S.chand books class 8 maths solution chapter 14 Factorisation Exercise 14 H

EXERCISE 14 H

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Factorise:

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Q1 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 1

2x² + 7x + 5

Sol :

$\begin{array}{r|l}2 & 10 \\\hline 5 & 5 \\\hline &1\end{array}$

$=2 x^{2}+2 x+5 x+5$

=2x(x+1)+5(x+1)

=(2 x+5)(x+1)

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Q2 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 2

4x² + 15x + 14

Sol :

=14×4=56

$\begin{array}{r|l}2 & 56 \\\hline 2 & 28 \\\hline 2 & 14 \\\hline 7 & 7 \\\hline & 1\end{array}$

$=4 x^{2}+8 x+7 x+14$

=4x(x+2)+7(x+2)

=(4x+7)(x+2)

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Q3 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 3

4x²+ 28x + 13

Sol :

=13×4=52

$\begin{array}{r|r}2 & 52 \\\hline 2& 26 \\\hline 13 & 13 \\\hline &1\end{array}$

$=4x^{2}+28x+13$

=2x(2 x+1)+13(2x+1)

=(2x+13)(2x+1)

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Q4 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 4

3x² + 13x + 14

Sol :

$=3 x^{2}+x+12 x+4$

=x(3 x+1)+4(3 x+1)

=(x+4)(3x+1)

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Q5 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 5

4x² + 8x - 5

Sol :

$=4 x^{2}-2 x+10x-5$

=2x(2x-1)+5(2x-1)

=(2x+5)(2x-1)

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Q6 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 6

2x² - 5x -12

Sol :

$=2x^{2}-8x+3x-12$

=2 x(x-4)+3(x-4)

=(2 x+3)(x-4)

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Q7 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 7

13a² + 37a - 6

Sol :

=13×6=78

$\begin{array}{r|l}2 & 78 \\\hline 3 & 39 \\\hline 13 & 13 \\\hline & 1\end{array}$

$=13 a^{2}+39 a-2 a-6$

=13 a(a+3)-2(a+3)

=(13 a-2)(a+3)

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Q8 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 8

40a² + a -6

Sol :

$=40 a^{2}-15 a+16 a-6$

=5a(8 a-3)+2(8 a-3)

=(5 a+2)(8 a-3)

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Q9 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 9

4a² - 16a + 15

Sol :

$=4 a^{2}-6x-10x+15$

=2a(2a-3)-5(2a+3)

=(2a-5)(2a-3)

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Q10 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 10

6 - 9y - 27y²

Sol :

⇒-27y²-9y+6 

⇒-3(9y²+3y-2)

LCM of (9×2=18) is 

2	18
3	9
3	3
	1

⇒-3(9y²+6y-3y-2)

⇒-3[3y(3y+2)-1(3y+2)]

⇒-3(3y-1)(3y+2)

⇒3(1-3y)(3y+2)

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Q11 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 11

1 - t - 6t²

Sol :

⇒-6t²-t+1

⇒-1(6t²+t-1)

2	6
3	3
	1

⇒-1(6t²+3t-2t-1)

⇒-1[3t(2t+1)-1(2t+1)]

⇒-1(3t-1)(2t+1)

⇒(1-3t)(2t+1)

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Q12 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 12

2a² + 7ab - 15b²

Sol :

$=2 a^{2}+10 a b-3 a b-15 b^{2}$

=2a(a+5b)-3b(a+5b)

=(2a-3b)(a+5b)

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Q13 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 13

2x² + 12x + 10

Sol :

$=2\left(x^{2}+6 x+5\right)$

$=2(x^{2}+6 x+5)$

$=2(x^{2}+x+5 x+5)$

=2x(x+1)+5(x+1)

=2(x+5)(x+1)

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Q14 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 14

6a² + a - 2

Sol :

=6×2=12

2	12
2	6
3	3
	1

$=6 a^{2}+4a-3 a-2$

=2a(3a+2)-1(3a+2)

=(2a-1)(3a+2)

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Q15 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 15

6a³ + 3a² - 3a

Sol :

$3a(2 a^{2}+a-1)$

$3a(2 a^{2}+2 a-a-1)$

3a[2a(a+1)-1(a+1)]

3a(2a-1)(a+1)

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Q16 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 16

3x⁵ - 11x³ - 4x

Sol :

$x\left(3 x^{4}-11 x^{2}-4\right)=0$

$x\left[3 x^{4}-11 x^{2}-4=0\right.$

$x\left[3 x^{4}-12 x^{2}+x^{3}-4\right]$

$\left.x\left[3 x^{2}( x^{2}-4\right)+1\left(x^{2}-4\right)\right]$

$x\left[\left(3 x^{2}+1\right)\left(x^{2}-4\right)\right]$

$(x)[(x+2)(x-2)]\left(3 x^{2}+1\right)$

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Q17 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 17

6a⁶ - 21a⁴ - 12a²

Sol :

$a^{2}\left(6 a^{4}-21 a^{2}-12\right)$

$3 a^{2}\left(2 a^{4}-7 a^{2}-4\right)$

$3 a^{2}\left(2 a^{4}-8 a^{2}+a^{2}-4\right)$

$3 a^{2}\left[2 a^{2}\left(a^{2}-4\right)+1\left(a^{2}-4\right)\right]$

$3 a^{2}\left[\left(2 a^{2}+1\right)\left(a^{2}-4\right)\right]$

$3 a^{2}\left(2 a^{2}+1\right)(a-2)(a+2)$

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Q18 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 18

-12m⁵ - m³ + m

Sol :

$-m\left[12 m^{4}+m^{2}-1\right]$

$-m\left[12 m^{4}+4 m^{2}-3 m^{2}-1\right]$

$-m\left[4 m^{2}\left(3 m^{2}+1\right)-1\left(3 m^{2}+1\right)\right]$

$-m\left[\left(4 m^{2}-1\right)\left(3 m^{2}+1\right)\right]$

$-m \left[(2 m)^{2}-(1)^{2}\right]\left(3 m^{2}+1\right)$

$(-m)\left(3 m^{2}+1\right)[(2 m+1)(2 m-1)]$

$m\left(3 m^{2}+1\right)(2 m+1)(1-2 m)$