/3
Let c be (-870)/(-75) - (-9 + 17 + -10 + (0 - 4)). What is h in c*h**2 - 20*h**3 - 34/5*h - 2*h**5 + 4/5 + 52/5*h**4 = 0?
1/5, 1, 2
Let s(g) be the second derivative of g**6/30 - 7*g**5/5 + 137*g**4/12 - 55*g**3/3 + 2*g - 38. Solve s(j) = 0 for j.
0, 1, 5, 22
Let f(g) be the first derivative of -7*g**4/30 + 103*g**3/15 + 6*g**2 + 113*g - 152. Let n(c) be the first derivative of f(c). Factor n(o).
-2*(o - 15)*(7*o + 2)/5
Find s such that s**2 - 4*s**2 - 55*s**4 - 175*s + 13*s**2 + s**2 + 175*s**3 + 30 + 14*s**2 = 0.
-1, 2/11, 1, 3
Suppose -2*v + 5*t = -15, -2*v = 4*t + 768 - 756. What is a in v - 1/8*a**5 + 0*a - 1/4*a**4 + 3/4*a**2 + 5/8*a**3 = 0?
-3, -1, 0, 2
Let v(c) = 5*c - 6. Let k be v(6). Suppose 0 = -13*a + 9*a + k. Solve s + 5*s**2 + a*s - 6*s + 9*s = 0.
-2, 0
Let p(z) = -59*z**2 - 6139*z - 4706312. Let r(x) = -276*x**2 - 30694*x - 23531560. Let y(q) = -28*p(q) + 6*r(q). Factor y(j).
-4*(j + 1534)**2
Suppose -5*p + 2*p + 126 = 0. Let d = p + -35. Determine o so that -5 - 8*o**3 + 4*o**4 - 2 + d + 4*o**2 = 0.
0, 1
Determine g, given that -23/2*g**3 + 119/4*g - 1/4*g**5 + 49/2 - 10*g**2 + 7/2*g**4 = 0.
-1, 2, 7
Let -61/5 - 184/5*h - 1/5*h**4 - 186/5*h**2 - 64/5*h**3 = 0. What is h?
-61, -1
Let j(i) be the third derivative of -i**7/56 - 71*i**6/480 + 8*i**5/5 - 19*i**4/24 - 4*i**3 + 183*i**2 - 3*i. Solve j(t) = 0.
-8, -2/5, 2/3, 3
Let i(c) = 7*c**3 + 169*c**2 - 30*c - 102. Let b(z) = z**3 + 33*z**2 - 6*z - 20. Let n(f) = 11*b(f) - 2*i(f). Factor n(x).
-(x - 8)*(x - 1)*(3*x + 2)
Let d(q) = 45*q**3 + 1239*q**2 + 24930*q + 115841. Let i(b) = -8*b**3 - 248*b**2 - 4986*b - 23168. Let y(v) = 2*d(v) + 11*i(v). Factor y(z).
2*(z - 143)*(z + 9)**2
Let t = -79709/6 + 13285. Let w(m) be the third derivative of -1/4*m**4 + 2/3*m**3 + 11*m**2 + 0 + 0*m - t*m**5. Factor w(z).
-2*(z + 1)*(5*z - 2)
Let b(r) be the second derivative of 1/30*r**6 - 17*r + 0*r**2 + 0*r**3 + 0*r**4 + 0 + 0*r**5. What is u in b(u) = 0?
0
Let q = -20121 - -181093/9. Let a(f) be the first derivative of 30 - q*f**3 - 10/3*f**2 - 8*f. Factor a(j).
-4*(j + 2)*(j + 3)/3
Let v(q) = 2*q**2 + 678*q. Let h(x) = 2*x**2 + 640*x. Let j(t) = 5*h(t) - 4*v(t). Let j(p) = 0. Calculate p.
-244, 0
Let u = -71 + 73. Suppose -3*h = 2*h - 2*x - 26, h = 3*x + 13. Determine c so that 9*c**2 - 6*c**3 - 8*c + 3*c - c + u*c + c**h = 0.
0, 1, 4
Let c(j) be the third derivative of j**6/40 + 9*j**5/10 + 29*j**4/8 - 24*j**3 - 4649*j**2. Factor c(n).
3*(n - 1)*(n + 3)*(n + 16)
Let p be ((-216)/(-45))/(297/110) - 4/(-18). Factor 2/3*b**p - 124/3*b + 1922/3.
2*(b - 31)**2/3
Factor -1/11*u**2 - 4112784/11 + 4056/11*u.
-(u - 2028)**2/11
Let o(r) be the first derivative of -r**5/100 + r**4/30 - r**3/30 + 44*r - 65. Let u(d) be the first derivative of o(d). Solve u(a) = 0.
