### Instruction: What is the quotient when $8x^3+16x^2-7x+4$ is divided by $2x+5$?### Response: I recognize this as a polynomial division problem, and I remember the long division algorithm for polynomials.
I write the dividend, $8x^3+16x^2-7x+4$, inside the long division symbol, and the divisor, $2x+5$, outside.
I ask myself, what do I need to multiply $2x+5$ by to get the first term of the dividend, $8x^3$?
I see that it is $4x^2$.
I write $4x^2$ above the long division symbol, and I multiply it by $2x+5$ to get $8x^3+20x^2$.
I subtract $8x^3+20x^2$ from the dividend, and I bring down the next term, $-7x$.
I repeat the process: what do I need to multiply $2x+5$ by to get the first term of the new dividend, $-4x^2-7x$?
I see that it is $-2x$.
I write $-2x$ above the long division symbol, and I multiply it by $2x+5$ to get $-4x^2-10x$.
I subtract $-4x^2-10x$ from the new dividend, and I bring down the last term, $4$.
I repeat the process one more time: what do I need to multiply $2x+5$ by to get the first term of the final dividend, $3x+4$?
I see that it is $\frac{3}{2}$.
I write $\frac{3}{2}$ above the long division symbol, and I multiply it by $2x+5$ to get $3x+\frac{15}{2}$.
I subtract $3x+\frac{15}{2}$ from the final dividend, and I get a remainder of $-\frac{7}{2}$.
I write the remainder over the divisor as a fraction, and I add it to the quotient.
I have completed the polynomial division.