Solved Questions of Algebraic Expressions
1. Which of the following is equivalent to the expression 4x2 - 12x + 9?
a) (2x - 3)2
b) (2x - 3) (2x + 3)
c) (2x - 3)3
d) (2x - 3) (2x2 + 3)
Answer: a) (2x - 3)2
Explanation: We have, 4x2 - 12x + 9,
4x2 - 12x + 9 = (2x)2 – 2 x (2x) x 3 + 32
Which satisfied, a2 – 2ab + b2 = (a – b)2 where a = 2 and b = 3
i.e., 4x2 - 12x + 9 = (2x – 3)2
2. What is the degree of the polynomial 3x3 + 5x2 - 2x + 1?
a) 1
b) 2
c) 3
d) 4
Answer: c) 3
Explanation: The degree of an algebraic expression is the highest power of the variables. Hence the degree of the expression is 3.
3. Which of the following is equivalent to the expression x2 + 2x + 1?
a) (2x - 3)2
b) (2x + 3)2
c) (x - 1)2
d) (x + 1)2
Answer: d) (x + 1)2
Explanation: We have, x2 + 2x + 1,
x2 + 2x + 1 = x2 + 2 × x × 1 + 12
Which satisfied, a2 + 2ab + b2 = (a + b)2 where a = x and b = 1
i.e., x2 + x + 1 = (x + 1)2
4. Which is the simplified form of the expression (2x – 5) (3x2 + 7x)?
a) x3 - x2 - 5x
b) 5x3 - 6x2 + 5x
c) 6x3 - x2 - 35x
d) 6x3 + x2 - 5x
Answer: c) 6x3 - x2 - 35x
Explanation: we have, (2x - 5) (3x2 + 7x)
= 2x (3x2 + 7x) – 5(3x2 + 7x)
= (6x3 + 14x2) - (15x2 + 35x)
= 6x3 + (14x2 - 15x2) - 35x
= 6x3 - x2 - 35x
5. What is the simplified form of the expression (x3 - 1) / (x - 1)?
a) x2 - x +1
b) x2 + x +1
c) x2 + x -1
d) x2 - x -1
Answer: b) x2 + x +1
Explanation: we have, (x3 - 1) / (x - 1)
which follows a3 - b3 = (a - b) (a2 + ab + b2)
= (x - 1) (x2 + x + 1) / (x - 1)
= x2 + x + 1
Practice Questions of Algebraic Expressions
1. What is the sum of the coefficients in the expansion of (x + 1)3?
a) 6
b) 7
c) 8
d) 9
Answer: c) 8
2. Which of the following is a factor of the expression x3 - 27?
a) (x - 3)
b) (x + 3)
c) (x2 + 3)
d) (x2 - 3x + 9)
Answer: a) (x - 3)
3. Which of the following is equivalent to the expression x3 + x2 - 4x - 4?
a) (2x - 1) (x + 4) (x - 1)
b) (x - 2) (x2 + 3x + 2)
c) (2x + 1) (x + 2) (x - 2)
d) (x + 1) (x2 + 2x - 4)
Answer: b) (x - 2) (x2 + 3x + 2)
4. What is the degree of the expression 3x4 + 2x2 - 5x + 1?
a) 4
b) 3
c) 2
d) 1
Answer: a) 4
5. What is the coefficient of x2 in the following expression (x2 – 3)3?
a) -27
b) -9
c) 9
d) 27
Answer: d) 27
6. What is the value of (a2 - b2) / (a - b) when a = 5 and b = 3?
a) 8
b) 10
c) 12
d) 14
Answer: a) 8
7. What is the simplified form of (x2 - 4) / (x + 2)?
a) x - 2
b) x + 2
c) x2 + 2x + 4
d) x + 4
Answer: a) x - 2
8. What is the product of (x - 3) (x + 5)?
a) x2 - 2x - 15
b) x2 + 2x + 15
c) x2 + 2x - 15
d) x2 - 2x + 15
Answer: c) x2 + 2x - 15
9. What is the simplified form of (2x2 + 3x - 1) + (3x2 - 2x + 4)?
a) 5x2 + x + 3
b) 5x2 + x - 3
c) 5x2 - 5x + 3
d) 5x2 - 5x - 3
Answer: a) 5x2 + x + 3
10. What is the value of the expression 2(x2 + 3) + 6x – 2, if x = -2?
a) 3
b) 2
c) 1
d) 0
Answer: d) 0
