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Divide. If there is a remainder, include it as a simplified fraction.\newline(5b2+3b2)÷(b+1)(5b^2 + 3b - 2) \div (b + 1)\newline______

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Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(5b2+3b2)÷(b+1)(5b^2 + 3b - 2) \div (b + 1)\newline______
  1. Polynomial Long Division: We will use polynomial long division to divide (5b2+3b2)(5b^2 + 3b - 2) by (b+1)(b + 1). First, we divide the first term of the dividend, 5b25b^2, by the first term of the divisor, bb, to get the first term of the quotient. 5b2÷b=5b5b^2 \div b = 5b
  2. First Term Division: Now, we multiply the entire divisor (b+1)(b + 1) by the first term of the quotient (5b)(5b) and subtract the result from the original polynomial.(5b)(b+1)=5b2+5b(5b)(b + 1) = 5b^2 + 5bSubtract this from the original polynomial:(5b2+3b2)(5b2+5b)=2b2(5b^2 + 3b - 2) - (5b^2 + 5b) = -2b - 2
  3. Subtraction and Multiplication: Next, we divide the new first term of the remaining polynomial, 2b-2b, by the first term of the divisor, bb. \newline2b÷b=2-2b \div b = -2
  4. New Term Division: We multiply the entire divisor (b+1)(b + 1) by the new term of the quotient (2)(-2) and subtract the result from the remaining polynomial.\newline(2)(b+1)=2b2(-2)(b + 1) = -2b - 2\newlineSubtract this from the remaining polynomial:\newline(2b2)(2b2)=0(-2b - 2) - (-2b - 2) = 0
  5. Final Quotient: Since the remainder is 00, we have no remainder and the division is exact.\newlineThe quotient is the sum of the terms we found: 5b25b - 2.

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