Factorise- 2 x3-2 x2-17 x-30

2x³ 3x² 17x+30 =(x 2)(2x²+x 15) =(x 2)(2x²+6x 5x 15) =(x 2)(x+3)(2x 5) ...

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Byju's Answer

Standard IX

Mathematics

Polynomials

factorise: 2 ...

Question

Factorise : $2 x^{3} - 3 x^{2} - 17 x + 30$

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Solution

We have, $2 x^{3} - 3 x^{2} - 17 x + 30$
$= 2 x^{3} - 4 x^{2} + x^{2} - 2 x - 15 x + 30$ [ $∵ - 3 x^{2} = - 4 x^{2} + x^{2}, - 17 x = - 2 x - 15 x$ ]
$= 2 x^{2} (x - 2) + x (x - 2) - 15 (x - 2)$
$= (x - 2) (2 x^{2} + x - 15)$
$= (x - 2) (2 x^{2} + 6 x - 5 x - 15)$ [ $∵ x = 6 x - 5 x$ ]
$= (x - 2) [2 x (x + 3) - 5 (x + 3)]$
$= (x - 2) (x + 3) (2 x - 5)$

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Factorise 2x^3-3x^2-17x+30

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2 x^{7} - 128 x

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

Q. Factories :

2 x^{3} - 11 x^{2} + 17 x - 6

Factorise:

$6 x^{2} - 17 x - 3$

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Factorise : 2x3−3x2−17x+30

We have, 2x3−3x2−17x+30=2x3−4x2+x2−2x−15x+30 [∵−3x2=−4x2+x2,−17x=−2x−15x]=2x2(x−2)+x(x−2)−15(x−2)=(x−2)(2x2+x−15)=(x−2)(2x2+6x−5x−15) [∵x=6x−5x]=(x−2)[2x(x+3)−5(x+3)]=(x−2)(x+3)(2x−5)

Factorise : $2 x^{3} - 3 x^{2} - 17 x + 30$