, 2
Let g(o) be the first derivative of 105*o**6/16 + 159*o**5/40 - 229*o**4/32 - 19*o**3/24 + 23*o**2/8 - o - 954. Let g(y) = 0. What is y?
-1, -4/7, 1/3, 2/5
Suppose 0*i = -6*i + 438. Let k = -3 + i. Solve k*t - 38*t + 6*t**2 - 38*t + 2 - 2*t**3 = 0 for t.
1
Let q = -3235 - -3239. Let c(a) be the first derivative of 10 + 1/2*a**4 - q*a**2 + 0*a + 0*a**3. Factor c(y).
2*y*(y - 2)*(y + 2)
Let h(u) = 2*u**2 - 114*u - 248. Let s be h(59). Let m be s/(-66) - (-8)/176*8. What is d in -m*d**2 - 18/11*d + 24/11 = 0?
-4, 1
Factor 55/3*z**2 - 1/3*z**3 + 473/3 - 527/3*z.
-(z - 43)*(z - 11)*(z - 1)/3
Suppose 0 = 24*r - 28*r - 188. Let d = 143/3 + r. Factor 0*q**2 + d*q - 2/3*q**3 + 0.
-2*q*(q - 1)*(q + 1)/3
Let o = -25 - -29. Suppose x - 15 = -2*w + 4*x, -o*x = 2*w + 6. Determine n, given that -w*n**2 + 5 + 75*n**5 - 139*n**3 + 15*n**4 + 48*n + 16*n**3 - 17 = 0.
-1, 2/5, 1
Factor -2*j + 1/3*j**2 + 3.
(j - 3)**2/3
Solve 52/7*m**4 + 1/7*m**5 + 865/7*m**3 - 10692/7*m + 3942/7*m**2 + 5832/7 = 0.
-18, 1
Find o such that -447/2*o**2 + 1/2 + 73*o = 0.
-1/149, 1/3
Let p(y) be the first derivative of -y**6/90 - 11*y**5/30 + 10*y**3 - 53. Let u(r) be the third derivative of p(r). Find x, given that u(x) = 0.
-11, 0
Let w(i) = i**3 - 24*i**2 - 75*i + 2257. Let d be w(23). Factor 0 + 5/2*l + 1/2*l**5 + 2*l**4 - d*l**3 - 2*l**2.
l*(l - 1)**2*(l + 1)*(l + 5)/2
Let p be ((-8)/10)/(5319/(-11820)). Factor -p*b**2 - 1/9*b**3 + 0 - 64/9*b.
-b*(b + 8)**2/9
Let b(i) = i**3 + 5*i**2 - 6*i - 6. Suppose -2*a + 5*o = -3*a - 5, -4*o = -2*a - 10. Let d be b(a). Factor -6*w**2 - d*w - 6*w**2 - 12 - 3*w**3 - 3*w**2.
-3*(w + 1)*(w + 2)**2
Let q(p) = 2*p**2 + 5*p + 6. Let k be q(-4). Suppose -4*m + k + 94 = 0. Find g, given that -23*g**3 - 3*g + 3*g + m*g**3 - 5*g**2 = 0.
0, 1
Let m(d) = 2*d**3 + 7*d**2 + 3*d + 2. Let a be m(-3). Let v = a + 1. Factor -2*o**5 - 2*o**5 - 12*o**v - 4*o**2 - 12*o**4 + 45 - 45.
-4*o**2*(o + 1)**3
Let v(o) be the second derivative of o**5/50 - 7*o**4/5 + 13*o**3/5 + 82*o**2/5 + 616*o. Let v(x) = 0. What is x?
-1, 2, 41
Let g be 69/12 - 731/172. Suppose -1/3*s**2 + 3*s**4 - g*s**5 - 4/3*s**3 + 1/6*s + 0 = 0. What is s?
-1/3, 0, 1/3, 1
Suppose 172 = -810*d + 853*d. Factor 12/7*y**5 - 8*y**d - 32/7*y**2 + 0 + 0*y + 80/7*y**3.
4*y**2*(y - 2)**2*(3*y - 2)/7
Let u(d) be the second derivative of d**6/10 + 31*d**5/10 - 31*d**4/4 - 18*d**3 + 22*d**2 + 17*d + 14. Solve u(x) = 0 for x.
-22, -1, 1/3, 2
Let m(s) = -81*s + 379. Let x be m(0). Let g = x - 1887/5. Factor 7/5*r - 2/5 + 3/5*r**3 - g*r**2.
(r - 1)**2*(3*r - 2)/5
Let t(v) be the third derivative of v**8/36960 - v**7/4620 + 43*v**5/60 - 13*v**2. Let d(i) be the third derivative of t(i). Let d(w) = 0. Calculate w.
