S.chand books class 8 maths solution chapter 14 Factorisation exercise 14 G

 EXERCISE 14 G

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

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Question 1

a² + 7a +12

Sol :

$\begin{array}{l|l}2 & 12 \\\hline 2 & 6 \\\hline 3 & 3 \\\hline & 1\end{array}$

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

=a(a+4)+3(a+4)

=(a+3)(a+4)

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

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Question 2

x² + 8x + 15

Sol :

$\begin{array}{l|l}3&15 \\5&\hline 5 \\&\hline 1\end{array}$

$=x^{2}+3 x+5 x+15$

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

=(x+5)(x+3)

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

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Question 3

x² + 13x + 42

Sol :

$\begin{array}{l|l}2 & 42 \\\hline 3 & 21 \\\hline 7 & 7 \\\hline &1\end{array}$

$=x^{2}+7 x+6 x+42$

=x(7 x+7)+6(x+7)

=(x+6)(x+7)

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

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Question 4

x² - 17x + 72
Sol :

$\begin{array}{l|l}2 & 72 \\\hline 2 & 36 \\\hline 2 & 18 \\\hline 3 & 9 \\\hline 3 & 3 \\ \hline &1\end{array}$

$=x^{2}-8 x-9 x+72$

=x(x-8)-9(x-8)

=(x-9)(x-8)

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

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Question 5

s² + 9s - 36

Sol :

$\begin{array}{l|l}2 & 36 \\\hline 2 & 18 \\\hline 3 & 9 \\\hline 3 & 3 \\\hline & 1\end{array}$

$=s^{2}-3 s+12 s-36$

=s(s-3)+12(s-3)

=(s+12)(s-3)

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

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Question 6

x² + 5x - 50
Sol :

$\begin{array}{l|l}2 & 50 \\\hline 5 & 25 \\\hline 5 & 5 \\\hline &1\end{array}$

$=x^{2}-5 x+10 x-50$

=x(x-5)+10(x-5)

=(x+10)(x-5)

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

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Question 7

a² - 10a + 16

Sol 

$\begin{array}{l|l}2 & 16 \\\hline 2 & 8 \\\hline 2 & 4 \\\hline 2 & 2 \\\hline & 1\end{array}$

$=a^{2}-8 a-2 a+16$

=a(a-8)-2(a-8)

=(a-2)(a-8)

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

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Question 8

x² - 4x - 5
Sol :

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

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

=(x-5)(x+1)

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

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Question 9

a² + 2a - 48
Sol :

$\begin{array}{l|l}2&48 \\2&\hline 24 \\2&\hline 12 \\2&\hline 6 \\3&\hline 3 \\&\hline 1\end{array}$

$=a^{2}+8 a-6 a-48$

=a(a+8)-6(a+8)

=(a-6)(a+8)

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

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Question 10

x² - 2x - 24
Sol :

$\begin{array}{l|l}2 & 24 \\\hline 2 & 12 \\\hline 2 & 6 \\\hline 3 & 3 \\\hline &1\end{array}$

$=x^{2}+4 x-6 x-24$

=x(x+4)-6(x+4)

=(x-6)(x+4)

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

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Question 11

a² - 3a - 40

$=\begin{array}{c|c}2 & 40 \\\hline 2 & 20 \\\hline 2 & 10 \\\hline 5 & 5 \\\hline &1\end{array}$

$=a^{2}-8 a+5 a-40$

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

=(a+5)(a-8)

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

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Question 12

y² - 11y + 24

Sol :

$\begin{array}{l|l}2 & 24 \\\hline 2 & 12 \\\hline 2 & 6 \\\hline 3 & 3 \\\hline & 1\end{array}$

$=y^2-3 y-8 y+24$

=y(y-3)-8(y-3)

=(y-8)(y-3)

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

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Question 13

48 + 22x -x²
Sol :

$\begin{array}{l|l}2 & 48 \\\hline 2 & 24 \\\hline 2 & 12 \\\hline 2 & 6 \\\hline 3 & 3 \\\hline & 1\end{array}$

$=48+24 x-2 x-x^{2}$

=24(2+x)-x(2+x)

=(24-x)(2+x)

=(24-x)(x+2)

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

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Question 14

a² - 29a + 204
Sol :

