 0 + 1/4*n**5 + 0*n**2 + 15*n + y*n**3. Factor u(i).
5*i*(i + 1)*(i + 4)
Factor 31250000/3 + 500*g**2 + 125000*g + 2/3*g**3.
2*(g + 250)**3/3
Let n(y) be the third derivative of -5*y**8/336 + 53*y**7/42 - 225*y**6/8 - 243*y**5/4 - 615*y**2 + 2. What is s in n(s) = 0?
-1, 0, 27
Let h(c) be the first derivative of 5*c**4/4 + 115*c**3/3 + 155*c**2 + 200*c + 488. Determine y, given that h(y) = 0.
-20, -2, -1
Let p(t) = -9*t**3 + t. Let k = 30 + -31. Let l be p(k). Factor 4 + g**2 + 0 + 7*g**2 + l*g - 4*g**2.
4*(g + 1)**2
Let m(t) = 3*t**3 - 13*t**2 - 10*t + 5. Let c be m(5). Suppose -24*y**3 - 16*y**4 + 144*y**2 - 25*y**c - 108*y + 13*y**5 + 16*y**5 = 0. What is y?
-3, 0, 1, 3
Let o = -985 + 976. Let h be (-37)/o + 144/(-48). Factor -8/9*p**3 + h*p**2 + 2/9*p**4 - 4/9*p + 0.
2*p*(p - 2)*(p - 1)**2/9
Let w be 1/5*-2 + (-2481)/(-15). Factor -75*z**4 - 857*z**3 - 5*z**4 + 657*z**3 - w*z**2 - 5 - 50*z.
-5*(z + 1)**2*(4*z + 1)**2
Let t be ((-11)/22)/(2/(-20)). Let r(l) = l**3 + 7*l**2 - 2*l - 3. Let d(j) = 2*j**3 + 13*j**2 - 2*j - 5. Let y(v) = t*r(v) - 3*d(v). Factor y(n).
-n*(n + 2)**2
Suppose -2*a = -34 + 36, -m - 3*a + 8 = 0. Suppose -2*v = -4*w - 4, m + 4 = 3*w. Find o, given that -3/2*o**2 + 21/2*o + v = 0.
-1, 8
Factor 142*o**4 + 8604*o**2 + 5*o**4 + 21546*o - 53*o**4 + 2*o**5 + 19494 + 1460*o**3.
2*(o + 3)**3*(o + 19)**2
Factor 2217*a + 4915089/2 + 1/2*a**2.
(a + 2217)**2/2
Let y(m) be the first derivative of 6*m + 1/3*m**2 - 28 - 7/18*m**3 + 1/12*m**4. Let z(w) be the first derivative of y(w). Determine u so that z(u) = 0.
1/3, 2
Let a = -35 + 23. Let y = a - -17. Factor 8*x - 9*x**3 - 4 - 4*x + y*x**3 + 3*x**2 + x**4.
(x - 2)**2*(x - 1)*(x + 1)
Let a be 117/(-195) - 31/(-35). Let i be 6*8/21 - 58/203. Determine c, given that 2/7 - a*c**i + 2/7*c**3 - 2/7*c = 0.
-1, 1
Let c = -33 - -40. Suppose -5*p = 5*r - 5, 5*p = -r + 6 + c. Solve -30*b**2 + 50*b - 45*b**p - 40 + 37*b + 13*b = 0 for b.
-2, 2/3
Let f(j) = -252 - 1584*j + 16*j**3 - 311 + 204*j**3 + 528*j**2 - 113. Let i(l) = -40*l**3 - 96*l**2 + 288*l + 123. Let s(n) = -5*f(n) - 28*i(n). Factor s(k).
4*(k - 2)*(k + 4)*(5*k + 2)
Solve -52/5*q - 54/5*q**2 + 0 - 2/5*q**3 = 0.
-26, -1, 0
Let z(c) be the third derivative of c**7/630 - 421*c**6/180 + 58799*c**5/60 + 88831*c**4/18 + 89042*c**3/9 - 304*c**2 - 6*c. Factor z(i).
(i - 422)**2*(i + 1)**2/3
Let o = 433530/247 - 33328/19. Let -o*g**3 - 48/13*g**4 - 8/13*g + 0 + 48/13*g**2 + 22/13*g**5 = 0. What is g?
-1, 0, 2/11, 1, 2
Let h(m) be the third derivative of -m**5/60 - m**4/24 + m**3/6 + 1185*m**2. Let j = -2 + 1. Let y(d) = 18*d**2 - 3. Let z(q) = j*y(q) - 15*h(q). Factor z(f).