0, 2
Let p(j) = 3*j**3 + 16*j**2 + 5*j + 2. Let m be p(-5). Let v = 349/4 - 87. Factor i**m + 0 + i + v*i**3.
i*(i + 2)**2/4
Factor 4 + 2/9*r**3 - 16/9*r**2 - 22/9*r.
2*(r - 9)*(r - 1)*(r + 2)/9
Let v be 46 + (31 - (74 + 1)). Factor 0 + 23/3*m - 1/6*m**v.
-m*(m - 46)/6
Suppose i + i - 123 = 5*x, 99 = -4*x + i. Let p = -23 - x. Factor -10 - 4*o**2 - 12*o + p + 0.
-4*(o + 1)*(o + 2)
Let j = -606677/28 + 86675/4. Factor 12/7*v**3 + 0 + 4/7*v**5 - j*v**4 + 0*v - 4/7*v**2.
4*v**2*(v - 1)**3/7
Suppose 184*o**4 + 21394*o**2 + 480*o**3 + 268*o**3 + 24*o + 342*o**3 - 166*o**3 - 20270*o**2 = 0. What is o?
-3, -2, -1/46, 0
Let p be 192*(2100/(-16))/25. Let u = p - -13110/13. Factor -10/13 + u*f**2 - 28/13*f.
2*(f - 5)*(3*f + 1)/13
Let l be ((105/(-9))/(-1*3))/(4390/5268). Let l*h**3 + 2/3*h - 2 + 22/3*h**2 = 0. What is h?
-1, 3/7
Let y(c) = 17*c + 1. Let o be y(1). Suppose -3*k - 23 = 3*j - 7*j, 0 = -4*j + 2*k + o. Factor 109*h**2 + h**3 - h**3 + h**3 - 112*h**2 + j*h.
h*(h - 2)*(h - 1)
Let b(v) be the first derivative of 2*v**3/9 + v**2/3 - 112*v/3 - 78. Factor b(m).
2*(m - 7)*(m + 8)/3
Suppose -65*x - 8 = -67*x. Factor -17*r**3 + 51*r**3 + 64*r**2 + 62*r**3 - 60*r**x + 8*r**5.
4*r**2*(r - 4)**2*(2*r + 1)
Let a = 55/251 - -206972/2761. Let c = a + -75. Determine l, given that 2/11*l**3 + 0 + 0*l + c*l**4 - 4/11*l**2 = 0.
-2, 0, 1
Let t(n) be the first derivative of 2*n**5/5 + 7*n**4/8 - 2*n**3 - 29*n**2/4 - 7*n - 4383. Factor t(p).
(p - 2)*(p + 1)**2*(4*p + 7)/2
Let j(d) be the first derivative of d**3/3 + 23*d**2/2 + 25*d - 77. Let w be j(-22). Determine l, given that 0 - 1/4*l**2 - 1/4*l**w + 0*l = 0.
-1, 0
Let p(t) be the second derivative of 1/18*t**4 + 2/3*t**2 - 1/15*t**6 - t + 7/9*t**3 - 7/30*t**5 - 3. Determine m, given that p(m) = 0.
-2, -1, -1/3, 1
Factor 2*q**2 - 57*q - 9*q + 210 + 14*q.
2*(q - 21)*(q - 5)
Let a(x) = -7*x**2 - 30*x - 2. Let i(m) = -8*m**2 - 30*m - 3. Let k = -130 + 127. Let u(r) = k*a(r) + 2*i(r). Solve u(s) = 0.
-6, 0
Let n(h) be the third derivative of -h**7/105 - 71*h**6/60 + h**5/10 + 215*h**4/12 + 142*h**3/3 - 1215*h**2. Factor n(g).
-2*(g - 2)*(g + 1)**2*(g + 71)
Let r = -7013 - -7018. Let n(d) be the first derivative of -7/5*d**3 - 3/25*d**r - 3/4*d**4 - 9/10*d**2 + 0*d + 24. Factor n(b).
-3*b*(b + 1)**2*(b + 3)/5
Let t(s) = -3394*s - 74666. Let i be t(-22). Factor -9/4*v - 27/8 - 3/8*v**i.
-3*(v + 3)**2/8
Suppose 48*g**3 - 1650 - 53*g**3 + 2343*g - 198*g - 810*g**2 + 320*g = 0. What is g?
-165, 1, 2
Let a(z) be the first derivative of -22/7*z**2 - 4/7*z**4 + 16/7*z + 2/35*z**5 + 2*z**3 - 14. Factor a(s).
2*(s - 4)*(s - 2)*(s - 1)**2/7
Let k(c) be the third derivative of -c**5/480 - 43*c**4/48 - 169*c**3/16 - 9640*c**2. Factor k(m).
