Division of algebraic expressions | Factorization | Assessment | English | Grade 8

The value of 25a³ ÷ 15a² is ________.

• 5a + 3

• 5a - 3

• 5a/3

• 5a × 3

Answer explanation

25a³ ÷ 15a² = (5 × 5 × a × a × a)/(5 × 3 × a × a) = (5 × a)/3 = 5a/3 So, option 3 is correct.

The value of 24a³b²c ÷ 8a³c is _________.

• 3b

• 3b²

• 3 + b²

• 3 - b²

Answer explanation

24a³b²c ÷ 8a³c = (2 × 2 × 2 × 3 × a × a × a × b × b × c)/(2 × 2 × 2× a × a × a × c) = 3 × b × b = 3b² So, option 2 is correct.

The value of (36p²q² + 18p²q + 9p³) ÷ 9p² is ______________.

• 4q² - 2q + p

• 4q² + 2q - p

• 4q² - 2q - p

• 4q² + 2q + p

Answer explanation

(36p²q² + 18p²q + 9p³) ÷ 9p² = [(2 × 2 × 3 × 3 × p × p × q × q ) + (2 × 3 × 3 × p × p × q) + (3 × 3 × p × p × p)] / (3 × 3 × p × p) = (3 × 3 × p × p)(2 × 2 × q × q + 2 × q + p )/(3 × 3 × p × p) = 4q² + 2q + p So, option 4 is correct.

The value of (4a³ + 4a² - 48a) ÷ (4a + 16) is _____________.

• a(a + 3)

• a(a/3)

• a(a - 3)

• a(a × 3)

Answer explanation

(4a³ + 4a² - 48a) ÷ (4a + 16) = 4a(a² + a - 12)/(4a + 16) {Note that 4 + (-3) = 1 and 4 x (-3) = -12} = 4a(a + 4)(a - 3)/4(a + 4) = a(a - 3) So, option 3 is correct.

If the distance travelled by a car is (t³ - 49t) and the time taken to cover that distance is (t - 7), then what will be the speed of the car?

• t² - 7t

• t² + 7t

• t²/7t

• t² × 7t

Answer explanation

We know that speed = distance/time So, Speed = (t³ - 49t)/ (t - 7) = t(t² - 49)/(t - 7) = t(t - 7)(t + 7)/(t - 7) = t(t + 7) = t² + 7t So, option 2 is correct.

If the volume of a cuboid is (24y⁴z³ + 8y³z² - 16y²z²) and its height is 8y²z, then what will be the area of the base of the given cuboid?

• 3y²z² - yz - 2z

• 3y²z² + yz + 2z

• 3y²z² - yz + 2z

• 3y²z² + yz - 2z

Answer explanation

Volume of a cuboid = area of base of cuboid × height of cuboid So, area of base of cuboid = volume of cuboid / height of cuboid Area of base of cuboid = (24y⁴z³ + 8y³z² - 16y²z²) / 8y²z = 3y²z² + yz - 2z So, option 4 is correct.

The value of 12xy (2x - 3y)² ÷ 4xy (4x² - 9y²) is __________.

• 3(2x - 3y)/(2x + 3y)

• 3(2x + 3y)/(2x - 3y)

• 3(3x - 2y)/(2x + 3y)

• 3(2x - 3y)/(3x + 2y)

Answer explanation

12xy(2x - 3y)² ÷ 4xy(4x² - 9y²) = 12xy(2x - 3y)(2x - 3y) / 4xy (2x - 3y) (2x + 3y) = 3 (2x - 3y) / (2x + 3y) Hence option 1 is correct answer.