Question:

Divide the given polynomial by the given monomial. 
  1. (5x26x)÷3x(5x^ 2 – 6x) ÷ 3x
  2. (3y84y6+5y4)÷y4 (3y^ 8 – 4y^ 6 + 5y ^4 ) ÷ y ^4
  3.  8(x3y2z2+x2y3z2+x2y2z3)÷4x2y2z28(x^ 3y^ 2 z^ 2 + x^ 2y ^3 z^ 2 + x^ 2y ^2 z ^3 ) ÷ 4x ^2y ^2 z ^2
  4.  (x3+2x2+3x)÷2x(x^ 3 + 2x^ 2 +3x) ÷ 2x
  5.  (p3q6p6q3)÷p3q3(p^ 3q^ 6 – p^ 6q ^3 ) ÷ p^ 3q ^3

Updated On: Dec 4, 2023
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Solution and Explanation

(i) 5x26x=x(5x6)5x^ 2 - 6x = x(5x - 6)

(5x26x)3x=x(5x6)3x=13(5x6)\frac{(5x^2-6x)}{3x}=\frac{x(5x-6)}{3x}=\frac{1}{3}(5x-6)


(ii)3y84y6+5y4=y4(3y44y2+5) 3y^ 8 - 4y ^6 + 5y^ 4 = y ^4 (3y^ 4 - 4y ^2 + 5)

(3y84y6+5y4)y4=y4(3y44y2+5)y4=3y44y2+5\frac{(3y^8-4y^6+5y^4)}{y^4}=\frac{y^4(3y^4-4y^2+5)}{y^4}=3y^4-4y^2+5


(iii) 8(x3y2z2+x2y3z2+x2y2z3)=8x2y2z2(x+y+z)8(x^ 3 y^ 2 z^ 2 + x ^2 y^ 3 z^ 2 + x ^2 y ^2 z^ 3 ) = 8x^ 2 y ^2 z ^2 (x + y + z)

8(x3y2z2+x2y3z2+x2y2z3)4x2y2z2=8x2y2z2(x+y+z)4x2y2z2=2(x+y+z)\frac{8(x^3y^2z^2+x^2y^3z^2+x^2y^2z^3)}{4x^2y^2z^2}=\frac{8x^2y^2z^2(x+y+z)}{4x^2y^2z^2}=2(x+y+z)


(iv) x3+2x2+3x=x(x2+2x+3)x^ 3 + 2x^ 2 + 3x = x(x ^2 + 2x + 3)

(x3+2x2+3x)2x=x(x2+2x+3)2x=12(x2+2x+3)\frac{(x^3+2x^2+3x)}{2x}=\frac{x(x^2+2x+3)}{2x}=\frac{1}{2}(x^2+2x+3)


(v) p3q6p6q3=p3q3(q3p3)p^ 3q^ 6 - p^ 6q^ 3 = p^ 3q^ 3 (q^ 3 - p ^3 )

(p3q6p6q3)p3q3=p3q3(q3p3)p3q3=q3p3\frac{(p^3q^6-p^6q^3)}{p^3q^3}=\frac{p^3q^3(q^3-p^3)}{p^3q^3}=q^3-p^3

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