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Introduction |
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Writing a polynomial as the product of two or more polynomials is called factorisation. If A = B x C, B and C are called factors of A. Most of the polynomials can be factorised by grouping the terms suitably and taking out the common factors. Identities studied in the previous chapter also help in factorisation. |
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Factorization |
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If a polynomial can be written as the product of two or more expressions, then each expression is called the factor of the given polynomial.
Methods of Factorisation: (i) Common factors
(ii) By expressing as difference of squares
(iii) By grouping
(iv) Trinomials
(v) Sum or difference of cubes. |
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Trinomials |
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Expressions of the form ax2 + bx + c are called trinomials. |
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Summary |
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If all the terms of the polynomial have a common factor, we take out the common factor and factorise.
If the polynomial can be expressed as the difference of two squares,
we use a2 - b2 = (a + b) (a - b).
Quadratic trinomials of the form x2 + ax + b can be factorised using the identity.
(x + a) (x + b) = x2 + x(a + b) + ab.
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Factorization |
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