Question

Divide the given polynomial by the given monomial. 

1. \((5x^ 2 – 6x) ÷ 3x \)
2. \( (3y^ 8 – 4y^ 6 + 5y ^4 ) ÷ y ^4 \)
3.  \(8(x^ 3y^ 2 z^ 2 + x^ 2y ^3 z^ 2 + x^ 2y ^2 z ^3 ) ÷ 4x ^2y ^2 z ^2 \)
4.  \((x^ 3 + 2x^ 2 +3x) ÷ 2x \)
5.  \((p^ 3q^ 6 – p^ 6q ^3 ) ÷ p^ 3q ^3\)

Answer 1

(i) \(5x^ 2 - 6x = x(5x - 6)\)

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

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(ii)\( 3y^ 8 - 4y ^6 + 5y^ 4 = y ^4 (3y^ 4 - 4y ^2 + 5)\)

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

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(iii) \(8(x^ 3 y^ 2 z^ 2 + x ^2 y^ 3 z^ 2 + x ^2 y ^2 z^ 3 ) = 8x^ 2 y ^2 z ^2 (x + y + z)\)

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

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(iv) \(x^ 3 + 2x^ 2 + 3x = x(x ^2 + 2x + 3)\)

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

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(v) \(p^ 3q^ 6 - p^ 6q^ 3 = p^ 3q^ 3 (q^ 3 - p ^3 )\)

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