Factorise - -2 x2 -3x -2

Given : √(2) x^2 +3x +√(2) We can further write it as #160; #160; √(2) x^2 +3x +√(2) = √(2) x^2 +x+ 2x+ √(2) By taking out the common terms ...

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Standard IX

Mathematics

Factorisation of Quadratic Polynomials- Middle Term Splitting

Factorise : ...

Question

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

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Solution

Given : $\sqrt{2} x^{2} + 3 x + \sqrt{2}$
We can further write it as
$\sqrt{2} x^{2} + 3 x + \sqrt{2}$ $= \sqrt{2} x^{2} + x + 2 x + \sqrt{2}$
By taking out the common terms
$\sqrt{2} x^{2} + 3 x + \sqrt{2}$ $= x (\sqrt{2} x + 1) + \sqrt{2} (\sqrt{2} x + 1)$
So we get,
$\sqrt{2} x^{2} + 3 x + \sqrt{2}$ $= (x + \sqrt{2}) (\sqrt{2} x + 1)$

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

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

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.
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Solve equation, given below, using factorisation method:

$2 (x^{2} - 6) = 3 (x - 4)$

$3 x^{3} + 2 x^{2} + 3 x + 2$ =?

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(d) $(3 x + 2) (x^{2} + 1)$

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Factorise : √2x2+3x+√2

Given : √2x2+3x+√2We can further write it as √2x2+3x+√2=√2x2+x+2x+√2By taking out the common terms √2x2+3x+√2=x(√2x+1)+√2(√2x+1)So we get, √2x2+3x+√2=(x+√2)(√2x+1)

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