$\begin{array}{c|c}2 & 204 \\\hline 2 & 102 \\\hline 3 & 51 \\\hline 17 & 17 \\\hline & 1\end{array}$

$=a^{2}-12 a-17 a+2 a$

=a(a-12)-17(a-12)

=(a-17)(a-12)

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

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Question 15

x² - 18x + 65
Sol :

$\begin{array}{r|l}5&65 \\\hline 13&13 \\\hline &1\end{array}$

$=x^{2}-13 x-5 x+65$

=x(x-13)-5(x-13)

=(x-5)(x-13)

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

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Question 16

a² - 5a - 176
Sol :

$\begin{array}{l|l}2 & 176 \\\hline 2 & 88 \\\hline 2 & 44 \\\hline 2 & 22 \\\hline 11 & 11 \\\hline & 1\end{array}$

$=a^{2}-16 a+11 a-176$

=a(a-16)+11(a-16)

=(a+11)(a-15)

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

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Question 17

x² + 16x - 225
Sol :

$\begin{array}{l|l}3 & 225 \\\hline 3 & 73 \\\hline 5 & 25 \\\hline 5 & 5 \\ \hline & 1\end{array}$

$=x^{2}+25 x-9 x-225$

=x(x+25)-9(x+25)

=(x-9)(x+2)

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

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Question 18

m² - 19m - 92
Sol :

$\begin{array}{l|l}2 & 92 \\\hline 2 & 46 \\\hline 23 & 23 \\\hline 1 \end{array}$

$=m^{2}+4 m-23 m-92$

=m(m+4)-23(m+4)

=(m-23)(m+4)

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Q19 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 19

36 - 21x + 3x²
Sol :

$\begin{array}{l|l}2 & 12 \\\hline 2 & 6 \\\hline 3 & 3 \\\hline & 1\end{array}$

$=3 x^{2}-21 x+36$

$=3\left(x^{2}-7 x+12\right)$

$3\left(x^{2}-4 x-3 x+12\right)$

=3[x(x-4)-3(x-4)]

=3[(x-3)(x-4)]

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Q20 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 20

2x² + 10x - 48
Sol :

$=2 \left[x^{2}+5 x-24\right]$

$=2\left[x^{2}+8 x-3 x-24\right]$

=2[x(x+8)-3(x+8)]

=2[(x-3)(x+8)]

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Q21 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 21

3x⁵ - 18x⁴ - 48x³
Sol :

$\begin{array}{l|l}2& 16 \\\hline 2 & 8 \\\hline 2 & 4 \\\hline 2 & 2 \\\hline &1\end{array}$

$=3 x^{3}\left(x^{2}-6 x-16\right)$

$=3 x^{3}\left(x^{2}+8 x-2 x-16\right)$

$=3 x^{3}[x(x+8)-2(x+8)]$

$=3 x^{3}[(x-2)(x+8)]$

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Q22 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 22

-2x³ + 22x² + 24x
Sol :

$\begin{array}{l|l} 2&12\\\hline 2&6 \\ \hline 3&3 \\ \hline & 1\end{array}$

$=-2 x\left(x^{2}-11 x-12\right)$

$=-2 x\left(x^{2}-12x+x-12\right)$

=-2x[x(x-12)+1(x-12)]

=(-2 x)(x+1)(x-12)

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Q23 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 23

b²c³ + 8bc⁴ + 12c⁵
Sol :

$=c^{3}\left(b^{2}+8 b c+12 c^{2}\right)$

$=c^{3}\left(b^{2}+6b c+2 b c+12 c^{2}\right)$

$=c^{3}[b(b+6 c)+2 c(b+6 c)]$

$=c^{3}[(b+2 c)(b+6 c)]$

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Q24 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 24

x⁴ - 11x² -80
Sol :

$\begin{array}{l|l}2 & 80 \\\hline 2 & 40 \\\hline 2& 20 \\\hline 2 & 10 \\\hline 5 & 5 \\\hline &1\end{array}$

$=x^{4}-16 x^{2}+5 x^{2}-80$

$=x^{2}\left(x^{2}-16\right)+5\left(x^{2}-16\right)$

$=\left(x^{2}+5\right)\left(x^{2}-16\right)$

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Q25 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 25

a⁴ - 7a² + 12

Sol :

$=a^{4}-4 a^{2}-3 a^{2}+12$

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

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