ML Aggarwal Solution Class 10 Chapter 6 Factorization MCQs
MCQs
Question 1
When x3−3x2+5x−7 is divided by x – 2,then the remainder is
(a) 0
(b) 1
(c) 2
(d) – 1
Sol :
f(x)=x3−3x2+5x−7
g(x) = x – 2, if x – 2 = 0, then x = 2
Remainder will be
∴f(2)=(2)3−3(2)2+5×2−7
=8-12+10-7=18-19=-1
∴Remainder=-1
Ans (d)
Question 2
When 2x3−x2−3x+5 is divided by 2x + 1, then the remainder is
(a) 6
(b) – 6
(c) – 3
(d) 0
Sol :
f(x)=2x3−x2−3x+5
g(x) = 2x + 1
Let 2x+1=0, then x=−12
Then remainder will be
f(−12)=2(−12)3−(−12)2−3(−12)+5
=2×−18−14+32+5
=−14−14+32+5
=−1−1+6+204=244=6
∴Remainder=6
Ans (a)
Question 3
If on dividing 4x2−3kx+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)=4x2−3kx+5
g(x)=x+2
Remainder = –3
Let x+2=0, then x=– 2
Now remainder will be
f(−2)=4(−2)2−3k(−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−(2k−7)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−(2k−7)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−(2k−7)(−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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