14

Q1. What is the quotient if 18(a²bc + ab²c + abc²) is divided by 6abc?

• a + b + c
• 3a + b + c
• 3(a + b + c)
• 3(a² +b² + c²)

Solution

As per the process of division    

Q2. a² - 2ab + b² =

• (a - 2b)²
• (a - b)³
• (a - b)²
• (a + b)²

Solution

a² - 2ab + b² = a² - ab - ab + b² = a(a - b) - b(a - b) = (a - b)²

Q3. x² + (a + b)x + ab can be factorised as ______ .                    

• (x + a) (x - b)
• (x + a) (x + b)
• (x - a) (x + b)
• (x - a) (x - b)

Solution

x² + (a + b)x + ab = x² + ax + bx + ab = x(x + a) + b(x + a) = (x + a) (x + b)

Q4. The highest common factor between 7x²y⁵z³ and 12x²y³z is_______ 

• xy³z
• x²yz
• x²y³
• x²y³z

Solution

Each of the three expressions have minimum 2 power of x; 3 power of y and 1 power of z, so the greatest common factor of the three expressions is x²y³z.

Q5. Identify the term whose irreducible factor form is: -11 x p x p x p x q x q x q x q x r x r

• 11p³q⁴r²
• -11p³q⁴r²
• -11p²q³r¹
• -11p³q⁴

Solution

-11 x p x p x p x q x q x q x q x r x r = -11p³q⁴r²

Q6. Which of the following is the factor of a²bc + ab²c + abc²?

• a²b²c²
• a² + b² + c²
• a + b + c
• a²bc

Solution

a²bc + ab²c + abc² = abc(a + b + c) Since the only factor among the given options is (a + b + c), hence option C.

Q7. Express 2pq + 4p + 5q + 10 in the factor form.

• (2p + 1)(q + 2)
• (2p + 5)(q + 2)
• (2p + 4)(q + 10)
• (p + 2)(2q + 5)

Solution

The given expression can be rearranged as

Q8. Express 6ab - 4b + 6 - 9a in the factor form.

• (3a - 2)(2b - 3)
• (3b - 2)(2a - 3)
• (2b + 3)(3a - 2)
• (3a + 2)(2b - 3)

Solution

Q9. What is the quotient if 4x² - 5x - 21 is divided by 4x + 7?

• x + 7
• x - 3
• 4x - 7
• 5x - 3

Solution

Q10. 36a²b⁵c³ - 49a²bc = ______

• a²b (6b²c - 7) (6b²c + 7)
• bc (6b²c - 7) (6b²c + 7)
• a²bc (6b²c - 7) (6b²c + 7)
• abc (6b²c - 7) (6b²c + 7)

Solution

36a²b⁵c³ - 49a²bc = a²bc [36b⁴c² - 49] = a²bc [(6b²c)² - (7)²] = a²bc (6b²c - 7) (6b²c + 7)

Q11. If x² - 6x - 40 = (x + 4)(x + a) then the value of a is:

• 10
• -10
• 5
• -5

Solution

x² - 6x - 40 = x² - 10x + 4x - 40 = x(x - 10) + 4(x - 10) = (x + 4)(x - 10) Thus, a = 4 OR a = -10

Q12. During factorisation of x² - 5x + 6, the coefficient of middle term would be splitted as the sum of

• 2, 3
• 2, -3
• -2, -3
• -2, 3

Solution

x² - 5x + 6 = x² - 3x - 2x + 6 Hence, -2, -3

Q13. Divide 7x² + 14x by (x + 2).

• 6x
• 4x
• 5x
• 7x

Solution

Q14. The irreducible factor form of 15a⁴ is:

• 3 x 5 x a x a x a
• 1 x 15 x a x a x a x a
• 15 x a x a x a x a
• 3 x 5 x a x a x a x a

Solution

15a⁴ = 3 x 5 x a x a x a x a

Q15. Find the quotient if 39x³(50x² - 98) is divided by 26x²(5x + 7)?

• 3(5x - 7)
• 3x(5x - 7)
• 2(25x - 49)
• 3x(5x + 7)

Solution

Applying the process of division Applying the method of cancellation

Q16. If p² + 12p + 32 = (p + a)(p + b) then the value of a and b is:

• a = 4, b = 8
• a = 2, b = 6
• a = 5, b = 7
• a = 10, b = 2

Solution

p² + 12p + 32 = p² + 4p + 8p + 32 = p(p + 4) + 8(p + 4) = (p + 4)(p + 8)

Q17. 9q² - 18q + 9 =

• (3q - 3)(3q + 3)
• (3q - 3)(3q - 3)
• (3q + 3)(3q + 3)
• (3q + 3)

Solution

9q² - 18q + 9 = (3q)² - 2(3q)(3) + 3² = (3q - 3)² = (3q - 3)(3q - 3)

Q18. If one factor of x² + 7x + 10 is (x + 2) then the other factor is:

• (x + 3)
• (x + 4)
• (x + 5)
• (x - 5)

Solution

x² + 7x + 10 = x² + 5x + 2x + 10 = x(x + 5) + 2(x + 5) = (x + 2)(x + 5)

Q19. Express 2x² - 11x + 15 in factor form.

• (x + 5)(x + 6)
• (2x + 5)(x + 6)
• (x - 3)(2x - 5)
• (x - 5)(x - 6)

Solution

Splitting the middle term of the given expression

Q20. Express 2ab² + 3a²b in the factor form.

• a(ab² + 3ab)
• b(2ab + 3a²)
• ab(2b + 3a)
• a²b(2b + ba)

Solution

The only factor common between the two terms of given polynomial is ab, hence, taking this ab common, the given expression can be rearranged as ab(2b +3a)