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This mock test of Test: Remainder Theorem for Class 9 helps you for every Class 9 entrance exam.
This contains 15 Multiple Choice Questions for Class 9 Test: Remainder Theorem (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If x² - 7x + a has a remainder 1 when divided by x + 1, then

Solution:

QUESTION: 2

The remainder when the polynomial p(x) = x^{3} -3x^{2} +2x-1 is divided by x-2 is

Solution:

QUESTION: 3

What is remainder when x^{3} – 2x^{2} + x + 1 is divided by (x -1)?

Solution:

QUESTION: 4

The remainder when x^{4} – 3x^{2} + 5x – 7 is divided by x + 1 is:

Solution:

**Correct Answer :- a**

**Explanation : **x + 1 = 0

x = -1

x^{4} – 3x^{2} + 5x – 7

(-1)^{4} - 3(-1)^{2} + 5(-1) - 7 = 0

1 - 3 - 5 - 7

= -14

QUESTION: 5

If x² - 7x + a has a remainder 1 when divided by x + 1, then

Solution:

QUESTION: 6

The remainder when x^{3} + x^{2} - 2x +1 is divided by (x+1) is

Solution:

for finding the remainder we need to use remainder theorom

let p(x)=x^{3}+x^{2}-2x+1

Here, the divisor is x+1 for dividend p(x), we need to equate it to 0 and put that value of x in p(x).

−x+1=0

∴x=−1

p(−1)=(-1)^{3}+(−1)^{2}-2(−1)+1=3

Hence, remainder=3

QUESTION: 7

For a polynomial p(x) = 2x^{4} - 3x^{3} + 2x^{2} + 2x-1 what is the remainder when it’s divided by x+4?

Solution:

QUESTION: 8

Find remainder when x^{3}+1 is divided by x+1

Solution:

QUESTION: 9

Using Remainder theorem, find the remainder when 3x^{4} - 4x^{3} - 3x - 1 by x - 1

Solution:

By remainder theorem if x-1 = 0 then x=1 using it in equation we get p(x)= 3x⁴-4x³-3x-1 p(1)= 3x1⁴-4x1³-3x1-1 p(1)= 3-4-3-1 p(1)= -5

QUESTION: 10

In the division of a cubic polynomial p(x) by a linear polynomial, the remainder is p(-2).So, the divisor must be

Solution:

QUESTION: 11

If x³ + 9x +5 is divided by x, then remainder is

Solution:

QUESTION: 12

Find the remainder when P(x) = x^{2} - 2x is divided by x - 2

Solution:

QUESTION: 13

Find p(1/3) for p(t) = t^{2} – t + 2

Solution:

1/9-1/3+2 =1/9-3/9-18/9 =16/9

QUESTION: 14

Using Remainder Theorem find the remainder when x^{3} - x^{2} + x - 1 is divided by x - 1

Solution:

QUESTION: 15

P(x) is a polynomial in x, ‘a’ is a real number. If (x-a) is a factor of p(x), then p (a) must be

Solution:

If p(x) is a polynomial of degree n which is greater than or equal to one and a is any real number which will be the divisor, then there will be two conditions fulfilled: If p (a) =0, then x-a is a factor of that polynomial p(x). x-a would be the factor of the polynomial if the r(x) i.e. remainder is 0.

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