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Page No 64:

Question 1:

Divide. Write the quotient and the remainder.
(1) 21m2 ÷ 7m
(2) 40a3 ÷ (−10a)
(3) (−48p4) ÷ (−9p2)
(4) 40m5 ÷ 30m3
(5) (5x3 − 3x2) ÷ x2
(6) (8p3 − 4p2) ÷ 2p2
(7) (2y3 + 4y2 + 3) ÷ 2y2
(8) (21x4 − 14x2 + 7x) ÷ 7x3
(9) (6x5 − 4x4 + 8x3 + 2x2) ÷ 2x2
(10) (25m4 − 15m3 + 10m + 8) ÷ 5m3

Answer:

(1) 21m2 ÷ 7m

=21m27m=3×7×m×m7×m=3m
So, quotient = 3m and remainder = 0

(2) 40a3 ÷ (−10a)
=40a3-10a=-4×-10a×a2-10a=-4a2
So, quotient = -4a2 and remainder = 0

(3) (−48p4) ÷ (−9p2)
=-48p4-9p2=-48p2×p2-9p2=16p23
So, quotient = 16p23 and remainder = 0.

(4) 40m5 ÷ 30m3
=40m530m3=4×10m3×m23×10m3=4m23
So, quotient = 4m23 and remainder = 0.

(5) (5x3 − 3x2) ÷ x2
=5x3-3x2x2=x25x-3x2=5x-3
So, quotient = 5x-3 and remainder = 0

(6) (8p3 − 4p2) ÷ 2p2
=8p3-4p22p2=2p24p-22p2=4p-2
So, quotient = 4p-2 and remainder = 0

(7) (2y3 + 4y2 + 3) ÷ 2y2
=2y3+4y2+32y2=2y2y+2+32y2=2y2y+22y2+32y2=y+2+32y2
So, quotient = y+2 and remainder = 3

(8) (21x4 − 14x2 + 7x) ÷ 7x3
=21x4-14x2+7x7x3=7x3×3x-14x2+7x7x3=7x3×3x7x3+-14x2+7x7x3=3x+-14x2+7x7x3
So, quotient = 3x and remainder = -14x2+7x

(9) (6x5 − 4x4 + 8x3 + 2x2) ÷ 2x2
=6x5-4x4+8x3+2x22x2=2x23x3-2x2+4x+12x2=3x3-2x2+4x+1
So, quotient = 3x3-2x2+4x+1 and remainder = 0

(10) (25m4 − 15m3 + 10m + 8) ÷ 5m3
=25m4-15m3+10m+85m3=5m35m-3+10m+85m3=5m35m-35m3+10m+85m3=5m-3+10m+85m3
So, quotient = 5m-3 and remainder = 10m+8



Page No 66:

Question 1:

Divide and write the quotient and the remainder.
(1) (y2 + 10y + 24) ÷ (y + 4)
(2) (p2 + 7p − 5) ÷ (p + 3)
(3) (3x + 2x2 + 4x3) ÷ (x − 4)
(4) (2m3 + m2 + m + 9) ÷ (2m − 1)
(5) (3x − 3x2 − 12 + x4 + x3) ÷ (2 + x2)
(6) (a4a3 + a2a + 1) ÷ (a3 − 2)
(7) (4x4 − 5x3 − 7x + 1) ÷ (4x − 1)

Answer:

(1) (y2 + 10y + 24) ÷ (y + 4)



So, quotient = y + 6 and remainder = 0

(2) (p2 + 7p − 5) ÷ (p + 3)



So, quotient = p + 6 and remainder = -17.

(3) (3x + 2x2 + 4x3) ÷ (x − 4)



So, quotient = 4x2+18x+75 and remainder = 300.

(4) (2m3 + m2 + m + 9) ÷ (2m − 1)



So, quotient = m2+m+1 and remainder = 10.

(5) (3x − 3x2 − 12 + x4 + x3) ÷ (2 + x2)



So, quotient = x2+x-5 and remainder = x - 2.

(6) (a4 − a3 + a2 − a + 1) ÷ (a3 − 2)



So, quotient = a-1 and remainder = a2+a-1.

(7) (4x4 − 5x3 − 7x + 1) ÷ (4x − 1)



So, quotient = x3-x2-x4-2916 and remainder = -1316.



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