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Grade 9 Exam  >  Grade 9 Tests  >  Test: Factorisation Factor Theorem - Grade 9 MCQ

Test: Factorisation Factor Theorem - Grade 9 MCQ


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20 Questions MCQ Test - Test: Factorisation Factor Theorem

Test: Factorisation Factor Theorem for Grade 9 2024 is part of Grade 9 preparation. The Test: Factorisation Factor Theorem questions and answers have been prepared according to the Grade 9 exam syllabus.The Test: Factorisation Factor Theorem MCQs are made for Grade 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Factorisation Factor Theorem below.
Solutions of Test: Factorisation Factor Theorem questions in English are available as part of our course for Grade 9 & Test: Factorisation Factor Theorem solutions in Hindi for Grade 9 course. Download more important topics, notes, lectures and mock test series for Grade 9 Exam by signing up for free. Attempt Test: Factorisation Factor Theorem | 20 questions in 20 minutes | Mock test for Grade 9 preparation | Free important questions MCQ to study for Grade 9 Exam | Download free PDF with solutions
Test: Factorisation Factor Theorem - Question 1
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x-a is a factor of p(x) = ax2+bx+c. Which of the following is true?​

Detailed Solution for Test: Factorisation Factor Theorem - Question 1

See if g(x) = x- a
Then g(x) is a factor of p(x)
The zero of polynomial = a
Therefore p(a)= 0

Test: Factorisation Factor Theorem - Question 2
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If x+1 is a factor of x3+3x2+3x+a, then a = ?

Detailed Solution for Test: Factorisation Factor Theorem - Question 2

Given, x3 + 3x2 + 3x + a = 0

and its factor is x + 1 = 0 

⇒ x = -1

Put the value in equation i.e. x3 + 3x2 + 3x + a = 0

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

⇒ -1 + 3 - 3 + a = 0

⇒ a = 1

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Test: Factorisation Factor Theorem - Question 3
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If (x-2) is the factor of x2 + 2x+ a, find the value of ‘a’.

Detailed Solution for Test: Factorisation Factor Theorem - Question 3

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

Test: Factorisation Factor Theorem - Question 4
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If a polynomial p(x) is divided by a linear divisor (x-a), then the remainder is
Test: Factorisation Factor Theorem - Question 5
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The value of p for which x + p is a factor of x2 + px + 3 – p is:
Test: Factorisation Factor Theorem - Question 6
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For two polynomials p(x) and q(x), x-a and x-b are their factors, respectively.Which of the following is true?​
Test: Factorisation Factor Theorem - Question 7
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Find the value of a such that (x – 2) is the factor of the polynomial x4 + ax3 + 2x2– 3x
Detailed Solution for Test: Factorisation Factor Theorem - Question 7

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

Test: Factorisation Factor Theorem - Question 8
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One of the linear factors of ​3x2 + 8x + 5 is
Test: Factorisation Factor Theorem - Question 9
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What is the value of b such that x+3 is a factor of x2 - bx -12?
Test: Factorisation Factor Theorem - Question 10
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Find the value of ‘a’ so that (x-1) is the factor of x2+a+1
Test: Factorisation Factor Theorem - Question 11
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For a polynomial p(x), x-2 is a factor, so p(2) is _______​
Test: Factorisation Factor Theorem - Question 12
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x+1 is a factor of p(x) = x3+3x2+3x+1, so what is the value of p(-1)
Test: Factorisation Factor Theorem - Question 13
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If (x-1) is a factor of ax – a, then find the value of a​
Detailed Solution for Test: Factorisation Factor Theorem - Question 13

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

Test: Factorisation Factor Theorem - Question 14
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For a polynomial p(x), p(-1) and p(2) are both equal to zero .So, we can conclude that,
Test: Factorisation Factor Theorem - Question 15
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For a polynomial, x2 – 3x +2, which of the following is a factor ?
Test: Factorisation Factor Theorem - Question 16
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If (2x + 5) is a factor of 2x2 – k, then the value of k is.
Detailed Solution for Test: Factorisation Factor Theorem - Question 16

Let p(x) = 2x2 − k
Since, (2x+5) is a factor of p(x), then by factor 
theorem,

Test: Factorisation Factor Theorem - Question 17
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(x + 2) is a factor of 2x3 + 5x2 - x - k. The value of k is:
Test: Factorisation Factor Theorem - Question 18
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If x-2 is a factor of ax2-x-6, so what should be the value of a?
Test: Factorisation Factor Theorem - Question 19
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Find the value of p(2) if p(x) has (x-2) as its factor
Test: Factorisation Factor Theorem - Question 20
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Which of the following polynomials has -3 as a zero?
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