Quizsummary
0 of 10 questions completed
Questions:
 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
Information
Polynomials
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Results
0 of 10 questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 points, (0)
Categories
 Not categorized 0%
 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 Answered
 Review

Question 1 of 10
1. Question
Factorize x^{4} – 81
Correct
Explanation: ( x^{2})^{2}– (3^{2})^{2} = (x^{2}+3^{2})(x^{2}3^{2}) = (x^{2}+3^{2})(x+3)(x3)=( x^{2}+9)(x+3)(x3)
Incorrect
Correct Answer: ( x^{2}+9) (x+3) (x3)
Explanation: ( x^{2})^{2}– (3^{2})^{2} = (x^{2}+3^{2}) (x^{2}3^{2}) = (x^{2}+3^{2})(x+3) (x3) = ( x^{2}+9) (x+3) (x3)

Question 2 of 10
2. Question
Factorize 3x^{2}+ 9x + 6
Correct
Explanation: 3x^{2}+ 9x + 6
a =3 b =9 c =6
Split b into two parts p and q such that p+q = 9 and pq = ac=6X3 = 18
P = 3 q= 6
3x^{2}+ 9x + 6 = 3x^{2}+ 3x + 6x + 6 = 3x(x+1) + 6(x+1) = (x+1) (3x+6) = 3(x+1)(x+2)
Incorrect
Correct Answer: 3(x+1)(x+2)
Explanation: 3x^{2}+ 9x + 6a =3 b =9 c =6
Split b into two parts p and q such that p+q = 9 and pq = ac=6X3 = 18
P = 3 q= 6
3x^{2}+ 9x + 6 = 3x^{2}+ 3x + 6x + 6 = 3x(x+1) + 6(x+1) = (x+1) (3x+6) = 3(x+1)(x+2)

Question 3 of 10
3. Question
Factorize x – y – x ^{2} + y^{2}
Correct
Explanation:
x – y – x ^{2} + y^{2 } = (xy) – (x^{2} –y^{2}) = (xy) – (x+ y) (xy) = (xy) [1(x+y)] = (xy) [ 1xy]
Incorrect
Correct Answer: (xy)(1xy)
Explanation:x – y – x ^{2} + y^{2 } = (xy) – (x^{2} –y^{2}) = (xy) – (x+ y) (xy) = (xy) [1(x+y)] = (xy) [ 1xy]

Question 4 of 10
4. Question
Factorize 18ab ^{3} – 8a^{3}
Correct
Explanation: 18ab ^{3} – 8a^{3}
2a [ 9b^{2}4a^{2}] = 2a [(3b)^{2} – (2a)^{2}] = 2a [(3b+2a)(3b2a)]= 2a(3b+2a)(3b2a)
Incorrect
Correct Answer: 2a(3b+2a)(3b2a)
Explanation: 18ab ^{3} – 8a^{3}2a [ 9b^{2}4a^{2}] = 2a [(3b)^{2} – (2a)^{2}] = 2a [(3b+2a)(3b2a)]=2a(3b+2a)(3b2a)

Question 5 of 10
5. Question
Factorize 4 – 25x^{2}
Correct
Explanation:
4 – 25x^{2 } = 2^{2} – (5x)^{2} = (2+5x)(25x)
Incorrect
Correct Answer: (2+5x)(25x)
Explanation:4 – 25x^{2 } = 2^{2} – (5x)^{2} = (2+5x)(25x)

Question 6 of 10
6. Question
Factorize x^{2} + 8x + 15
Correct
Explanation:
x^{2} + 8x + 15
a=1 b=8 c=15
Split the middle term i.e. b into p and q so that
p+q = 8 and pq = ac = 1 X 15 = 15
p= 5 q =3
x^{2} + 8x + 15
= x^{2 }+ 5x +3x + 15 = x(x+5) + 3(x+5) = (x+5) (x+3)
Incorrect
Correct Answer: (x+5) (x+3)
Explanation:x^{2} + 8x + 15
a=1 b=8 c=15
Split the middle term i.e. b into p and q so that
p+q = 8 and pq = ac = 1 X 15 = 15
p= 5 q =3
x^{2} + 8x + 15
= x^{2 }+ 5x +3x + 15 = x(x+5) + 3(x+5) = (x+5) (x+3)

