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Polynomials
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Question 1 of 10
1. Question
The zero of the polynomial p(x) = 7x – 21 is
Correct
Explanation:For a polynomial p(x), if p(a) = 0 ,then we say a is the zero of the polynomial.
p(x) = 0
7x 21 = 0
7x = 21
X = 21/7 = 3
Incorrect
Explanation:For a polynomial p(x), if p(a) = 0 ,then we say a is the zero of the polynomial.
p(x) = 0
7x 21 = 0
7x = 21
X = 21/7 = 3

Question 2 of 10
2. Question
5 is the zero of the polynomial p(x) = x5 .State true/false
Correct
Explanation:
p(x) = x 5
p(5) = 5 – 5 = 0
Thus, 5 is the zero of the polynomial.Incorrect
Explanation:
p(x) = x 5
p(5) = 5 – 5 = 0
Thus, 5 is the zero of the polynomial. 
Question 3 of 10
3. Question
4 is the zero of the polynomial p(x) = x – 4. State true/false
Correct
Explanation:
p(x) = x – 4
p(4) = – 4 – 4 = 8
Thus, 4 is not the zero of the polynomial.Incorrect
Explanation:
p(x) = x – 4
p(4) = – 4 – 4 = 8
Thus, 4 is not the zero of the polynomial. 
Question 4 of 10
4. Question
2 and 3 are the zeros of the polynomial p(x) = (x2)(x3). State true/false.
Correct
Explanation:
For a polynomial p(x), if p(a) = 0 ,then we say a is the zero of the polynomial.
p(x) = (x2)(x3)
When x = 2 , p(2) = (22)(x3) = 0 X (x3) = 0
When x = 3 , p(3) = (x2) (33) = (x2) X 0 = 0Incorrect
Explanation:
For a polynomial p(x), if p(a) = 0 ,then we say a is the zero of the polynomial.
p(x) = (x2)(x3)
When x = 2 , p(2) = (22)(x3) = 0 X (x3) = 0
When x = 3 , p(3) = (x2) (33) = (x2) X 0 = 0 
Question 5 of 10
5. Question
0 and 4 are the zeros of the polynomial g(x) = x^{2} – 4x. State true/false
Correct
Explanation:
For a polynomial p(x), if p(a) = 0 ,then we say a is the zero of the polynomial.
g(x) = x2 4x
g(0) = 02 – 4 X 0 = 0 – 0 = 0
g(4) = 42 – 4 X 4 = 16 16 = 0
Thus, both 0 and 4 are the zeros of the given polynomial g(x)Incorrect
Explanation:
For a polynomial p(x), if p(a) = 0 ,then we say a is the zero of the polynomial.
g(x) = x2 4x
g(0) = 02 – 4 X 0 = 0 – 0 = 0
g(4) = 42 – 4 X 4 = 16 16 = 0
Thus, both 0 and 4 are the zeros of the given polynomial g(x) 
Question 6 of 10
6. Question
3 is the zero of the polynomial p(x) = x^{2}+x12. State true/false.
Correct
Explanation: For a polynomial p(x), if p(a) = 0 ,then we say a is the zero of the polynomial.
p(x) = x^{2}+x12
p(3) = 3^{2} + 3 12 = 9+ 3 12 = 12 12 =0
Incorrect
Explanation: For a polynomial p(x), if p(a) = 0 ,then we say a is the zero of the polynomial.
p(x) = x^{2}+x12
p(3) = 3^{2} + 3 12 = 9+ 3 12 = 12 12 =0

Question 7 of 10
7. Question
The remainder of the polynomial f(x) = x^{3} + 4x^{2}+2 when it is divided by (x3) is
Correct
Explanation:
By remainder theorem,
If f(x) is a polynomial of degree n ≥1 and a be any real number then when we divide f(x) by (xa) the remainder is f(a).
x3 = 0 x = 3
By remainder theorem, when f(x) is divided by (x3) the remainder is f(3).
f(3) = 3^{3 }+ 4 X 3^{2 }+ 2 = 27 + 4 X 9 + 2 = 27 + 36 +2 = 65.
Incorrect
Explanation:
By remainder theorem,
If f(x) is a polynomial of degree n ≥1 and a be any real number then when we divide f(x) by (xa) the remainder is f(a).
x3 = 0 x = 3
By remainder theorem, when f(x) is divided by (x3) the remainder is f(3).
f(3) = 3^{3 }+ 4 X 3^{2 }+ 2 = 27 + 4 X 9 + 2 = 27 + 36 +2 = 65.

Question 8 of 10
8. Question
The remainder of the polynomial p(x) = 9x^{3}+3x^{2}+2x+6 when it is divided by (2x+3 ) is
Correct
Explanation: 2x+3 = 0 x = 3/2
By remainder theorem we know that when p(x) is divided by (2x+3) ,the remainder is p(3/2)
p(3/2) = 9 X (3/2)^{3} + 3 (3/2)^{2} + 2(3/2) + 6
= 9 X (27/8) + 3 (9/4) – 3 + 6
= 243/8 + 27/4 + 3
= (243 + 52 +24)/8 = 347/8
Incorrect
Explanation: 2x+3 = 0 x = 3/2
By remainder theorem we know that when p(x) is divided by (2x+3) ,the remainder is p(3/2)
p(3/2) = 9 X (3/2)^{3} + 3 (3/2)^{2} + 2(3/2) + 6
= 9 X (27/8) + 3 (9/4) – 3 + 6
= 243/8 + 27/4 + 3
= (243 + 52 +24)/8 = 347/8

Question 9 of 10
9. Question
Check whether the polynomial f(y) = 4y^{3}+4y^{2}y1 is a multiple of (2y+1).
Correct
Explanation:
2y+1 = 0 y = 1/2
(2y+1) is factor of f(y) =4y^{3}+4y^{2}y1 if on dividing f(y) by (2y+1) the remainder is 0.
p(1/2) = 4 (1/2) ^{3} + 4 (1/2) ^{2} – (1/2) 1
= 4 (1/8) + 4 (1/4) +1/21
= 1/2 +1 1/2 = 1 1 =0
Incorrect
Explanation:
2y+1 = 0 y = 1/2
(2y+1) is factor of f(y) =4y^{3}+4y^{2}y1 if on dividing f(y) by (2y+1) the remainder is 0.
p(1/2) = 4 (1/2) ^{3} + 4 (1/2) ^{2} – (1/2) 1
= 4 (1/8) + 4 (1/4) +1/21
= 1/2 +1 1/2 = 1 1 =0

Question 10 of 10
10. Question
If the polynomials p(x) = 3x^{2}+4x+5 and g(x) = x^{2}+5x+b leave the same remainder when divided by (x3), then the value of b is
Correct
Explanation:
p(3) = 3 X 3^{2}+ 4X3 +5=27+12+5 = 44
g(3) = 3^{2} + 5X3 + b= 9+ 15+b = 24 +b
24+b = 44
b = 20
Incorrect
Explanation:
p(3) = 3 X 3^{2}+ 4X3 +5=27+12+5 = 44
g(3) = 3^{2} + 5X3 + b= 9+ 15+b = 24 +b
24+b = 44
b = 20