Topics
Compound Interest
- Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
- Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
- Use of Formula
- Finding CI from the Relation CI = A – P
Commercial Mathematics
Goods and Services Tax (G.S.T.)
Banking
Algebra
Geometry
Shares and Dividends
Symmetry
Mensuration
Linear Inequations
Quadratic Equations
- Quadratic Equations
- Method of Solving a Quadratic Equation
- Factorisation Method
- Quadratic Formula (Shreedharacharya's Rule)
- Nature of Roots of a Quadratic Equation
- Equations Reducible to Quadratic Equations
Trigonometry
Statistics
Problems on Quadratic Equations
- Method for Solving a Quadratic Word Problem
- Problems Based on Numbers
- Problems on Ages
- Problems Based on Time and Work
- Problems Based on Distance, Speed and Time
- Problems Based on Geometrical Figures
- Problems on Mensuration
- Problems on C.P. and S.P.
- Miscellaneous Problems
Ratio and Proportion
Probability
Remainder Theorem and Factor Theorem
- Function and Polynomial
- Division Algorithm for Polynomials
- Remainder Theorem
- Factor Theorem
- Applications of Factor Theorem
Matrices
Arithmetic Progression
Geometric Progression
Reflection
- Co-ordinate Geometry
- Advanced Concept of Reflection in Mathematics
- Invariant Points
- Combination of Reflections
- Using Graph Paper for Reflection
Section and Mid-Point Formulae
Equation of a Line
Similarity
Loci
- Locus
- Points Equidistant from Two Given Points
- Points Equidistant from Two Intersecting Lines
- Summary of Important Results on Locus
- Important Points on Concurrency in a Triangle
Angle and Cyclic Properties of a Circle
Tangent Properties of Circles
Constructions
Volume and Surface Area of Solids (Cylinder, Cone and Sphere)
- Mensuration of Cylinder
- Hollow Cylinder
- Mensuration of Cones
- Mensuration of a Sphere
- Hemisphere
- Conversion of Solids
- Solid Figures
- Problems on Mensuration
Trigonometrical Identities
Heights and Distances
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Graphical Representation of Statistical Data
Measures of Central Tendency (Mean, Median, Quartiles and Mode)
Probability
CISCE: Class 10
Definition: Factors of Polynomial
A polynomial g(x) is called a factor of the polynomial f(x) if g(x) divides f(x) exactly, giving 0 as the remainder.
CISCE: Class 10
Key Points: Factor Theorem
Statement
If a polynomial f(x) is divided by (x − a) and the remainder is zero, then (x − a) is a factor of f(x).
Result
(x − a) is a factor of f(x) ⟺ f(a) = 0
To check whether (x − a) is a factor → find f(a)
-
If f(a) = 0 → factor
-
If f(a) ≠ 0 → not a factor
Important Forms
- (x − a) is a factor ⇔ f(a) = 0
-
(x + a) is a factor ⇔ f(−a) = 0
- (ax + b) is a factor ⇔ \[f(-\frac{b}{a})\] = 0
Shaalaa.com | Factor Theorem Part 1
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Factor Theorem Part 1
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The Factor Theorem and Remainder Theorem
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Factor Theorem Part 2 (Example)
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Factor Theorem Part 3 (How to factorise a cubic polynomial Method 1)
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Factor Theorem Part 4 (How to factorise a cubic polynomial Method 2)
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Factor Theorem Part 5 (How to solve a cubic equation by factorising)
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Factor Theorem Part 6 (How to find constants in a polynomial given factors )
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