EXERCISE 14 G
Q1 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q2 | Ex-14A | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q3 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q4 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q5 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q6 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q7 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q8 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
Question 8
x2 - 4x - 5
Sol :
$=x^{2}+x-5 x-5$
=x(x+1)-5(x+1)
=(x-5)(x+1)
Q9 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q10 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q11 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q12 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q13 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q14 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q15 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q16 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q17 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q18 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q19 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)]
Q20 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)]
Q21 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
Question 21
3x5 -
18x4 - 48x3
Sol :
$\begin{array}{l|l}2& 16 \\\hline 2 & 8 \\\hline 2 & 4 \\\hline 2 & 2 \\\hline &1\end{array}$
$=3 x^{3}\left(x^{2}-6 x-16\right)$
$=3 x^{3}\left(x^{2}+8 x-2 x-16\right)$
$=3 x^{3}[x(x+8)-2(x+8)]$
$=3 x^{3}[(x-2)(x+8)]$
Q22 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q23 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
Question 23
b2c3 + 8bc4 + 12c5
Sol :
$=c^{3}\left(b^{2}+8 b c+12 c^{2}\right)$
$=c^{3}\left(b^{2}+6b c+2 b c+12 c^{2}\right)$
$=c^{3}[b(b+6 c)+2 c(b+6 c)]$
$=c^{3}[(b+2 c)(b+6 c)]$
Q24 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
Question 24
x4 - 11x2 -80
Sol :
$\begin{array}{l|l}2 & 80 \\\hline 2 & 40 \\\hline 2& 20 \\\hline 2 & 10 \\\hline 5 & 5 \\\hline &1\end{array}$
$=x^{4}-16 x^{2}+5 x^{2}-80$
$=x^{2}\left(x^{2}-16\right)+5\left(x^{2}-16\right)$
$=\left(x^{2}+5\right)\left(x^{2}-16\right)$
Q25 | Ex-14G | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
Question 25
a4 - 7a2 + 12
Sol :
$=a^{4}-4 a^{2}-3 a^{2}+12$
$=a^{2}\left(a^{2}-4\right)-3\left(a^{2}-4\right)$
$=\left(a^{2}-3\right)\left(a^{2}-4\right)$
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