
-3, 2/7
Suppose -2*g - 16 = -3*n, -3*n - 5*g + 2 = -0*n. Factor -22*o**4 - 455*o**2 + 600*o + 75*o**n + 23*o**4 - 150*o**3 - 180 + 49*o**4.
5*(o - 2)*(o + 2)*(5*o - 3)**2
Suppose 2704 + 32*o**2 + 2*o**3 - 41*o**2 + 1144*o - 44*o**2 - 47*o**2 = 0. Calculate o.
-2, 26
Let o = -33/551 - -947/6612. Let l(j) be the first derivative of o*j**3 + j - 17 - 5/8*j**2. Solve l(c) = 0 for c.
1, 4
Let t be (-2985)/(-796) - (-12)/(-4). Let z(j) = j - 5. Let g be z(6). Find i such that 1/4*i**2 - t*i**3 + 2*i + g = 0.
-1, -2/3, 2
Let p be (-1)/(-2)*8/(2/1). Let s(c) be the second derivative of 1/30*c**4 - 1/50*c**5 + 0 + 1/3*c**3 + 9*c + 3/5*c**p. Determine h so that s(h) = 0.
-1, 3
Let v(z) be the first derivative of -z**6/10 - 27*z**5/10 - 17*z**4/4 + 106*z - 204. Let u(h) be the first derivative of v(h). Factor u(q).
-3*q**2*(q + 1)*(q + 17)
Let l(z) be the third derivative of z**5/270 - 55*z**4/54 + 3025*z**3/27 - z**2 - 1303*z. Solve l(i) = 0.
55
Let l(z) be the second derivative of -z**6/180 + z**5/15 - 5*z**4/72 - 7*z**3/18 - 509*z - 1. Solve l(k) = 0.
-1, 0, 2, 7
Factor -2/15*n**2 + 40/3 + 66/5*n.
-2*(n - 100)*(n + 1)/15
Let i be ((-1)/40)/(1 - (-441)/105). Let z = 63/208 - i. Find s, given that 2/13*s**2 - z*s + 2/13*s**3 + 0 = 0.
-2, 0, 1
Let r(j) = -j**3 + 10*j**2 - 15*j - 3. Let c be r(8). What is s in -2*s**c + 87*s**2 - 18*s**3 - 10*s**4 + 2*s**3 - 95*s**2 = 0?
-2, -1, 0
Let k be (32/(-6) - -5)*(288/4)/(-6). Let x(w) be the second derivative of -3*w**2 - 1/4*w**k - w + 3/2*w**3 + 0. Factor x(p).
-3*(p - 2)*(p - 1)
Let c(w) = 19*w**4 - 41*w**3 - 70*w**2 + 217*w - 115. Let x(h) = -16*h**4 + 40*h**3 + 68*h**2 - 216*h + 116. Let q(a) = -4*c(a) - 5*x(a). What is t in q(t) = 0?
-3, 1, 10
Let i be (-2)/408*-467 - 60/1530. Factor 9/4 + 15/2*k**3 + 23/2*k**2 + i*k**4 + 1/4*k**5 + 33/4*k.
(k + 1)**3*(k + 3)**2/4
Let s(c) be the first derivative of 4*c**5 + 12*c**4 + 4*c**3/3 - 12*c**2 + 898. Solve s(d) = 0 for d.
-2, -1, 0, 3/5
Let r(a) be the first derivative of a**6/8 + 117*a**5/5 + 1521*a**4 + 35152*a**3 + 698. What is v in r(v) = 0?
-52, 0
Let 705/2*g**2 - 20532*g - 3/2*g**3 - 20886 = 0. What is g?
-1, 118
Let m(z) = 2*z**2 - 48*z - 390. Let u(y) = 5*y**2 - 146*y - 1170. Let t(d) = -11*m(d) + 4*u(d). Factor t(r).
-2*(r + 13)*(r + 15)
Suppose 91*g**4 - 333*g**2 + 33*g**3 + 1296*g - 42*g**4 - 51*g**2 - 50*g**4 + 24*g**2 = 0. Calculate g.
0, 9, 12
Let j(g) be the first derivative of 3*g**5/160 + g**4/32 - g**3/4 - 3*g**2/4 - 168*g + 28. Let w(n) be the first derivative of j(n). Factor w(r).
3*(r - 2)*(r + 1)*(r + 2)/8
Let z(w) be the second derivative of w**4/42 + 104*w**3/21 - 15*w**2 - 7*w - 389. Solve z(o) = 0 for o.
-105, 1
Let x be 2/(-10)*(206 - 291) + -10 - 4. Factor 16/5*d**2 + 38/5*d + 12/5 - 2*d**x.