-3*(f - 4)*(f - 1)
Let m be 178 + -168 - (-510)/(-52). Let a(c) be the first derivative of m*c**4 - 9 + 4/13*c - 5/13*c**2 + 2/39*c**3 - 6/65*c**5. Find d, given that a(d) = 0.
-1, 2/3, 1
Factor 179776*c**2 - 4236*c**4 + c**5 - 4*c**5 + 13*c**5 + 511773*c**3 - 69769*c**3 + 5740*c**3.
2*c**2*(c - 212)**2*(5*c + 2)
Let t = -934 + 937. Suppose 0*x = 4*x - 160. Determine z so that 5*z**4 + 47 - 30*z + 45 + 30*z**t + x*z**2 - 137 = 0.
-3, -1, 1
Let y(p) be the second derivative of 27*p**4/14 + 354*p**3/7 + 3481*p**2/7 + 487*p + 1. Factor y(f).
2*(9*f + 59)**2/7
Let h(t) be the first derivative of -2*t**3/3 - 1594*t**2 - 1270418*t - 7738. Factor h(w).
-2*(w + 797)**2
Suppose 32/3*k - 32/3*k**3 + 4/3*k**2 + 0 - 4/3*k**4 = 0. Calculate k.
-8, -1, 0, 1
Determine s so that -3806*s**2 - 12*s**5 + 11*s**5 + 962479 - 570*s**3 - 974458 - 39*s**4 - 11253*s = 0.
-11, -3
Let y be (-836)/(-28842)*(-23)/(-6). Suppose 4*t - 10 - 6 = 0. Solve -1/9*g**t + 0 + 0*g**3 + y*g**2 + 0*g = 0 for g.
-1, 0, 1
Suppose -7 + 19/2*x - 7/2*x**3 + 3/2*x**2 - 1/2*x**4 = 0. What is x?
-7, -2, 1
Let a(z) be the first derivative of 6/7*z**2 + 8/7*z**4 - 69 + 2/21*z**6 - 4/3*z**3 - 2/7*z - 18/35*z**5. Factor a(r).
2*(r - 1)**4*(2*r - 1)/7
Let p(s) = 3*s**2 - 4. Let z(l) = -14*l**2 + 37*l + 20. Let u(c) = -5*p(c) - z(c). Factor u(a).
-a*(a + 37)
Suppose -3/5*l**2 + 354/5 + 351/5*l = 0. Calculate l.
-1, 118
Let g(c) be the first derivative of -1/3*c**4 + 234 - 20*c**3 - 1936/3*c - 352*c**2. Factor g(f).
-4*(f + 1)*(f + 22)**2/3
Let z = 481/10446 - -210/1741. Find h such that -7/6*h + 4/3 - z*h**2 = 0.
-8, 1
Let d(a) = -8*a**3 - 1405*a**2 - 62450*a - 23232. Let z(g) = -g**2 - 5*g. Let l(x) = d(x) + 6*z(x). What is t in l(t) = 0?
-88, -3/8
Let x be 20/3 - (-50)/30*60/(-25). Factor -2/3 + x*r**2 + 2*r.
2*(r + 1)*(4*r - 1)/3
Let k = 5142127/5 + -1028425. Suppose 0 + 0*a**2 + k*a**5 - 2*a**3 + 0*a**4 + 8/5*a = 0. Calculate a.
-2, -1, 0, 1, 2
Let v(f) be the second derivative of f**5/5 + 23*f**4/3 + 68*f**3 - 3411*f. Suppose v(g) = 0. What is g?
-17, -6, 0
Suppose -26*w - 129 - 341 = -120*w. Let l(v) be the first derivative of 13 + 5/3*v**3 - v**w - 5/2*v**2 + 5/4*v**4 + 0*v. Factor l(y).
-5*y*(y - 1)**2*(y + 1)
Let u = 2048135 + -2048131. Factor 0 - 2/7*g**u + 2/7*g**2 + 10/7*g**3 - 10/7*g.
-2*g*(g - 5)*(g - 1)*(g + 1)/7
Let o(z) be the second derivative of -z**6/10 + 357*z**5/20 + z**4/4 - 119*z**3/2 - 45*z + 87. Factor o(x).
-3*x*(x - 119)*(x - 1)*(x + 1)
Let l = 3 + 0. Suppose 5*i - 684 = l*i. Factor 343*t**2 + 25 - t - i*t**2 + 11*t.
(t + 5)**2
Let u(v) be the third derivative of -500*v**4 - 1/4*v**6 + 15*v**5 + 1/560*v**7 + 0*v + 0 + 10000*v**3 + 44*v**2. Factor u(g).
3*(g - 20)**4/8
Solve 832/3*x + 1024 + 1/3*x**3 - 61/3*x**2 = 0.
-3, 32
Let s = -435874/5 + 87176. Factor -6/5*b**3 + 1/5*b**4 + 4/5*b**2 - 1 + s*b.
