Question

1. Simplify: –45p3 ÷ 9p2
2. Simplify: 4x2y2(3z – 24), 36xy(z – 8)
3. Divide: 81x3(50x2 – 98) by 27x2 (5x + 7)
4. Which of the following is the remainder when z(5z2 – 80) is divided by 5z(z – 4):
(a) z + 4(b) z – 4(c) 5(d) 0
5. Which of the following is the quotient when 44(x4 – 5x3 – 24x2) is divided by 22x(x – 8):
(a) x(x + 3)(b) 2x(x + 3)(c) 2(x – 3)(d) x(x – 3)
6. Which of the following is factorization of (1 – x2)
(a) (1 + x) (1 + x)
(b) (1 – x) (1 – x)
(c) (1 – x) (1 + x)
(d) none of these
7. By which of the following a4 – b4 be divided to get quotient (a2 + b2) (a – b) and, remainder as 0.
(a) a2 + b2(b) a – b(c) a + b(d) a2 – b2
8. Is (a – 1) (b – 1) the factorisation of (ab – a – b +1) or (ab – a + b – 1)?

Answer 1

hope it will help you

Answer 2

Answer:

Step-by-step explanation:

1. –45p3 ÷ 9p2

= -45p³/9p²

= -5p

2. 4x²y²(3z - 24) /(36xy (z-8)

= 12x²y²(z - 8)/(36xy (z-8)

= xy/3

3. 81x³ (50x² - 98)/(27x²(5x + 7))

= 3x * 2*(25x² - 49)/(5x + 7)

= 6x (5x + 7)(5x - 7)/(5x + 7)

= 6x(5x - 7)

= 30x² - 42x

4.  z(5z² – 80)/(5z(z-4))

= 5(z² - 16) /5(z-4)

= (z + 4)(z-4)/(z-4)

= z + 4

remainder = 0

44(x⁴ - 5x³ - 24x²)/(22x(x-8))

= 2x²(x² - 5x - 24)/(x(x - 8))

= 2x(x-8)(x+3)/(x-8)

= 2x(x + 3)

2x(x + 3) is Quotient

1 – x²

= (1 + x)(1-x)

(c) (1 – x) (1 + x)

a⁴ - b⁴ = (a² + b²)(a² - b²)

so to be divided by a² - b² to get Quotient a² + b²