-2*(d - 3)*(d + 1)*(5*d + 2)/5
Let j(z) = -3*z**3 + 65*z**2 + 249*z + 78. Let d(v) = 3*v**3 - 67*v**2 - 255*v - 79. Let h(x) = 3*d(x) + 2*j(x). Factor h(t).
(t - 27)*(t + 3)*(3*t + 1)
Let 165/8 + 3/8*x**2 - 62*x = 0. Calculate x.
1/3, 165
Suppose 237*z - 248*z = -484. Find y such that -12 + z*y - 6*y**3 + 46*y - 57*y - 15*y**2 = 0.
-4, 1/2, 1
Factor 0 + 2/9*h**3 - 10/3*h**2 - 32/9*h.
2*h*(h - 16)*(h + 1)/9
Let m(v) = 2*v**2 - v**2 + v**2 - 23 + 10. Let i be m(-3). Factor -255*d**2 - 13*d + i*d + 261*d**2 + 2.
2*(d - 1)*(3*d - 1)
What is b in 1/6*b**4 + 662976*b**2 + 764410177/3*b + 1727/3*b**3 + 1524845951/6 = 0?
-1151, -1
Let y(o) = -o**2 + 12*o + 65. Let q be y(16). Let p = -611 - -1223/2. Factor -p*g**2 + q + 1/2*g.
-(g - 2)*(g + 1)/2
Let w = 13349/596655 + -2/13259. Let y(r) be the second derivative of 0*r**2 + 1/18*r**4 + 1/9*r**3 + 48*r - 1/30*r**5 + 0 - w*r**6. Solve y(l) = 0 for l.
-1, 0, 1
Let s(u) = 2*u**2 + 17*u + 70. Let q be s(-5). Suppose -10*j + q = -3*j. Suppose -1/2*i**4 - 3/4*i - 1/4*i**j + i**3 + 1/2*i**2 + 0 = 0. Calculate i.
-3, -1, 0, 1
Let h = 5641053/1645301 - 3/235043. Suppose 0*s + 2/7*s**4 + h*s**3 + 0*s**2 + 0 = 0. Calculate s.
-12, 0
Let j(h) be the first derivative of -2*h**3/3 - 17*h**2 - 83. Determine f, given that j(f) = 0.
-17, 0
Let m(i) be the first derivative of 2*i**7/105 - i**6/15 - 13*i**5/15 - 5*i**4/3 - 81*i**2 + 110. Let w(q) be the second derivative of m(q). Factor w(f).
4*f*(f - 5)*(f + 1)*(f + 2)
Let t be (-9)/(-12)*-1 - (2574/(-520) + -9). What is m in t*m - 363/5 - 3/5*m**2 = 0?
11
Factor 793*m**3 - 147*m**3 + 1032*m**2 - 649*m**3 + 2076*m.
-3*m*(m - 346)*(m + 2)
Suppose -137*w = -142*w + 10, 4*w - 8 = -2*y + 4*y. Let -4/3*o**4 + y + 1/3*o**5 + 10/3*o**2 + 8/3*o - o**3 = 0. What is o?
-1, 0, 2, 4
Let b(s) be the second derivative of 4 + 1/42*s**4 + s**2 - 8/21*s**3 + 7*s. Factor b(t).
2*(t - 7)*(t - 1)/7
Factor -939/4*b - 3/4*b**2 - 933/2.
-3*(b + 2)*(b + 311)/4
Let s be ((-2112)/80)/((6/5)/(-3)). Let z be (-3)/(8 + 1) - (-44)/s. Factor -1/3 - 2/3*a - z*a**2.
-(a + 1)**2/3
Let a(i) be the first derivative of i**8/560 + 3*i**7/140 + i**6/24 - 2*i**3/3 - 61*i**2/2 - 31. Let g(s) be the third derivative of a(s). Factor g(p).
3*p**2*(p + 1)*(p + 5)
Let 156/7*u + 0 + 2/7*u**5 - 470/7*u**2 - 162/7*u**4 + 474/7*u**3 = 0. What is u?
0, 1, 78
Let v = 14 + -10. Let i(b) = -3*b**3 + 76*b**2 - 27*b + 54. Let r be i(25). Let 30 - 30 - v*h**2 + r*h**4 = 0. What is h?
-1, 0, 1
Let t(i) = -24*i - 168. Let h be t(-7). Suppose d = 2*r + 3, h*r = d + r - 3. Factor 2/5*k - 2/5*k**d + 1/5*k**2 - 1/5.
-(k - 1)*(k + 1)*(2*k - 1)/5
Determine t, given that 2*t**3 - 51*t + 241*t + 1344*t**2 - 1296*t**2 = 0.
