Dividing Polynomials Divide. 1) (2n^3+5n^2+n)div 6n^2 2) (27r^4+27r^3+9r^2)div 9r 3) (4p^3+2p^2+3p)div 4p 4) (8b^3+4b^2+4b)div 4b^2 5) (50b^3+5b^2+40b)div 10b 6) (27b^4+b^3+9b^2)div 9b 7) (12x^4+4x^3+4x^2)div 4x 8) (20m^3+2m^2+m)div 4m^3 9) (36n^3+36n^2+n)div 9n 10) (5x^3+18x^2+4x)div 9x Simplify each difference. 11) (6+7r)-(3+6r) 13) (7-4n-2n^2)-(4n-6-2n^2) 15) (2m^4+5m^3+5)-(3m^3-7+8m^4) Find each product. 17) (4m-3)(8m+1) 19) (5n-4)(4n^2+4n-1) 12) (7+p^2)-(p^2-2) 14) (5x^4+5x^3+2x)-(2x^4-8x^3+5x) 16) (6r^2-2r^3+6r)-(8r^2+7r-5r^3) 18) (7x+5)(4x-4) 20) (n-6)(n^2+7n+4)

1) $(2n^{3}+5n^{2}+n)\div 6n^{2}$<br />To divide this expression, we can divide each term in the numerator by the denominator:<br />$\frac{2n^{3}}{6n^{2}} + \frac{5n^{2}}{6n^{2}} + \frac{n}{6n^{2}}$<br />Simplifying each term, we get:<br />$\frac{1}{3}n + \frac{5}{6} + \frac{1}{6n^{2}}$<br /><br />2) $(27r^{4}+27r^{3}+9r^{2})\div 9r$<br />Dividing each term in the numerator by the denominator:<br />$\frac{27r^{4}}{9r} + \frac{27r^{3}}{9r} + \frac{9r^{2}}{9r}$<br />Simplifying each term, we get:<br />$3r^{3} + 3r^{2} + r$<br /><br />3) $(4p^{3}+2p^{2}+3p)\div 4p$<br />Dividing each term in the numerator by the denominator:<br />$\frac{4p^{3}}{4p} + \frac{2p^{2}}{4p} + \frac{3p}{4p}$<br />Simplifying each term, we get:<br />$p^{2} + \frac{1}{2}p + \frac{3}{4}$<br /><br />4) $(8b^{3}+4b^{2}+4b)\div 4b^{2}$<br />Dividing each term in the numerator by the denominator:<br />$\frac{8b^{3}}{4b^{2}} + \frac{4b^{2}}{4b^{2}} + \frac{4b}{4b^{2}}$<br />Simplifying each term, we get:<br />$2b + 1 + \frac{1}{b}$<br /><br />5) $(50b^{3}+5b^{2}+40b)\div 10b$<br />Dividing each term in the numerator by the denominator:<br />$\frac{50b^{3}}{10b} + \frac{5b^{2}}{10b} + \frac{40b}{10b}$<br />Simplifying each term, we get:<br />$5b^{2} + \frac{1}{2}b + 4$<br /><br />6) $(27b^{4}+b^{3}+9b^{2})\div 9b$<br />Dividing each term in the numerator by the denominator:<br />$\frac{27b^{4}}{9b} + \frac{b^{3}}{9b} + \frac{9b^{2}}{9b}$<br />Simplifying each term, we get:<br />$3b^{3} + \frac{1}{9}b + 1$<br /><br />7) $(12x^{4}+4x^{3}+4x^{2})\div 4x$<br />Dividing each term in the numerator by the denominator:<br />$\frac{12x^{4}}{4x} + \frac{4x^{3}}{4x} + \frac{4x^{2}}{4x}$<br />Simplifying each term, we get:<br />$3x^{3} + x^{2} + x$<br /><br />8) $(20m^{3}+2m^{2}+m)\div 4m^{3}$<br />Dividing each term in the numerator by the denominator:<br />$\frac{20m^{3}}{4m^{3}} + \frac{2m^{2}}{4m^{3}} + \frac{m}{4m^{3}}$<br />Simplifying each term, we get:<br />$5 + \frac{1}{2m} + \frac{1}{4m^{2}}$<br /><br />9) $(36n^{3}+36n^{2}+n)\div 9n$<br />Dividing each term in the numerator by the denominator:<br />$\frac{36n^{3}}{9n} + \frac{36n^{2}}{9n} + \frac{n}{9n}$<br />Simplifying each term, we get:<br />$4n^{2} + 4n + \frac{1}{9}$<br /><br />10) $(5x^{3}+18x^{2}+4x)\div 9x$<br />Dividing each term in the numerator by the denominator:<br />$\frac{5x^{3}}{9x} + \frac{18x^{2}}{9x} + \frac{4x}{9x}$<br />Simplifying each term, we get:<br />$\frac{5}{9}x^{2} + 2x + \frac