(b - 5)*(b - 1)**2*(b + 1)/5
Let b(g) = 34*g**3 + 6*g**2 + 206*g - 1074. Let h(v) = 43*v**3 + 6*v**2 + 205*v - 1073. Let u(y) = -5*b(y) + 4*h(y). Factor u(n).
2*(n - 7)**2*(n + 11)
Let p(t) be the third derivative of t**6/30 + 452*t**5/15 + 449*t**4/6 - 1804*t**3/3 - 665*t**2. Factor p(j).
4*(j - 1)*(j + 2)*(j + 451)
Suppose -282*w - 2400 = -287*w. Solve 10200 - 2579 - 1142 - w*t + 4*t**2 + 7921 = 0.
60
Let n be (-25)/(-2) - 12/24. Let o be 3*((-140)/n)/(-7). Factor -4*s**2 + 3*s**5 - o*s**5 + 57*s**3 + 4*s**4 - 57*s**3 + 2*s.
-2*s*(s - 1)**3*(s + 1)
Let h(n) be the third derivative of -13*n**7/168 + 29*n**6/80 - 13*n**5/48 - n**4/2 + n**3/6 - 2013*n**2. Solve h(f) = 0 for f.
-2/5, 1/13, 1, 2
Suppose -24*s + 473 = -67*s. Let t be (2/23)/(s + 45/4). Suppose -2/23*w**2 - 8/23 + t*w = 0. What is w?
2
Determine o so that 3/4*o**3 + 435 + 217*o - 2611/4*o**2 = 0.
-2/3, 1, 870
Let h = -1126/3 + 7888/21. Let l(x) = -x**2 - 5*x + 8. Let r be l(-6). Determine z so that -22/7*z**r - 50/7 + 10*z + h*z**3 = 0.
1, 5
Let h(y) be the second derivative of y**5/90 + 11*y**4/27 + 19*y**3/9 + 2797*y. Solve h(q) = 0.
-19, -3, 0
Suppose 3337*g + 25227044*g**2 + 9610000 - 25227043*g**2 + 2863*g = 0. What is g?
-3100
Suppose -3365*y + 17765 - 940 = 0. Factor 4*g**3 - 14*g - 2/3*g**y - 2*g**4 + 6 + 20/3*g**2.
-2*(g - 1)**3*(g + 3)**2/3
Let w be -28 + 26 + 10 + -6. Let c(z) be the first derivative of -9 + 3/2*z**w + 2*z + 1/3*z**3. Factor c(j).
(j + 1)*(j + 2)
Let w = 53319 - 53316. Find x such that -2 + 3/2*x**2 + 0*x + 1/2*x**w = 0.
-2, 1
Let k(r) be the first derivative of -4*r**3/3 - 3440*r**2 + 13776*r - 2095. Let k(o) = 0. What is o?
-1722, 2
Let d(k) be the first derivative of 72/11*k - 53 + 60/11*k**2 + 50/33*k**3. Determine c so that d(c) = 0.
-6/5
Let h(k) = -k**3 + 7*k**2 - 5*k - 3. Let g be h(6). Factor 19*a + 6*a - g*a**2 - 2*a - 2*a - 18.
-3*(a - 6)*(a - 1)
Let t(i) = -24*i + 22*i - 206*i**2 + 162*i**2. Let s(y) = y**2 - y. Let w(o) = 6*s(o) - t(o). Let w(z) = 0. Calculate z.
0, 2/25
Let b(u) = 15*u**3 + 343*u**2 + 26420*u + 254130. Let o(a) = a**3 + 2*a**2 - 2*a - 1. Let y(f) = -b(f) + 14*o(f). Suppose y(k) = 0. Calculate k.
-152, -11
Let v(m) = -7*m**4 - 85*m**3 + 267*m**2 - 267*m + 92. Let i(s) = -3*s**4 + s**3 + s + 1. Let h(n) = -6*i(n) + 3*v(n). Factor h(q).
-3*(q - 1)**3*(q + 90)
Let f(a) be the first derivative of 3/35*a**5 - 17/7*a**3 + 0*a + 27/14*a**2 + 3/4*a**4 - 168. What is v in f(v) = 0?
-9, 0, 1
Let x(k) be the first derivative of -2*k**3/9 + 46*k**2 + 560*k/3 + 3552. Factor x(i).
-2*(i - 140)*(i + 2)/3
Let w(m) = -20*m**3 - 235*m**2 + 6053*m + 12952. Let j(v) = 11*v**3 + 118*v**2 - 3027*v - 6474. Let k(l) = 11*j(l) + 6*w(l). Let k(s) = 0. Calculate s.
-2, 57
Let k(b) be the second derivative 