ML Aggarwal Solution Class 10 Chapter 6 Factorization MCQs

MCQs

Question 1

When x33x2+5x7 is divided by x – 2,then the remainder is

(a) 0

(b) 1

(c) 2

(d) – 1

Sol :

f(x)=x33x2+5x7

g(x) = x – 2, if x – 2 = 0, then x = 2

Remainder will be

f(2)=(2)33(2)2+5×27
=8-12+10-7=18-19=-1
∴Remainder=-1
Ans (d)


Question 2

When 2x3x23x+5 is divided by 2x + 1, then the remainder is

(a) 6

(b) – 6

(c) – 3

(d) 0

Sol :

f(x)=2x3x23x+5

g(x) = 2x + 1

Let 2x+1=0, then x=12

Then remainder will be 
f(12)=2(12)3(12)23(12)+5

=2×1814+32+5
=1414+32+5
=11+6+204=244=6

∴Remainder=6

Ans (a)

Question 3

If on dividing 4x23kx+5 by x+2, the remainder is – 3 then the value of k is
(a) 4
(b) – 4
(c) 3
(d) – 3
Sol :
f(x)=4x23kx+5
g(x)=x+2
Remainder = –3
Let x+2=0, then x=– 2
Now remainder will be

f(2)=4(2)23k(2)+5
=16+6k+5
=21+6k

∴21+6k=-3
6k=-3-21=-24

k=246=4
∴k=-4

Ans (b)


Question 4

If on dividing 2x3+6x2(2k7)x+5 by x+3, the remainder is k – 1 then the value of k is
(a) 2
(b) – 2
(c) – 3
(d) 3
Sol :
f(x)=2x3+6x2(2k7)x+5
g(x) = x + 3
Remainder = k – 1

If x+3=0, then x=-3
∴Remainder will be 
f(3)=2(3)3+6(3)2(2k7)(3)+5
=-54+54+3(2 k-7)+5
=-54+54+6 k-21+5
=6 k-16

∴6k-16=k-1
6k-k=-1+16
⇒5k=15
k=155=3

∴k=3

Ans (d)

Question 5

If x + 1 is a factor of 3x3 + kx2 + 7x + 4, then the value of k is
(a) – 1
(b) 0
(c) 6
(d) 10
Solution:
f(x) = 3x3 + kx2 + 7x + 4
g(x) = x + 1
Remainder = 0

Let x+1=0, then x=-1
f(1)=3(1)3+k(1)2+7(1)+4
=-3+k-7+4=k-6
∵Remainder=0
∴k-6=0
⇒k=6

Ans (c)

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