponents
- Terms and Coefficients
- Degree is highest power
- Types by Terms
- Monomial 1 term
- Binomial 2 terms
- Trinomial 3 terms
- Types by Degree
- Constant degree 0
- Linear degree 1
- Quadratic degree 2
- Cubic degree 3
- Zeroes
- p of a equals 0
- Linear has exactly one zero
- Constant has no zero
- Zero polynomial all reals
- Remainder Theorem
- Divide by x minus a
- Remainder equals p of a
- No long division needed
- Factor Theorem
- x minus a is factor if p of a equals 0
- Trial zeroes for cubics
- Split middle term for quadratics
- Algebraic Identities
- Sum square identity
- Difference square identity
- Trinomial square
- Sum of cubes
- Difference of cubes
- Special case x plus y plus z equals 0
- Definition
Polynomials
The map in words
- Polynomials
- Definition of Polynomial
- Types by Number of Terms
- Types by Degree
- Zeroes of a Polynomial
- Remainder Theorem
- Factor Theorem
- Algebraic Identities
- Factorisation Methods
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