Question

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Answer 1

Answer:

(i)Toys excavated from the Indus valley civilization (3010–1500 BCE) include small carts, whistles shaped like birds, and toy monkeys which could slide down a string. The earliest toys are made from materials found in nature, such as rocks, sticks, and clay.

(ii)Three levels of governments are present in India: the central government, the state government and the local bodies (Municipal corporations and panchayats). The powers are distributed among these three levels of the government to easily manage the administration of the country.

Explanation:

Answer 2

Given polynomial: x²-2x-15

Therefore,

Let f(x) = x2–2x–15,

(x+ k) is a factor of the polynomial x2–2x–15

⇒ f(-k) = 0

⇒ f(-k) = (-k)2–2(-k) –15 = 0

⇒ k2+ 2k –15 = 0

⇒ (k + 5)(k - 3) = 0

⇒ k = -5 or 3.

Other given polynomial: x³+a

Therefore,

Let f(x) = x3+ a,

(x + k) is a factor of the polynomial x3+ a

⇒ (x + 3) is a factor of the polynomial x3+ a

⇒ f(-3) = 0

⇒ (-3)3+ a = 0

⇒ -27 + a = 0

⇒ a = 27

OR

⇒ (x - 5) is a factor of the polynomial x3+ a

⇒ f(5) = 0

⇒ (5)3+ a = 0

⇒ 125 + a = 0

⇒ a = -125.

☆ K= -5 or 3

☆ a= 27 or -125