Factorise- 2x-2- 13x -15-x- 5- -2x -3-x- 5- -2x - 3- x - 5- - 2x - 3-x-5- -2x - 3-

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Byju's Answer

Standard IX

Mathematics

Division of a Polynomial by a Monomial

Factorise 2x...

Question

Factorise $2 x^{2} + 13 x + 15$

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(x+ 5) (2x + 3)

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(x+ 5) (2x - 3)

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(x- 5) (2x + 3)

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Solution

The correct option is B
(x+ 5) (2x + 3)

$2 x^{2} + 13 x + 15$
= $2 x^{2} + 10 x + 3 x + 15$ ( Since 15 x 2 = 30 and (3 ) + (10) = 13 and (3 x 10 ) = 30 )
= ( $2 x (x + 5) + 3 (x + 5)$

= (x+ 5) (2x + 3)

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Similar questions

Q. Factorise:
(i)

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

(ii)

x^{3} - 3 x^{2} - 9 x - 5

(iii)

x^{3} + 13 x^{2} + 32 x + 20

(iv)

2 y^{3} + y^{2} - 2 y - 1

Solve :

$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

\frac{10 x^{2} + 15 x + 63}{5 x^{2} - 25 + 12} = \frac{2 x + 3}{x - 5}

Q. Factorise:

(i) x^{3} - 2 x^{2} - x + 2

(i i) x^{3} - 3 x^{2} - 9 x - 5

(i i i) x^{3} + 13 x^{2} + 32 x + 20

[3 Marks]

Q. Factorise

3 x^{5} - 6 x^{4} - 2 x^{3} + 4 x^{2} + x - 2

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Factorise 2x2+13x+15

The correct option is B (x+ 5) (2x + 3) 2x2+13x+15 = 2x2+10x+3x+15 ( Since 15 x 2 = 30 and (3 ) + (10) = 13 and (3 x 10 ) = 30 ) = (2x(x+5)+3(x+5) = (x+ 5) (2x + 3)

Factorise $2 x^{2} + 13 x + 15$

The correct option is B
(x+ 5) (2x + 3)

$2 x^{2} + 13 x + 15$
= $2 x^{2} + 10 x + 3 x + 15$ ( Since 15 x 2 = 30 and (3 ) + (10) = 13 and (3 x 10 ) = 30 )
= ( $2 x (x + 5) + 3 (x + 5)$

= (x+ 5) (2x + 3)