0, 1
Let h be 49/((-674)/674 + (78/4)/3). Find z such that -140/11*z - 50/11*z**2 - h = 0.
-7/5
Let q be (5/(-1))/((-2)/((-24)/3)). Let v(u) = u**3 + 25*u**2 + 100*u + 4. Let b be v(q). Find s such that -1/3*s**2 - s**3 - 1/3*s**b + 2/3 + s = 0.
-2, -1, 1
Factor -69309*c + 18237*c - 908*c**2 + 350*c**3 + 51984 - 354*c**3.
-4*(c - 1)*(c + 114)**2
Suppose 5*k + 5 = -5*b, 4*k + 5*b - 2 = -9. Find q such that -10*q + 2*q**2 + q**k + 24*q + 19*q - 4*q**2 = 0.
0, 33
Let w(m) be the second derivative of 1/3*m**4 - 34*m - 12*m**3 + 34*m**2 + 4. Factor w(f).
4*(f - 17)*(f - 1)
Let u(f) be the third derivative of -f**5/60 + 31*f**4/8 + 95*f**3/3 - 1665*f**2. Factor u(o).
-(o - 95)*(o + 2)
Let x(z) be the first derivative of -z**4 + 548*z**3/3 + 840*z**2 + 1674. Let x(f) = 0. Calculate f.
-3, 0, 140
Let 0 - 339/4*m - 3/4*m**3 + 171/2*m**2 = 0. Calculate m.
0, 1, 113
Let g be 48654/1134 - (38/42 + -1). Suppose -26*u - 22*u = -g*u. Suppose 0*f - 1/2*f**2 + 1/4*f**3 - 1/4*f**5 + u + 1/2*f**4 = 0. Calculate f.
-1, 0, 1, 2
Let h(x) be the first derivative of -x**6/18 + 5*x**4/36 + 89*x + 39. Let d(y) be the first derivative of h(y). Determine f, given that d(f) = 0.
-1, 0, 1
Let h be 2 - 2 - (-12688)/32452 - (-2)/(-7). Factor -h*a**3 - 66/19 - 14/19*a**2 + 82/19*a.
-2*(a - 3)*(a - 1)*(a + 11)/19
Suppose -469864 + 5*p**2 - 829278 + 4759206 + 2344391 - 13790*p + 3703750 = 0. What is p?
1379
Let d(k) be the second derivative of k**5/50 + 13*k**4/30 + 56*k**3/15 + 16*k**2 - 4*k + 10. Factor d(w).
2*(w + 4)**2*(w + 5)/5
Let z = -1526/3 + 1528/3. Let l(n) be the third derivative of 1/60*n**6 + 0*n - 1/12*n**4 + 0 + 6*n**2 - z*n**3 + 1/15*n**5. Factor l(p).
2*(p - 1)*(p + 1)*(p + 2)
Let p(z) be the first derivative of -525/4*z**2 - 5/12*z**6 + 90 - 3*z**5 + 125*z + 25/4*z**4 + 130/3*z**3. Determine w, given that p(w) = 0.
-5, 1, 2
Let d(f) be the second derivative of -f**5/180 + f**4/18 + 2*f**3/3 - 87*f**2/2 - f + 36. Let p(h) be the first derivative of d(h). Factor p(v).
-(v - 6)*(v + 2)/3
Let v(f) = 2*f**2 - f + 8. Let q(d) = 14*d**2 - 994*d + 122066. Let m(c) = -q(c) + 6*v(c). Let m(t) = 0. Calculate t.
247
Factor 0*w + 2/3*w**4 - 18*w**2 + 0 - 52/3*w**3.
2*w**2*(w - 27)*(w + 1)/3
Let a(j) be the second derivative of -j**5/200 - 3*j**4/40 + j**3/60 + 9*j**2/20 + 124*j - 6. Factor a(q).
-(q - 1)*(q + 1)*(q + 9)/10
Let u(o) = 23*o**3 - 38*o**2 - 441*o + 12. Let a(i) = 6*i**3 + i**2 + 3. Let j(z) = -8*a(z) + 2*u(z). Solve j(q) = 0 for q.
-21, 0
Let c = -1699 - -5101/3. Let y = 407/9 - 45. Factor -2/9*f + c - 4/3*f**2 + y*f**3.
2*(f - 6)*(f - 1)*(f + 1)/9
Let f(y) be the third derivative of -y**5/630 - 851*y**4/252 - 850*y**3/63 + 21*y**2 - 37. Solve f(i) = 0.
