Factorise- x2-12-35x-1-35

X^2+12/35x+1/35 ⇒1/35 [35x^2+12x+1] ⇒1/35 [35x^2+12x+1] ⇒1/35 [35x^2+7x+5x+1] (by splitting the middle term) ⇒1/35 [7x(5x+1)+1(5x+1)] ⇒1/35 [(7x+1)(5x+1)] ...

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Byju's Answer

Standard IX

Mathematics

Factorisation of Quadratic Polynomials- Middle Term Splitting

Factorise: x2...

Question

Factorise:
$x^{2} + \frac{12}{35} x + \frac{1}{35}$

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Solution

$x^{2} + \frac{12}{35} x + \frac{1}{35} \Rightarrow \frac{1}{35} [35 x^{2} + 12 x + 1] \Rightarrow \frac{1}{35} [35 x^{2} + 12 x + 1] \Rightarrow \frac{1}{35} [35 x^{2} + 7 x + 5 x + 1] (by splitting the middle term) \Rightarrow \frac{1}{35} [7 x (5 x + 1) + 1 (5 x + 1)] \Rightarrow \frac{1}{35} [(7 x + 1) (5 x + 1)]$

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Factorise: x2+1235x+135

x2+1235x+135⇒135[35x2+12x+1]⇒135[35x2+12x+1]⇒135[35x2+7x+5x+1] (by splitting the middle term)⇒135[7x(5x+1)+1(5x+1)]⇒135[(7x+1)(5x+1)]

Factorise:
$x^{2} + \frac{12}{35} x + \frac{1}{35}$