R.d Sharma 2022 Mcqs Solutions for Class 9 Maths Chapter 5 Factorization Of Algebraic Expressions are provided here with simple step-by-step explanations. These solutions for Factorization Of Algebraic Expressions are extremely popular among class 9 students for Maths Factorization Of Algebraic Expressions Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the R.d Sharma 2022 Mcqs Book of class 9 Maths Chapter 5 are provided here for you for free. You will also love the ad-free experience on Meritnation’s R.d Sharma 2022 Mcqs Solutions. All R.d Sharma 2022 Mcqs Solutions for class 9 Maths are prepared by experts and are 100% accurate.
Page No 55:
Question 1:
The factors of x3 −x2y − xy2+ y3 are
(a)(x + y) (x2 − xy + y2)
(b) (x + y) (x2 + xy + y2)
(c) (x + y)2 (x − y)
(d) (x − y)2 (x + y)
Answer:
The given expression to be factorized is
Take common from the first two terms and
from the last two terms. That is
Finally, take commonfrom the two terms. That is
So, the correct choice is (d).
Page No 55:
Question 2:
The factors of x3 − 1 + y3 + 3xy are
(a) (x − 1 + y) (x2 + 1 + y2 + x + y − xy)
(b) (x + y + 1) (x2 + y2 + 1 −xy − x − y)
(c) (x − 1 + y) (x2 − 1 − y2 + x + y + xy)
(d) 3(x + y −1) (x2 + y2 − 1)
Answer:
The given expression to be factorized is
This can be written in the form
Recall the formula
Using the above formula, we have
So, the correct choice is (a).
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Question 3:
The factors of 8a3 + b3 − 6ab + 1 are
(a) (2a + b − 1) (4a2 + b2 + 1 − 3ab − 2a)
(b) (2a − b + 1) (4a2 + b2 − 4ab + 1 − 2a + b)
(c) (2a + b + 1) (4a2 + b2 + 1 −2ab − b − 2a)
(d) (2a − 1 + b) (4a2 + 1 − 4a − b − 2ab)
Answer:
The given expression to be factorized is
This can be written in the form
Recall the formula
Using the above formula, we have
So, the correct choice is (c).
Page No 55:
Question 4:
(x + y)3 − (x − y)3 can be factorized as
(a) 2y (3x2 + y2)
(b) 2x (3x2 + y2)
(c) 2y (3y2 + x2)
(d) 2x (x2+ 3y2)
Answer:
The given expression to be factorized is
Recall the formula for difference of two cubes
Using the above formula, we have,
So, the correct choice is (a).
Page No 55:
Question 5:
The expression (a − b)3 + (b − c)3 + (c −a)3 can be factorized as
(a) (a − b) (b − c) (c −a)
(b) 3(a − b) (b − c) (c −a)
(c) −3(a − b) (b −c) (c − a)
(d) (a + b + c) (a2 + b2 + c2 − ab − bc − ca)
Answer:
The given expression is
Let,
and
. Then the given expression becomes
Note that:
Recall the formula
When, this becomes
So, we have the new formula
, when
.
Using the above formula, the value of the given expression is
So, the correct choice is (b).
Page No 55:
Question 6:
The value of
(a) 2
(b) 3
(c) 2.327
(d) 2.273
Answer:
The given expression is
This can be written in the form
Assumeand
. Then the given expression can be rewritten as
Recall the formula for difference of two cubes
Using the above formula, the expression becomes
Note that both a and b are positive, unequal. So, neithernor any factor of it can be zero.
Therefore we can cancel the termfrom both numerator and denominator. Then the expression becomes
So, the correct choice is (a).
Page No 55:
Question 7:
The value of is
(a) 0.006
(b) 0.02
(c) 0.0091
(d) 0.00185
Answer:
The given expression is
Assumeand
. Then the given expression can be rewritten as
Recall the formula for sum of two cubes
Using the above formula, the expression becomes
Note that both and b are positive. So, neither
nor any factor of it can be zero.
Therefore we can cancel the termfrom both numerator and denominator. Then the expression becomes
So, the correct choice is (b).
