Divide by using long division. (10x^(2)+9x-1)÷(2x-1)

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Set up division: Set up the long division. We will divide the polynomial 10x^2 + 9x - 1 by the binomial 2x - 1 using long division.Find quotient: Determine how many times the leading term of the divisor (2x) goes into the leading term of the dividend (10x^2). 10x^2 divided by 2x is 5x. Write 5x above the long division bar.Multiply quotient and divisor: Multiply the entire divisor (2x - 1) by the quotient found in Step 2 (5x). 5x * (2x - 1) = 10x^2 - 5x. Write this result under the dividend.Subtract result: Subtract the result of Step 3 from the dividend. (10x^2 + 9x - 1) - (10x^2 - 5x) = 14x - 1. Bring down the next term if necessary.Determine new quotient: Determine how many times the leading term of the divisor (2x) goes into the new term (14x). 14x divided by 2x is 7. Write 7 above the long division bar, next to 5x.Multiply new quotient: Multiply the entire divisor (2x - 1) by the new quotient found in Step 5 (7). 7 * (2x - 1) = 14x - 7. Write this result under the 14x - 1.Subtract result: Subtract the result of Step 6 from the new term (14x - 1). (14x - 1) - (14x - 7) = 6. This is the remainder.Write final answer: Write the final answer. The quotient is 5x + 7 with a remainder of 6. The final answer is written as 5x + 7 + 6/(2x - 1).

Divide by using long division. $\newline$ $\left(10 x^{2}+9 x-1\right) \div(2 x-1)$

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Divide by using long division.\newline(10x2+9x−1)÷(2x−1)\left(10 x^{2}+9 x-1\right) \div(2 x-1)(10x2+9x−1)÷(2x−1)

Divide by using long division. $\newline$ $\left(10 x^{2}+9 x-1\right) \div(2 x-1)$