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Polynomials
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Question 1 of 10
1. Question
For what value of b is the polynomial g(x) = 3x^{4} + bx^{3}+5 exactly divisible by (x1)
Correct
Explanation:
x1 = 0 x = 1
For g9x) to be exactly divisible by (x1) , g(1) = 0
g(1) = 3X (1)^{4} + b X (1)^{3 }+5 = 0
3 + b + 5 = 0
b = 8
Incorrect
Correct Answer: b = 8
Explanation:
x1 = 0 x = 1
For g9x) to be exactly divisible by (x1) , g(1) = 0
g(1) = 3X (1)^{4} + b X (1)^{3 }+5 = 0
3 + b + 5 = 0
b = 8

Question 2 of 10
2. Question
For what value of c is p(x) = cx^{3}+2x^{2}+6x exactly divisible by (x3).
Correct
Explanation:
x – 3 = 0 x =3
For p(x) to be exactly divisible by (x3) , p(3) = 0
p(3) = c X 3^{3} + 2 x 3^{2 }+ 6 X 3 = 0
9c + 18 +18 = 0
9c + 36 = 0 9c = 36 c = 4
Incorrect
Correct Answer: c = 4
Explanation:x – 3 = 0 x =3
For p(x) to be exactly divisible by (x3) , p(3) = 0
p(3) = c X 3^{3} + 2 x 3^{2 }+ 6 X 3 = 0
9c + 18 +18 = 0
9c + 36 = 0 9c = 36 c = 4

Question 3 of 10
3. Question
Factorize 4x^{2}+20xy
Correct
Explanation:
4x(x+5y) (By taking 4x common)
Incorrect
Correct Answer: 4x(x+5y)
Explanation:4x(x+5y) (By taking 4x common)

Question 4 of 10
4. Question
Factorize 40a^{3}b + 56 a^{4}b^{2}c
Correct
Explanation: 8a^{3}b ( 5 + abc ) (By taking out common factors)
Incorrect
Explanation: 8a^{3}b ( 5 + abc ) (By taking out common factors)

Question 5 of 10
5. Question
Factorize ax + bx + ad + bd
Correct
Explanation: ax+bx+ad+bd = (a+b)x + (a+b)d = (a+b)(x+d)
Incorrect
Explanation: ax+bx+ad+bd = (a+b)x + (a+b)d = (a+b)(x+d)

Question 6 of 10
6. Question
Factorize 6a(c+d) – 7b(c+d)
Correct
Explanation: (c+d)(6a7b) [By taking (c+d) common]
Incorrect
Explanation: (c+d)(6a7b) [By taking (c+d) common]

Question 7 of 10
7. Question
Factorize x^{2}+4x+x+4
Correct
Explanation: x^{2}+4x+x+4
=x(x+4) + (x+4)
=(x+4)(x+1)
Incorrect
Explanation: x^{2}+4x+x+4
=x(x+4) + (x+4)
=(x+4)(x+1)

Question 8 of 10
8. Question
Factorize 16x^{2}– 25y^{2}
Correct
Explanation: 16x^{2}– 25y^{2 } = (4x)^{2} – (5y)^{2} = (4x+5y)(4x5y)
Options:
(4x+5y)(4x5y)
(5y+4x)(5y4x)
Incorrect
Answer: (4x+5y)(4x5y)
Explanation: 16x^{2}– 25y^{2 } = (4x)^{2} – (5y)^{2} = (4x+5y)(4x5y)Options:
(4x+5y)(4x5y)
(5y+4x)(5y4x)

Question 9 of 10
9. Question
Factorize x^{2}+5x + 6
Correct
Explanation:
The equation is in the form ax^{2}+bx+c
Split the coefficient of the middle term b such that b = p+q
So that p + q =b
pq = ca
Split the middle term 6x so that 5 = 3+2
x^{2 }+6x + 6 = x^{2}+ 3x+2x + 6 = x(x+3) + 2(x+3) = (x+3)(x+2)
Incorrect
Explanation:
The equation is in the form ax^{2}+bx+c
Split the coefficient of the middle term b such that b = p+q
So that p + q =b
pq = ca
Split the middle term 6x so that 5 = 3+2
x^{2 }+6x + 6 = x^{2}+ 3x+2x + 6 = x(x+3) + 2(x+3) = (x+3)(x+2)

Question 10 of 10
10. Question
Factorize 36 – 49x^{2}
Correct
Explanation:
36 – 49x^{2 }= 6^{2} – (7x)^{2} = (6+7x)(67x)
Incorrect
Explanation:
36 – 49x^{2 }= 6^{2} – (7x)^{2} = (6+7x)(67x)