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Goods and Services Tax (G.S.T.)
Commercial Mathematics
Compound Interest
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- Finding CI from the Relation CI = A – P
Banking
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Quadratic Equations
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- Factorisation Method
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- Nature of Roots of a Quadratic Equation
- Equations Reducible to Quadratic Equations
Statistics
Ratio and Proportion
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Factorisation of Polynomials
- Function and Polynomial
- Division Algorithm for Polynomials
- Remainder Theorem
- Factor Theorem
- Applications of Factor Theorem
Matrices
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Co-ordinate Geometry
- Co-ordinate Geometry
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Area and Volume of Solids (Cylinder, Cone and Sphere)
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Statistics : basic concepts, Mean, Median, Mode. Histograms and Ogive
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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