EXERCISE 14 H
Factorise:
Q1 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q2 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q3 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q4 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q5 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
Question 5
4x2 + 8x - 5
Sol :
$=4 x^{2}-2 x+10x-5$
=2x(2x-1)+5(2x-1)
=(2x+5)(2x-1)
Q6 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
Question 6
2x2 - 5x -12
Sol :
$=2x^{2}-8x+3x-12$
=2 x(x-4)+3(x-4)
=(2 x+3)(x-4)
Q7 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q8 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q9 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
Question 9
4a2 - 16a + 15
Sol :
$=4 a^{2}-6x-10x+15$
=2a(2a-3)-5(2a+3)
=(2a-5)(2a-3)
Q10 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
Question 10
6 - 9y - 27y2
Sol :
⇒-27y2-9y+6
⇒-3(9y2+3y-2)
LCM of (9×2=18) is
⇒-3(9y2+6y-3y-2)
⇒-3[3y(3y+2)-1(3y+2)]
⇒-3(3y-1)(3y+2)
⇒3(1-3y)(3y+2)
Q11 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
Question 11
1 - t - 6t2
Sol :
⇒-6t2-t+1
⇒-1(6t2+t-1)
⇒-1(6t2+3t-2t-1)Q12 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q13 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q14 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
Question 14
6a2 + a - 2
Sol :
=6×2=12
$=6 a^{2}+4a-3 a-2$
=2a(3a+2)-1(3a+2)
=(2a-1)(3a+2)
Q15 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
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)
Q16 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
Question 16
3x5 - 11x3 - 4x
Sol :
$x\left(3 x^{4}-11 x^{2}-4\right)=0$
$x\left[3 x^{4}-11 x^{2}-4=0\right.$
$x\left[3 x^{4}-12 x^{2}+x^{3}-4\right]$
$\left.x\left[3 x^{2}( x^{2}-4\right)+1\left(x^{2}-4\right)\right]$
$x\left[\left(3 x^{2}+1\right)\left(x^{2}-4\right)\right]$
$(x)[(x+2)(x-2)]\left(3 x^{2}+1\right)$
Q17 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
Question 17
6a6 - 21a4 - 12a2
Sol :
$a^{2}\left(6 a^{4}-21 a^{2}-12\right)$
$3 a^{2}\left(2 a^{4}-7 a^{2}-4\right)$
$3 a^{2}\left(2 a^{4}-8 a^{2}+a^{2}-4\right)$
$3 a^{2}\left[2 a^{2}\left(a^{2}-4\right)+1\left(a^{2}-4\right)\right]$
$3 a^{2}\left[\left(2 a^{2}+1\right)\left(a^{2}-4\right)\right]$
$3 a^{2}\left(2 a^{2}+1\right)(a-2)(a+2)$
Q18 | Ex-14H | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper
Question 18
-12m5 - m3 + m
Sol :
$-m\left[12 m^{4}+m^{2}-1\right]$
$-m\left[12 m^{4}+4 m^{2}-3 m^{2}-1\right]$
$-m\left[4 m^{2}\left(3 m^{2}+1\right)-1\left(3 m^{2}+1\right)\right]$
$-m\left[\left(4 m^{2}-1\right)\left(3 m^{2}+1\right)\right]$
$-m \left[(2 m)^{2}-(1)^{2}\right]\left(3 m^{2}+1\right)$
$(-m)\left(3 m^{2}+1\right)[(2 m+1)(2 m-1)]$
$m\left(3 m^{2}+1\right)(2 m+1)(1-2 m)$
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