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This mock test of Test: Factorisation Factor Theorem for Class 9 helps you for every Class 9 entrance exam.
This contains 20 Multiple Choice Questions for Class 9 Test: Factorisation Factor Theorem (mcq) to study with solutions a complete question bank.
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QUESTION: 1

x-a is a factor of p(x) = ax^{2}+bx+c. Which of the following is true?

Solution:

See if g(x) = x- a

Then g(x) is a factor of p(x)

The zero of polynomial = a

Therefore p(a)= 0

QUESTION: 2

If x+1 is a factor of x^{3}+3x^{2}+3x+a, then a = ?

Solution:

Given, x^{3} + 3x^{2} + 3x + a = 0

and its factor is x + 1 = 0

⇒ x = -1

Put the value in equation i.e. x^{3} + 3x^{2} + 3x + a = 0

it becomes = (-1) + 3 (1) + 3(-1) + a = 0

⇒ -1 + 3 - 3 + a = 0

⇒ a = 1

QUESTION: 3

If (x-2) is the factor of x^{2} + 2x+ a, find the value of ‘a’.

Solution:

If x-2 is a factor then 2 is the zero of the polynomial

by substituting 2 in the given polynomial,we get

2^2+2(2)+a=0

8+a=0

a=-8

QUESTION: 4

If a polynomial p(x) is divided by a linear divisor (x-a), then the remainder is

Solution:

QUESTION: 5

The value of p for which x + p is a factor of x^{2} + px + 3 – p is:

Solution:

QUESTION: 6

For two polynomials p(x) and q(x), x-a and x-b are their factors, respectively.Which of the following is true?

Solution:

QUESTION: 7

Find the value of a such that (x – 2) is the factor of the polynomial x^{4} + ax^{3} + 2x^{2}– 3x

Solution:

Zero of the polynomial is x -2 =0 =>x = 2 put the value of x = 2 (2²)² + a(2)³ + 2(2)² - 3(2) = 16 + 8a + 8 - 6 = 18 + 8a = 0 = 8a = -18 = a = -18/8 = a = -9/4

QUESTION: 8

One of the linear factors of 3x^{2} + 8x + 5 is

Solution:

QUESTION: 9

What is the value of b such that x+3 is a factor of x^{2} - bx -12?

Solution:

QUESTION: 10

Find the value of ‘a’ so that (x-1) is the factor of x^{2}+a+1

Solution:

QUESTION: 11

For a polynomial p(x), x-2 is a factor, so p(2) is _______

Solution:

QUESTION: 12

x+1 is a factor of p(x) = x^{3}+3x^{2}+3x+1, so what is the value of p(-1)

Solution:

QUESTION: 13

If (x-1) is a factor of ax – a, then find the value of a

Solution:

**ANSWER :- d**

**Solution :- f(x) = ax - a……………………..(1)**

**x - 1 = 0**

**x = 1**

**Putting in eq(1)**

**(1)x - 1 => x - 1**

**For eg :- if we put x = 100**

**Putting in eq(1)**

**(100)x - 100 => x - 100**

**So, all the values of a**

QUESTION: 14

For a polynomial p(x), p(-1) and p(2) are both equal to zero .So, we can conclude that,

Solution:

QUESTION: 15

For a polynomial, x^{2} – 3x +2, which of the following is a factor ?

Solution:

QUESTION: 16

If (2x + 5) is a factor of 2x^{2} – k, then the value of k is.

Solution:

Let p(x) = 2x^{2} − k

Since, (2x+5) is a factor of p(x), then by factor

theorem,

QUESTION: 17

(x + 2) is a factor of 2x^{3} + 5x^{2} - x - k. The value of k is:

Solution:

QUESTION: 18

If x-2 is a factor of ax^{2}-x-6, so what should be the value of a?

Solution:

QUESTION: 19

Find the value of p(2) if p(x) has (x-2) as its factor

Solution:

QUESTION: 20

Which of the following polynomials has -3 as a zero?

Solution:

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