Introductory Algebra for College Students (7th Edition)

5x$^4$-3x$^2$-x
Divide the polynomial by the monomial by separating the polynomial into individual terms and dividing each one by the monomial. Then cancel out common factors of the coefficients and subtract the powers of the variables to simplify. $\frac{25x^7-15x^5-5x^4}{5x^3}$=$\frac{25x^7}{5x^3}$-$\frac{15x^5}{5x^3}$-$\frac{5x^4}{5x^3}$=5x$^{(7-3)}$-3x$^{(5-3)}$-1x$^{(4-3)}$=5x$^4$-3x$^2$-x Check the answer. 5x$^3$(5x$^4$-3x$^2$-x)=25x$^{(3+4)}$-15x$^{(3+2)}$-5x$^{(3+1)}$=25x$^7$-15x$^5$-5x$^4$