Form 2 Mathematics(Operation Of polynomial) 40MARKS

Question1:
FIND THE Remainder: (x^3+7x^2+12x+8)/(x^2+5x+1)

x + 2
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x^2+5x+1 / x^3 + 7x^2 + 12x + 8
x^3 + 5x^2 + x
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2x^2 + 11x + 8
2x^2 + 10x + 2
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x + 6

Hence the remainder is (x + 6)
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Question 2
Find the remainder When
6x^4-3x^3-2x^2-4 is divided by 2x-3

3x^3 + 3x^2 + 7x/2
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2x - 3 / 6x^4 - 3x^3 - 2x^2 - 4
6x^4 - 9x^3
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6x^3 - 2x^2 - 4
6x^3 - 9x^2
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7x^2 - 4
7x^2 - 21/2
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13/2

Hence the remainder is 13/2 (or 6.5)

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Question 3
(35x^3-15x^2-25x)/(-5x)

= (-5x)(-7x^2 + 3x + 5x) / (-5x)
= -7x^2 + 3x + 5

Hence the answer is (-7x^2 + 3x + 5)

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Question 4
48a^5 b^2 c^7 / 6a^4 b c^8

= 6(a^4)(b)(c^7) (8ab) / [6(a^4)(b)(c^8)]
= 8ab / c

Hence the answer is 8ab/c

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Question 5
(x-x^2+1)^2

= (x-x^2+1)(x-x^2+1)
= x^2 - x^3 + x - x^3 + x^4 - x^2 + x - x^2 + 1
= x^4 - 2x^3 - x^2 + 2x + 1

Question 3
(35x^3-15x^2-25x)/(-5x)
=35x^3-15x^2+5x

Question 4
48a^5 b^2 c^7 / 6a^4 b c^8
=8ab/c

Question 5
(x-x^2+1)^2
=(x-x^2+1)X(x-x^2+1)
=x^2-x^3+x-x^3+x^4-x^2+x-x^2+1
=x^4-2x^3-x^2+2x+1