Page No 55:
Question 8:
Mark the correct alternative in each of the following:
The factors of a2 − 1 − 2x − x2 are
(a) (a − x + 1) (a − x − 1)
(b) (a + x − 1) (a − x + 1)
(c) (a + x +1) (a − x + 1)
(d) none of these
Answer:
The given expression to be factorized is
Take commonfrom the last three terms and then we have
So, the correct choice is (c).
Page No 55:
Question 9:
The factors of x4 + x2 + 25 are
(a) (x2 + 3x + 5) (x2 − 3x + 5)
(b) (x2+ 3x + 5) (x2 + 3x − 5)
(c) (x2 + x +5) (x2 − x + 5)
(d) none of these
Answer:
The given expression to be factorized is
This can be written in the form
So, the correct choice is (a).
Page No 55:
Question 10:
The factors of x2 + 4y2 + 4y − 4xy − 2x − 8 are
(a) (x − 2y −4) (x − 2y + 2)
(b) (x − y + 2) (x − 4y − 4)
(c) (x + 2y − 4) (x + 2y + 2)
(d) none of these
Answer:
The given expression to be factorized is
This can be arrange in the form
Let. Then the above expression becomes
Put.
So, the correct choice is (a).
Page No 55:
Question 11:
The factors of x3 − 7x + 6 are
(a) x (x − 6) (x − 1)
(b) (x2 − 6) (x − 1)
(c) (x + 1) (x + 2) (x + 3)
(d) (x − 1) (x + 3) (x − 2)
Answer:
The given expression to be factorized is
This can be written in the form
Take common x from the first two terms andfrom the last two terms. Then we have
Finally, take commonfrom the above expression,
So, the correct choice is (d).
Page No 55:
Question 16:
If then the value x3 – y3 is
(a) 1
(b) –1
(c) 0
(d)
Answer:
Given: .....(1)
Now,
Hence, the correct answer is option (c).
Page No 55:
Question 17:
Which of the following is a factor of (x + y)3 – (x3 + y2)?
(a) x2 + y2 + 2xy
(b) x2 + y2 – xy
(c) xy2
(d) 3xy
Answer:
Disclaimer: In the question, y3 is incorrectly written as y2 and the calculations are shown accordingly.
(x + y)3 – (x3 + y3)
Thus, there are two factors 3xy and (x + y).
Hence, the correct answer is option (d).
Page No 55:
Question 18:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) âStatement-1 is false, Statement-2 is true.
Statement-1 (Assertion): (a – b)3 + (b – c)3 + (c – a)3 = 3(a – b) (b – c) (c – a)
Statement-2 (Reason): If a + b + c = 0, then a3 + b3 + c3 = 3abc
Answer:
Statement-2 (Reason): If a + b + c = 0 then a3 + b3 + c3 = 3abc
Thus, Statement-2 is true.
Statement-1 (Assertion): (a – b)3 + (b – c)3 + (c – a)3 = 3(a – b) (b – c) (c – a)
Here, a – b + b – c + c – a = 0
Now, According to the Statement-2
Thus, Statement-1 is true.
So, Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Hence, the correct answer is option (a).
Page No 55:
Question 19:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) âStatement-1 is false, Statement-2 is true.
Statement-1 (Assertion): If 3x = a + b + c, then
(x – a)3 + (x – b)3 + (x – c)3 = 3(x – a) (x – b) (x – c)
Statement-2 (Reason): If a + b + c = 0 then a3 + b3 + c3 = 3abc
Answer:
Statement-2 (Reason): If a + b + c = 0 then a3 + b3 + c3 = 3abc
Thus, Statement-2 is true.
Statement-1 (Assertion): If 3x = a + b + c, then (x – a)3 + (x – b)3 + (x – c)3 = 3(x – a) (x – b) (x – c)
Given that, 3x = a + b + c
Here,
Now, According to the Statement-2
Thus, Statement-1 is true.
So, Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Hence, the correct answer is option (a).
Page No 55:
Question 20:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) âStatement-1 is false, Statement-2 is true.
