Question

please write the answer

Answer 1

Answer:

y5. ( 5y3 + 3y2 - 4 )

................

................

................

Answer 2

$\sf{\underline{\underline{ \purple{ \huge{Question:}}}}}$

Divide:

$\star \: \sf{ \blue{3 {y}^{7} - 4 {y}^{5} + 5 {y}^{4} \: by \: {y}^{4} }}$

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{Answer:}}}}}$

$\\ \star \: \sf{ \blue{3 {y}^{7} - 4 {y}^{5} + 5 {y}^{4} \: by \: {y}^{4} }}$

ㅤㅤㅤㅤㅤ

• Here, we are dividing a polynomial ( 3y⁷ - 4y⁵ + 5y⁴ ) by a monomial ( y⁴ ). Divide each term of the polynomial by the monomial and then simplify.

$\\ \\ \implies\sf \dfrac{3 {y}^{7} - 4 {y}^{5} + 5 {y}^{4}}{ {y}^{4}}$

ㅤㅤㅤㅤㅤ

Divide each term of the polynomial by the monomial, we have

$\implies{ \sf{ \dfrac{3 {y}^{7} }{ {y}^{4} } - \dfrac{4 {y}^{5} }{ {y}^{4} } + \dfrac{5 {y}^{4} }{ {y}^{4} }} }$

$\\ \\ \implies \sf (3 {y})^{7 - 4} - (4 {y})^{5 - 4} +( 5 {y})^{4 - 4}$

$\\ \\ \implies \sf3 {y}^{3} - 4y + 5 {y}^{0}$

Any number raise to power ⁰ is 1

$\implies \sf3 {y}^{3} - 4y + 5 \times 1$

$\\ \\ \implies \sf3 {y}^{3} - 4y + 5$

$\sf{ \blue{ \therefore Final \: Answer = \green{ \underline{ \boxed{ \sf{3 {y}^{3} - 4y + 5 }}}}}}$

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{More:}}}}}$

ㅤㅤㅤㅤㅤ

$\sf{x}^{m} \div {x}^{n} = \dfrac{ {x}^{m} }{ {x}^{n} } = {x}^{m - n}$

• If m > n

$\\ \sf{x}^{m} \div {x}^{n} = \dfrac{ {x}^{m} }{ {x}^{n} } = \dfrac{1}{ {x}^{m - n} }$

• if n > m

══════════════════════