√(2)x^2+3x+√(2) ⇒√(2)x^2 + 2x + x + √(2) ⇒√(2)x (x + √(2)) + 1 (x + √(2)) ⇒ (√(2)x + 1)(x + √(2)) ...

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Byju's Answer

Standard IX

Mathematics

Factorisation of Quadratic Polynomials- Middle Term Splitting

Factorise: √2...

Question

Factorise:
$\sqrt{2} x^{2} + 3 x + \sqrt{2}$

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Solution

$\sqrt{2} x^{2} + 3 x + \sqrt{2} \Rightarrow \sqrt{2} x^{2} + 2 x + x + \sqrt{2} \Rightarrow \sqrt{2} x (x + \sqrt{2}) + 1 (x + \sqrt{2}) \Rightarrow (\sqrt{2} x + 1) (x + \sqrt{2})$

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Similar questions

Q. Factorise :
1.

2 x^{2} - x - 3

- 2 x^{2} + 3 x + 9

Factorise the following:

\sqrt{2} x^{2} + 3 x + \sqrt{2}

Factorise:
$2 x^{2} + 3 x - 90$

Q. Factorise the trinomial

2 x^{2} + 7 x + 6

Using the FActor theroem, show that:
(i) (x-2) is a factor fo $x^{3} - 2 x^{2} - 9 x + 18$ Hence factories the expression
(ii) (x+5) is a factor of $2 x^{3} + 5 x^{2} - 28 x - 15$ Hence factorise fthe expression $2 x^{3} + 5 x^{2} - 28 x - 18$ completely.
(iii) (3x+2) is a factor fo $3 x^{3} + 2 x^{2} - 3 x - 2.$ Hence factorise the expression
$3 x^{3} + 2 x^{2} - 3 x - 2$ completely

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Factorise: √2x2+3x+√2

√2x2+3x+√2⇒√2x2+2x+x+√2⇒√2x(x+√2)+1(x+√2)⇒(√2x+1)(x+√2)

Factorise:
$\sqrt{2} x^{2} + 3 x + \sqrt{2}$

$\sqrt{2} x^{2} + 3 x + \sqrt{2} \Rightarrow \sqrt{2} x^{2} + 2 x + x + \sqrt{2} \Rightarrow \sqrt{2} x (x + \sqrt{2}) + 1 (x + \sqrt{2}) \Rightarrow (\sqrt{2} x + 1) (x + \sqrt{2})$