Final answer:
To find the quotient when 2x²+5x−4 is divided by x−2, we can use polynomial long division. The quotient is 2x+5-4/x or 2x+5-4x^(-1).
Step-by-step explanation:
To find the quotient when 2x²+5x−4 is divided by x−2, we can use polynomial long division. Divide the first term of the dividend, 2x², by the first term of the divisor, x, which gives us 2x as the first term of the quotient. Multiply the divisor x−2 by 2x and subtract the result from the dividend: 2x(x−2)=2x²−4x. Bring down the next term, 5x, and repeat the process:
Divide 5x by x to get 5 as the next term of the quotient. Multiply the divisor x−2 by 5 and subtract the result from the current dividend: 5(x−2)=5x−10. Finally, bring down the last term, −4, and divide it by x, which gives us -4/x as the last term of the quotient. The final quotient is 2x+5-4/x or 2x+5-4x^(-1).