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SChand CLASS 9 Chapter 4 Factorisation TEST

 TEST

Question 1

8x2y3x5

Sol :

=8x2y3x5=x2(8y3x3)=x2[(2y)3(x)3]=x2(2y3)(yy2+2xy+x2)


Question 2

x2+1x2+22x2x

Sol :

=x2+1x2+22x2x=(x+1x)22(x+1x)=(x+1x)(x+1x2)


Question 3

2x² – x – 6

Sol :

=2x2x6
=2x24x+3x6
=2x(x-2)+3(x-2)
=(x-2)(2x+3)


Question 4

a³ – 0.216

Sol :

=a30.226=(a)3(0.6)3=(a0.6)(a2+a×0.6+(0.6)2]=(a0.6)(a2+0.6a+0.36)


Question 5

6x²y – xy – 2y

Sol :

=6x2yxy2y=y[6x2x2)=y[6x24x+3x2]=y[2x(3x2)+2(3x2)}=y[2x(3x2)+1(3x2)]=y(3x2)(2x+1)

Question 6

(x² – 3x)² – 8(x² – 3x) – 20

Sol :

(x23x)28(x23x)20

Let x23x=y, then

=y28y20=y210y+2y20=y(y10)+2(y10)=(y10)(y+2)
Now,
=(x23x10)(x23x+2)
={x25x+2x10}{x2x2x+2}
={x(x5)+2(x5)}{x(x1)2(x1)}
=(x5)(x+2)(x1)(x2)

Question 7

One of the factors of (x – 1) – (x² – 1) is

(a) x² – 1

(b) x + 1

(c) x – 1

(d) x + 4

Sol :

=(x1)(x21)

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

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

So, x-1 is its factor 


option (C) is correct


Question 8

If xy+yx=1 (x, y ≠ 0), then the value of x³ – y³ is

(a) 1

(b) – 1

(c) 12

(d) 0

Sol :

=xy+yx=1


=x2+y2xy=1


=x2+y2=xy


=x3y3=(xy)(x2+xy+y2)....(formula)


=(x-y)×0=0

Option (d) is correct


Question 9

The product of =(x1x)(x+1x)(x2+1x2)

(a) x4+1x4

(b) x3+1x32

(c) x41x4

(d) x2+1x2+2

Sol :

=(x1x)(x+1x)(x2+1x2)

=(x21x2)(x2+1x2)

=(x2)2(1x2)2=x41x4

Option (C) is correct


Question 10

If x – 2y= 11 and xy = 8, then the value of x³ – 8y³ is

(a) 1860

(b) 1600

(c) 1859

(d) 2000

Sol :

x-2y=11 , xy=8
x-2y=11
(x2y)3=(11)3 {(i) using both sides}

x38y33xx×(2y)(x2y)=1331

x38y36xy(x2y)=1331

x38y36×8×11=1331

x38y3528=1331

x38y3=1331+528

x38y3=1859

So, option (C) is correct

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