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Divide. If there is a remainder, include it as a simplified fraction.\newline(y3+7y2+10y)÷(y+5)(y^3 + 7y^2 + 10y) \div (y + 5)\newline______

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Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(y3+7y2+10y)÷(y+5)(y^3 + 7y^2 + 10y) \div (y + 5)\newline______
  1. Divide leading terms: We will use polynomial long division to divide (y3+7y2+10y)(y^3 + 7y^2 + 10y) by (y+5)(y + 5). First, we divide the leading term of the numerator, y3y^3, by the leading term of the denominator, yy, to get the first term of the quotient. y3÷y=y2y^3 \div y = y^2
  2. Multiply and subtract: Now, we multiply the entire divisor (y+5)(y + 5) by the first term of the quotient (y2)(y^2) and subtract the result from the original polynomial.(y+5)(y2)=y3+5y2(y + 5)(y^2) = y^3 + 5y^2(y3+7y2+10y)(y3+5y2)=2y2+10y(y^3 + 7y^2 + 10y) - (y^3 + 5y^2) = 2y^2 + 10y
  3. Divide new polynomial: Next, we divide the leading term of the new polynomial 2y22y^2 by the leading term of the divisor yy to get the next term of the quotient.2y2y=2y\frac{2y^2}{y} = 2y
  4. Multiply and subtract: We multiply the entire divisor (y+5)(y + 5) by the new term of the quotient (2y)(2y) and subtract the result from the new polynomial.(y+5)(2y)=2y2+10y(y + 5)(2y) = 2y^2 + 10y(2y2+10y)(2y2+10y)=0(2y^2 + 10y) - (2y^2 + 10y) = 0
  5. Division complete: Since we have no remainder, the division is complete. The quotient is the sum of the terms we found: y2+2yy^2 + 2y.

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