Statement-1 (Assertion): If a + b + c = 5 and ab + bc + ca = 10, then a3 + b3 + c3 – 3abc = 25
Statement-2 (Reason): a3 + b3 + c3 – 3abc = (a + b + c) {(a + b + c)2 – 3(ab + bc + ca)}
Answer:
Statement-2 (Reason): a3 + b3 + c3 – 3abc = (a + b + c) {(a + b + c)2 – 3(ab + bc + ca)}
Since
Now,
Thus, Statement-2 is true.
Statement-1 (Assertion): If a + b + c = 5 and ab + bc + ca = 10, then a3 + b3 + c3 – 3abc = 25
Given that, a + b + c = 5 and ab + bc + ca = 10.
Thus, Statement-1 is false.
So, Statement-1 is false, Statement-2 is true.
Hence, the correct answer is option (d).
Page No 55:
Question 21:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) âStatement-1 is false, Statement-2 is true.
Statement-1 (Assertion): If a, b, c are all non-zero such that a + b + c = 0, then
Statement-2 (Reason): If a + b + c = 9 and a2 + b2 + c2 = 35, then ab + bc + ca = 23
Answer:
Statement-2 (Reason): If a + b + c = 9 and a2 + b2 + c2 = 35, then ab + bc + ca = 23
Given that, a + b + c = 9 and a2 + b2 + c2 = 35.
Thus, Statement-2 is true.
Statement-1 (Assertion): If a, b, c are all non-zero such that a + b + c = 0, then
Given that, a + b + c = 0
As we know that, if a + b + c = 0, then a3 + b3 + c3 = 3abc .....(1)
Thus, Statement-1 is true.
So, Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
Hence, the correct answer is option (b).
Page No 56:
Question 12:
The expression x4 + 4 can be factorized as
(a) (x2 + 2x + 2) (x2 − 2x + 2)
(b) (x2 + 2x + 2) (x2 + 2x − 2)
(c) (x2 − 2x − 2) (x2− 2x + 2)
(d) (x2 + 2) (x2 − 2)
Answer:
The given expression to be factorized is
This can be written in the form
So, the correct choice is (a).
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Question 13:
If 3x = a + b + c, then the value of (x − a)3 + (x −b)3 + (x − c)3 − 3(x − a) (x − b) (x −c) is
(a) a + b + c
(b) (a − b) (b − c) (c − a)
(c) 0
(d) none of these
Answer:
The given expression is
Recall the formula
Using the above formula the given expression becomes
Given that
Therefore the value of the given expression is
So, the correct choice is (c).
Page No 56:
Question 14:
If (x + y)3 − (x − y)3 − 6y(x2 − y2) = ky3, then k =
(a) 1
(b) 2
(c) 4
(d) 8
Answer:
The given equation is
Recall the formula
Using the above formula, we have
, provided
.
So, the correct choice is (d).
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Question 15:
If x3 − 3x2 + 3x − 7 = (x + 1) (ax2 + bx + c), then a + b + c =
(a) 4
(b) 12
(c) −10
(d) 3
Answer:
The given equation is
x3 − 3x2 + 3x − 7 = (x + 1) (ax2 + bx + c)
This can be written as
Comparing the coefficients on both sides of the equation.
We get,
c = -7 .......(4)
Putting the value of a from (1) in (2)
We get,
So the value of a, b and c is 1, – 4 and -7 respectively.
Therefore,
a + b + c =1 - 4 - 7 = -10
So, the correct choice is (c).
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Question 22:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) âStatement-1 is false, Statement-2 is true.
Statement-1 (Assertion): The value of is 0.05.
Statement-2 (Reason): a3 – b3 = (a – b)(a2 – ab + b2)
Answer:
Statement-2 (Reason): a3 – b3 = (a – b)(a2 – ab + b2)
Thus, Statement-2 is false.
Statement-1 (Assertion): The value of
Thus, Statement-1 is true.
So, Statement-1 is true, Statement-2 is false.
Hence, the correct answer is option (c).
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