This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Remainder Theorem”.
1. What is the remainder if we divide 6x3 + x2 – 2x + 4 by x-2 ?
a) 48
b) 52
c) -26
d) -24
View Answer
Answer: b
Explanation: According to remainder theorem, if p(x) be any polynomial of degree greater than or equal to one and let “a” be any real number. If p(x) is divided by the linear polynomial x-a, then the remainder is p(a).
So to know the value of remainder, we have to find the value of p(2).
p(2) = 6(2)3 + (2)2 – 2(2) + 4
= 6(8) + 4 – 4 + 4
= 48 + 4
= 52.
Explanation: According to remainder theorem, if p(x) be any polynomial of degree greater than or equal to one and let “a” be any real number. If p(x) is divided by the linear polynomial x-a, then the remainder is p(a).
So to know the value of remainder, we have to find the value of p(2).
p(2) = 6(2)3 + (2)2 – 2(2) + 4
= 6(8) + 4 – 4 + 4
= 48 + 4
= 52.
2. x2 + 8x + 16 is a multiplier of x+4.
a) True
b) False
View Answer
Answer: a
Explanation: p(x) is said to be multiplier of x-a if p(a) = 0.
Therefore, checking whether p(-4) is zero of p(x) or not.
p(-4) = (-4)2 + 8(-4) + 16
= 16 – 32 +16
= 32 – 32
= 0
p(-4) = 0, so we can say that x2 + 8x + 16 is a multiplier of x+4.
Or in other words, we can say that there we get “0” as a remainder when we divide x2 + 8x + 16 by x+4.
Explanation: p(x) is said to be multiplier of x-a if p(a) = 0.
Therefore, checking whether p(-4) is zero of p(x) or not.
p(-4) = (-4)2 + 8(-4) + 16
= 16 – 32 +16
= 32 – 32
= 0
p(-4) = 0, so we can say that x2 + 8x + 16 is a multiplier of x+4.
Or in other words, we can say that there we get “0” as a remainder when we divide x2 + 8x + 16 by x+4.
Sanfoundry Global Education & Learning Series – Mathematics – Class 9.
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