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Euclid's Division Lemma

Divide. Write...

Question

Divide. Write the quotient and the remainder.
(a) $(5 x^{3} - 3 x x^{2}) \div x^{2}$
(b) $(8 p^{3} - 4 p^{2}) \div 2 p^{2}$
(c) $(2 y^{3} + 4 y^{2} + 3) \div 2 y^{2}$

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Solution

(a) $\frac{5 x^{3} - 3 x x^{2}}{x^{2}} = \frac{5 x^{3} - 3 x^{3}}{x^{2}} = 2 x ⟹$ quotient $= 2 x$ , remainder $= 0$
(b) $\frac{8 p^{3} - 4 p^{2}}{2 p^{2}} = \frac{2 p^{2} (4 p - 2)}{2 p^{2}} = 4 p - 2 ⟹$ quotient $= 4 p - 2$ ,remainder $= 0$
(c) $\frac{2 y^{3} + 4 y^{2} + 3}{2 y^{2}} = \frac{2 y^{2} (y + 2)}{2 y^{2}} + \frac{3}{2 y^{2}} ⟹$ quotient $= y + 2$ ,remainder $= 3$

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Q. Solve the following and write the quotient and remainder:

(8 p^{3} - 4 p^{2}) \div 2 p^{2}

Q. Divide and write the quotient and the remainder

(8 p^{3} - 4 p^{2}) \div 2 p^{2}

({2 y}^{3} + {4 y}^{2} + 3) \div {2 y}^{2}

Q. Divide and write the quotient and the remainder

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