-850, -1
Let t(c) = -c**2 + 12*c + 14. Let y be t(7). Let w = -45 + y. Find f such that w*f**2 + 45*f + 180 + f**2 + 15*f = 0.
-6
Let b(v) be the second derivative of 37*v - 784/17*v**2 - 1/102*v**4 - 56/51*v**3 + 0. Suppose b(t) = 0. Calculate t.
-28
Let u = 379 + -371. Suppose u = 22*n - 18*n. Suppose -1/4*m**n + 1/4*m + 1/2 = 0. What is m?
-1, 2
Let s(t) = 202 - 386 + 80*t**2 + 1930*t - 1795*t**2 - 361. Let p(j) = -245*j**2 + 276*j - 78. Let d(a) = -15*p(a) + 2*s(a). Determine h so that d(h) = 0.
4/7
Let h be (((-25800)/(-70))/10)/(6/21) + -9. Let 16/3*q**4 - 48*q**3 + 100/3 + h*q + 244/3*q**2 = 0. What is q?
-1/2, 5
Factor -341/2*w**2 - 3/2*w**3 - 116 + 405*w.
-(w - 2)*(w + 116)*(3*w - 1)/2
Let j(m) be the second derivative of -m**5/6 - 77*m**4/18 - 3*m**3 + 15*m**2 + 7069*m. Determine b so that j(b) = 0.
-15, -1, 3/5
Determine n, given that -4/3*n**3 + 16/3*n + 0 + 2/9*n**4 - 8/9*n**2 = 0.
-2, 0, 2, 6
Factor -3/5*u**3 - 384/5*u + 672/5 + 66/5*u**2.
-3*(u - 14)*(u - 4)**2/5
Let v(i) be the first derivative of -35*i**3/6 + 18245*i**2/4 - 2605*i + 1313. Factor v(n).
-5*(n - 521)*(7*n - 2)/2
Find m, given that 2/7*m**4 + 0*m + 2/7*m**5 + 0*m**2 - 4/7*m**3 + 0 = 0.
-2, 0, 1
Let q be (10/(-15))/((-12)/18). Let w(n) = -11*n**2 - 11*n + 60. Let y(h) = -h**2 - h. Let c(g) = q*w(g) - 6*y(g). Determine a, given that c(a) = 0.
-4, 3
Let b(g) be the third derivative of -29 + 1/12*g**4 + 0*g - 1/20*g**5 - 2*g**2 + 0*g**3 + 1/210*g**7 + 0*g**6. What is a in b(a) = 0?
-2, 0, 1
Let i(v) be the first derivative of v**4/20 - 4*v**3/3 + 18*v**2/5 - 645. Factor i(r).
r*(r - 18)*(r - 2)/5
Solve 48*x - 3352 - 3*x**5 + x**5 + 3352 - 6*x**4 + 56*x**2 + 12*x**3 = 0 for x.
-2, 0, 3
Let i(l) be the first derivative of -78 - l**3 + 1/20*l**4 + 24/5*l**2 - 44/5*l. Factor i(r).
(r - 11)*(r - 2)**2/5
Find m such that -5*m**4 - 369*m**3 + 125*m**4 + 205*m**3 - 1272*m**2 + 4*m**5 - 992*m = 0.
-31, -2, -1, 0, 4
Let r = 1070627/2 + -535295. Factor r*x + 6 - 1/2*x**5 + 19*x**2 - x**4 + 6*x**3.
-(x - 4)*(x + 1)**3*(x + 3)/2
Let j(s) be the third derivative of s**7/42 - 16*s**6/3 + 661*s**5/2 + 5200*s**4/3 + 21125*s**3/6 - 1082*s**2. Factor j(h).
5*(h - 65)**2*(h + 1)**2
Let y be ((-9)/12)/((15/(-20))/(152/684)). Solve 8/9 - 2/9*j**3 - y*j**2 + 8/9*j = 0 for j.
-2, -1, 2
Let c(q) be the first derivative of q**6/10 - 93*q**5/25 + 9*q**4/2 + 6921. Solve c(f) = 0.
0, 1, 30
Let c(k) = -34*k**2 - 2516*k + 6866. Let a(f) = 11*f**2 + 834*f - 2289. Let w(b) = 19*a(b) + 6*c(b). Factor w(n).
5*(n - 3)*(n + 153)
Let i(k) = 560*k**2 - 154*k - 298. Let v(r) = -93*r**2 + r - 1. Let h(w) = -i(w) - 6*v(w). Suppose h(u) = 0. Calculate u.
-2, 76
Factor 85/3 + 169/6*j - 1/6*j**2.
-(j - 170)*(j + 1)/6
Determine o so that -16/3 + 1/3*o**3 - 22/3*o - 5/3*o**