-19, -5, 0
Let l(s) be the first derivative of -14*s**6 + 5 - 6*s**2 + 59*s**3 - 33*s**5 - 12*s + 11 + 55353*s**4 - 55329*s**4. Let l(x) = 0. Calculate x.
-2, -1, -1/4, 2/7, 1
Let w be (28/70)/(2/20). Determine d so that -d**3 - 3*d**3 + 2*d**w + 0*d**4 + 8*d**3 = 0.
-2, 0
Suppose 26*g + 5 = 27*g. Factor 1083*i**2 + 5*i + 2*i**5 + 4*i**4 + i**4 - 1093*i**2 + 3*i**5 + g - 10*i**3.
5*(i - 1)**2*(i + 1)**3
Let j be (130 - 139)*15/(-45). Let 0*a**2 + 2/5*a**j + 24/5 - 26/5*a = 0. What is a?
-4, 1, 3
Factor 1111*f + 81*f**2 - 26*f**3 + 3600 + 42*f**2 - 2*f**4 + 1009*f - 7*f**2.
-2*(f - 9)*(f + 2)*(f + 10)**2
Let u = 372 - 366. Factor 3 + 2*y**3 - u - 6*y + 0 + 1 - 2.
2*(y - 2)*(y + 1)**2
Suppose 439*q - 840 = 112 - 74. Factor -1/4*i - 1/4*i**q + 1/4*i**3 + 1/4*i**4 + 0.
i*(i - 1)*(i + 1)**2/4
Let o(w) be the first derivative of -w**6/30 + 146*w**5/25 - 1005*w**4/4 - 1500*w**3 + 13536. Let o(i) = 0. What is i?
-4, 0, 75
Let l(q) = 2*q**5 - 2*q**4 - 70*q**3 - 262*q**2 - 252*q - 16. Let c(d) = d**4 + d**2 + 4. Let h(s) = 4*c(s) + l(s). Solve h(o) = 0.
-3, -2, 0, 7
Let o be (-4)/3*(33/(-2) - -3). Determine f, given that 3*f**2 - o*f + 20024 - 20024 = 0.
0, 6
Let u(k) = -33*k**2 - 7524*k. Let p be u(-228). Determine j, given that p + 11/4*j**4 + 0*j - 1/2*j**2 - j**5 - 5/4*j**3 = 0.
-1/4, 0, 1, 2
Find h such that -510 - 517*h + 288*h - h**2 + 320*h = 0.
6, 85
Let b(l) be the second derivative of l**7/42 + 2*l**6/15 - 7*l**5/10 - 14*l**4/3 - 59*l**3/6 - 10*l**2 - 3*l - 449. Suppose b(r) = 0. Calculate r.
-5, -1, 4
Let c(p) be the first derivative of -p**3 + 1200*p**2 - 480000*p - 627. Factor c(v).
-3*(v - 400)**2
Let 518940*j - 3*j**3 + 2212*j**2 + 2*j**3 + 3*j**3 + 3*j**3 + 32174280 + 578*j**2 = 0. What is j?
-186
Let f be -36*((-14)/3 + 4). Let o = 29 - f. Solve 12*i**2 - 3*i**o + 6 - 6 + 0*i - 3*i + 12*i**4 - 18*i**3 = 0.
0, 1
Let h be (-267630)/231 + (-3)/7. Let l = -15065/13 - h. Factor -10/13*i**2 - l*i**3 - 8/13 - 16/13*i.
-2*(i + 1)*(i + 2)**2/13
Let j(b) be the first derivative of -b**7/2940 + b**6/126 + b**5/420 - 5*b**4/42 + 155*b**3/3 - 45. Let n(z) be the third derivative of j(z). Factor n(x).
-2*(x - 10)*(x - 1)*(x + 1)/7
Let i = 39 - 259. Let o be (-1 - -1) + 40/(i/(-11)). Factor 3/2 + 3/4*f**o + 9/4*f.
3*(f + 1)*(f + 2)/4
Let h be 10/42*(-3)/5*101/(-101). Let d(x) be the second derivative of 29*x + 3/28*x**4 + h*x**2 + 1/28*x**5 + 1/210*x**6 + 0 + 1/6*x**3. Factor d(c).
(c + 1)**3*(c + 2)/7
Let p(i) be the second derivative of -i**6/40 - 3*i**5/5 - 47*i**4/16 + 25*i**3/2 + 99*i**2/2 - 10*i + 150. Find b such that p(b) = 0.
-11, -6, -1, 2
Let u(s) = 3548*s - 17738. Let r be u(5). Factor -154/13*l**r - 3040/13*l - 2888/13 - 2/13*l**3.
-2*(l + 1)*(l + 38)**2/13
Suppose -6*z - 6 = -18. Suppose -63*w - z*b + 4 = -61*w,