Question 7 of 10
7. Question
Factorize 5x^{2 }– x – 6
Correct
Explanation: Coefficient of middle term , b = 1
Coefficient of 1^{st} and the 3^{rd} term i.e. a = 5 and c = 6
Split the middle term into two parts p and q such that p + q = 1 and pq = 5 X (6) = 30
Proceed for splitting of middle term as follows:
Tip: Always start with p value as the required sum and q value as 0 and proceed.
p q
1 0 (sum, p+q = 1 , product pq = 0)
2 1 (sum, p+q = 1 , product pq = 2)
3 2 (sum, , p+q = 1 , product pq = 6)
4 3 (sum, , p+q = 1 , product pq = 12)
5 4 (sum, , p+q = 1 , product pq = 20)
6 5 (sum, , p+q = 1 , product pq = 30) which is required
5x^{2 }– x – 6
= 5x^{2 }+ 5x –6 x– 6 (After splitting the middle term)
= 5x(x+1)6(x+1)
= (x+1) (5x6)
Incorrect
Correct Answer: (x+1) (5x6) Explanation: Coefficient of middle term , b = 1 Coefficient of 1st and the 3rd term i.e. a = 5 and c = 6 Split the middle term into two parts p and q such that p + q = 1 and pq = 5 X (6) = 30 Proceed for splitting of middle term as follows: Tip: Always start with p value as the required sum and q value as 0 and proceed. p q 1 0 (sum, p+q = 1 , product pq = 0) 2 1 (sum, p+q = 1 , product pq = 2) 3 2 (sum, , p+q = 1 , product pq = 6) 4 3 (sum, , p+q = 1 , product pq = 12) 5 4 (sum, , p+q = 1 , product pq = 20) 6 5 (sum, , p+q = 1 , product pq = 30) which is required 5x2 – x – 6 = 5x2 + 5x –6 x– 6 (After splitting the middle term) = 5x(x+1)6(x+1) = (x+1) (5x6)

Question 8 of 10
8. Question
Factorize 2x^{2 }– 7x – 9
Correct
Explanation: Coefficient of the middle term b = 7
Coefficient of the first and the last terms are a = 2 and c= 9
Spilt the middle term into two parts p and q such that p+q= b = 7 and pq = ca = 2 X (9) = 18
Proceed for splitting of terms as follows:
Tip: Always start with p value as the required sum and q value as 0 and proceed.
p q
.7 0 (sum p+q=7 , product pq = 0)
6 1 (sum p+q=7 , product pq = 6)
5 2 (sum p+q=7 , product pq = 10)
. .
. .
. .
If we proceed this way product will always be positive but we require negative product so no use proceeding this way. So, proceed the other way.
p q
7 0 (sum p+q=7 , product pq = 0)
8 1 ( sum p+q=7 , product pq = 8)
9 2 (sum p+q=7 , product pq = 18) , which are the required values.
2x^{2}7x9
= 2x^{2 }+ 2x – 9x 9
=2x(x+1) – 9(x+1)
= (x+1)(2x9) (Taking (x+1) common)
Incorrect
Correct Answer: (x+1)(2x9)
Explanation: Coefficient of the middle term b = 7
Coefficient of the first and the last terms are a = 2 and c= 9
Spilt the middle term into two parts p and q such that p+q= b = 7 and pq = ca = 2 X (9) = 18
Proceed for splitting of terms as follows:
Tip: Always start with p value as the required sum and q value as 0 and proceed.
p q
.7 0 (sum p+q=7 , product pq = 0)
6 1 (sum p+q=7 , product pq = 6)
5 2 (sum p+q=7 , product pq = 10)
. .
. .
. .
If we proceed this way product will always be positive but we require negative product so no use proceeding this way. So, proceed the other way.
p q
7 0 (sum p+q=7 , product pq = 0)
8 1 ( sum p+q=7 , product pq = 8)
9 2 (sum p+q=7 , product pq = 18) , which are the required values.
2x^{2}7x9
= 2x^{2 }+ 2x – 9x 9
=2x(x+1) – 9(x+1)
= (x+1)(2x9) (Taking (x+1) common)