-(m + 3)*(m + 169)/8
Let v(i) be the third derivative of 2/27*i**5 + 0*i - 75*i**2 + 0*i**3 - 2 + 1/540*i**6 - 7/36*i**4. Factor v(w).
2*w*(w - 1)*(w + 21)/9
Suppose 5*o + 54*p = 50*p + 44, 4*o = p - 11. Factor 2/5*b**5 + o + 12/5*b**4 + 0*b + 18/5*b**3 + 8/5*b**2.
2*b**2*(b + 1)**2*(b + 4)/5
Find n, given that -2416/3 + 4/3*n**2 + 400*n = 0.
-302, 2
Factor -19/12*m - 1/12*m**2 + 23/3.
-(m - 4)*(m + 23)/12
Let s(h) be the first derivative of 28*h**3/15 - 634*h**2/5 + 72*h + 2320. Factor s(x).
4*(x - 45)*(7*x - 2)/5
Suppose 26*l + 4 = 28*l. Let 85817*p**3 + 102*p + 32760*p**l + 2954*p + 76548*p**3 + 96 + 37044*p**4 - 40649*p**3 = 0. Calculate p.
-3, -2/21
Suppose k = 2*u - 6, 0*k - 5*k = -2*u + 14. Let p(i) = i - 1. Let t be p(5). What is j in 2*j - j**3 - 6*j**3 - u + j**t + j**2 + j + 4*j**3 = 0?
-1, 1, 2
Factor -4905*p + 40 + 2210*p - 43*p**2 + 2460*p + 13*p**2.
-5*(p + 8)*(6*p - 1)
Factor -576 + 48*x - 51/2*x**3 + 111*x**2 + 3/2*x**4.
3*(x - 8)**2*(x - 3)*(x + 2)/2
Let f(l) = -l**2 + 41*l + 110. Let z be f(43). Let b be (-1 + (-15)/(-9))/(z/9). Factor -1/2*x + 0 + b*x**4 - 1/4*x**2 + 1/2*x**3.
x*(x - 1)*(x + 1)*(x + 2)/4
Let d(w) be the first derivative of -w**6/120 - w**5/20 - w**4/16 + 54*w - 133. Let t(f) be the first derivative of d(f). Factor t(p).
-p**2*(p + 1)*(p + 3)/4
Determine o so that 10*o**2 + 33*o - 24*o + 5*o**2 - 3*o**3 + 3*o**2 - 24*o = 0.
0, 1, 5
Let n(g) be the third derivative of g**6/30 + 13*g**5/15 - 3*g**4/2 - 78*g**3 - 1470*g**2. Factor n(m).
4*(m - 3)*(m + 3)*(m + 13)
Factor -4/7*z**3 + 9600/7*z - 328/7*z**2 - 61056/7.
-4*(z - 12)**2*(z + 106)/7
Suppose 0 = 119*a - 534 - 61. Let k(o) be the first derivative of 5/24*o**6 + 0*o**4 + 1/2*o**a + 0*o - 5/8*o**2 - 5/6*o**3 - 43. Factor k(i).
5*i*(i - 1)*(i + 1)**3/4
Let q(u) = 56*u**2 - 68*u + 324. Let z(i) = 51*i**2 - 68*i + 325. Let a(p) = -11*q(p) + 12*z(p). Suppose a(k) = 0. What is k?
-21, 4
Factor -1/10*v**3 + 3*v + 0 + 13/10*v**2.
-v*(v - 15)*(v + 2)/10
Let -16*o**3 + 25*o**4 - 68*o**3 - 30*o**3 - 1060*o - 1470*o**2 - 221*o**3 + 680 = 0. What is o?
-2, 2/5, 17
Suppose -108 = -44*w + 41*w. Let z be 2/(-3) - (0 + (-24)/w). Factor -3/4*f**5 + 0*f**2 + 0 - 3/4*f + 3/2*f**3 + z*f**4.
-3*f*(f - 1)**2*(f + 1)**2/4
Let p(f) = -8*f**4 + 12*f**3 + 12*f**2 - 52*f. Let n(j) = 7*j**4 - 12*j**3 - 13*j**2 + 51*j. Let z = -579 + 582. Let x(g) = z*p(g) + 4*n(g). Factor x(b).
4*b*(b - 3)*(b - 2)*(b + 2)
Let i(w) be the third derivative of w**8/840 - 6*w**7/175 + 17*w**6/300 - 21*w**2 + 18*w. Factor i(c).
2*c**3*(c - 17)*(c - 1)/5
Let s(q) be the third derivative of 11*q**7/3780 - 7*q**6/810 + 56*q**3/3 - 77*q**2. Let c(k) be the first derivative of s(k). Determine g, given that c(g) = 0.
0, 14/11
Factor 3/5*d**4 + 0*d**2 + 0*d - 1041/5*d**3 + 0.
3*d**3*(d - 347)/5
Let u(b) be the f