Question 9 of 10
9. Question
Factorize 8x^{2} 12x +4
Correct
Explanation:
8x^{2} 12x +4
Here a= +8 , b= 12 , c =+4
Split the middle term b into two parts p and q such that
p+q = 12
pq = 8 X 4 = 32
Proceed for splitting of terms as follows:
Tip: Always start with p value as the required sum and q value as 0 and proceed.
P q
12 0 ( sum p+q=12 , product pq=0)
13 +1 ( sum p+q=12 , product pq=13)
14 +2 ( sum p+q=12 , product pq=28)
. .
. .
If we proceed this way product we will get will always be negative ,but we require a positive product so proceed the other way.
p q
12 0 ( sum p+q=12 , product pq=0)
11 1 ( sum p+q=12 , product pq=11) (We need to proceed this way as product that we are getting is positive)
10 2 ( sum p+q=12 , product pq=20)
9 3 ( sum p+q=12 , product pq=27)
8 4 (( sum p+q=12 , product pq=32) which are the required values.
8x^{2} 12x +4
= 8x^{2} 8x 4x+4
=8x(x1) 4(x1)
=(x1) (8x4)
= (x1) .4. (2x1)
= 4 (x1) (2x1)
Incorrect
Correct Answer: 4 (x1) (2x1)
Explanation:
8x^{2} 12x +4
Here a= +8 , b= 12 , c =+4
Split the middle term b into two parts p and q such that
p+q = 12
pq = 8 X 4 = 32
Proceed for splitting of terms as follows:
Tip: Always start with p value as the required sum and q value as 0 and proceed.
P q
12 0 ( sum p+q=12 , product pq=0)
13 +1 ( sum p+q=12 , product pq=13)
14 +2 ( sum p+q=12 , product pq=28)
. .
. .
If we proceed this way product we will get will always be negative ,but we require a positive product so proceed the other way.
p q
12 0 ( sum p+q=12 , product pq=0)
11 1 ( sum p+q=12 , product pq=11) (We need to proceed this way as product that we are getting is positive)
10 2 ( sum p+q=12 , product pq=20)
9 3 ( sum p+q=12 , product pq=27)
8 4 (( sum p+q=12 , product pq=32) which are the required values.
8x^{2} 12x +4
= 8x^{2} 8x 4x+4
=8x(x1) 4(x1)
=(x1) (8x4)
= (x1) .4. (2x1)
= 4 (x1) (2x1)

Question 10 of 10
10. Question
Factorize x^{2} – 9x +14
Correct
Explanation:
x^{2} – 9x +14
Here, a =1 b=9 c = +14
Split the middle term b=9 into two parts p and q such that
p+q = 9
pq = ca = 1 x 14 = 14
Proceed for splitting of terms as follows:
Tip: Always start with p value as the required sum and q value as 0 and proceed.
p q
9 0 ( sum p+q=9 , product pq=0)
10 1 ( sum p+q=9 , product pq=10)
. .
. .
If we proceed this way product will always be negative but we want a positive product so we proceed the other way.
p q
9 0 ( sum p+q=9 , product pq = 0)
8 1 ( sum p+q=9 , product pq = 8)
7 2 ( sum p+q=9 , product pq = 14) , which are the required values.
x^{2} – 9x +14
= x^{2} – 7x – 2x +14
= x(x7) – 2(x7)
= (x7)(x2)
Incorrect
Correct Answer: (x7)(x2)
Explanation:
x^{2} – 9x +14
Here, a =1 b=9 c = +14
Split the middle term b=9 into two parts p and q such that
p+q = 9
pq = ca = 1 x 14 = 14
Proceed for splitting of terms as follows:
Tip: Always start with p value as the required sum and q value as 0 and proceed.
p q
9 0 ( sum p+q=9 , product pq=0)
10 1 ( sum p+q=9 , product pq=10)
. .
. .
If we proceed this way product will always be negative but we want a positive product so we proceed the other way.
p q
9 0 ( sum p+q=9 , product pq = 0)
8 1 ( sum p+q=9 , product pq = 8)
7 2 ( sum p+q=9 , product pq = 14) , which are the required values.
x^{2} – 9x +14
= x^{2} – 7x – 2x +14
= x(x7) – 2(x7)
= (x7)(x2)