*l - 12 = 247*l. Let c be 9/4 + (l/(-3) - 2). Let -c*o**2 - 5 + 5*o = 0. What is o?
2
Let y(b) be the first derivative of -3*b**5/20 + 15*b**4/16 - 9*b**3/4 + 21*b**2/8 - 3*b/2 - 2419. Factor y(v).
-3*(v - 2)*(v - 1)**3/4
Let d be 693/2772*314/(-28)*24. Let i = -67 - d. Factor -1/7*q**4 + 2/7*q + 0 - i*q**3 + 1/7*q**2.
-q*(q - 1)*(q + 1)*(q + 2)/7
Let s be (-21)/1*(-1)/3. Let h(u) = 4*u**3 - 7*u**2 - 9*u + 3. Let f(l) = -9*l**3 + 15*l**2 + 17*l - 7. Let d(v) = s*h(v) + 3*f(v). What is p in d(p) = 0?
-2, 0, 6
Let h be (-3542)/69*(-1 - 0 - 2). Find z such that 2592*z + 82*z**3 + 146*z**2 - 2*z**2 - h*z**3 + 74*z**3 = 0.
-36, 0
Suppose -2*f = -2*c - 2, -4*f = -c + 2 - 18. Let g(d) be the second derivative of -1/14*d**c + 0*d**2 + 2/35*d**5 - 1/21*d**3 - 22*d + 0. Factor g(y).
2*y*(y - 1)*(4*y + 1)/7
Let s(g) be the second derivative of -g**5/110 + 59*g**4/66 - 280*g**3/11 - 900*g**2/11 - 1506*g. Factor s(p).
-2*(p - 30)**2*(p + 1)/11
Determine y so that 68*y**2 + 6710*y - 93*y**3 + 158*y**2 + 18150 - 88*y**3 + 183*y**3 = 0.
-55, -3
Let s be 38/209 - (-262968)/231. Let k = s + -1138. Factor k*h**2 + 16/7*h**3 + 0 + 0*h.
4*h**2*(4*h + 1)/7
Let x(d) be the second derivative of 0 + 1/18*d**4 + 0*d**3 + 0*d**2 - 1/90*d**5 + 185*d. Find l, given that x(l) = 0.
0, 3
Let k = 277450/69 - 4021. Let i(l) be the second derivative of k*l**6 + 0*l**2 + 7/138*l**4 - 1/483*l**7 + 16*l - 2/69*l**3 - 9/230*l**5 + 0. Factor i(o).
-2*o*(o - 2)*(o - 1)**3/23
Let g(b) be the first derivative of -25*b**6/6 + 1779*b**5 - 390685*b**4/2 - 1749730*b**3/3 - 1119645*b**2/2 - 160205*b + 6195. Suppose g(r) = 0. What is r?
-1, -1/5, 179
Suppose -18*w - 60 = 2*w. Let r be 8/(-32)*0/w. Let r*s - 3/7*s**2 + 0 = 0. What is s?
0
Let s(p) = 13*p**2 + 38*p + 286. Let j(a) = -9*a**2 - 37*a - 286. Let l(g) = 6*j(g) + 4*s(g). Factor l(y).
-2*(y + 13)*(y + 22)
Let z(q) = -2*q**3 + 72*q**2 + 6. Let o = -778 + 814. Let x be z(o). Determine t so that 3*t**3 + 0 + 6*t**4 - 9/2*t - x*t**2 + 3/2*t**5 = 0.
-3, -1, 0, 1
Let l be 1830/(-1) - (-72)/24. Let q = l + 14637/8. Factor 3*f + 3/8*f**2 + q.
3*(f + 1)*(f + 7)/8
Suppose 0 = n - 5*n - 4*w + 76, 5*w = 2*n - 10. Let f be 2 + -1 - (n + -18). Suppose c**3 - 5*c**3 + 2*c**3 - 13*c**f + 5*c**4 = 0. What is c?
-1/4, 0
Suppose 20 = -239*a + 244*a. Suppose b - 10 = -b + 2*h, -3*b - 20 = a*h. Factor 4/7*u**2 - 4/7*u**4 + b*u**3 + 0*u + 0.
-4*u**2*(u - 1)*(u + 1)/7
Determine i so that 213*i - 90 - 50*i**4 + 177*i + 5*i**5 - 340*i**2 - 105*i + 190*i**3 = 0.
1, 2, 3
Let k be ((-10)/((-2)/(-1)))/(1 + 0). Let t be (-30)/(-1 - (-1 - (k + 3))). Factor -20*x**3 + 8*x**2 - 4*x**5 - 41*x**4 - t*x**4 + 72*x**4.
-4*x**2*(x - 2)*(x - 1)**2
Let f = -5064 - -40513/8. Let s(j) be the first derivative of 1/10*j**5 + 3/4*j**2 + f*j**4 + 0*j + 4 - 5/6*j**3. Factor s(y).
y*(y - 1)**2*(y + 3)/2
Let k(w) = w**3 - 10*w**2 + 2*w - 15. Let h be k(10). Suppose -5*g - 16 = -g, 2*g = -h*f + 182. Factor -20*c**3 + 2 + 66*c**2 - 7 + 18*c**4 - 30*c - f*c**3 + 9.
2*(c - 1)**3*(9*c - 2)
Let k(q) be the third derivative of q**8/5040 - q**7/140 + 7*q**6/90 - q**5/60 + q**3/3 - 36*q**2. Let f(l) be the third derivative of k(l). Factor f(h).
4*(h - 7)*(h - 2)
Let u(s) be the second derivative of 1/7*s**7 - 2*s + 0*s**4 + 0*s**3 - 8/15*s**6 + 2/5*s**5 + 0*s**2 - 22. Find a, given that u(a) = 0.
0, 2/3, 2
Let l be (22 - (-2275)/(-105))*6. Factor -10/3*o**l - 14/3*o - 2 - 2/3*o**3.
-2*(o + 1)**2*(o + 3)/3
Let u be 95*5*6/150. Solve 50 - u*f**3 - 3*f**3 - 37*f**3 - 55*f**2 + 45*f + 5*f**4 + 14*f**3 = 0.
-1, 1, 10
Let w(r) be the third derivative of -1/16*r**4 - 41*r**2 - 1/480*r**6 + 0*r**3 + 0*r - 1/48*r**5 + 0. Factor w(s).
-s*(s + 2)*(s + 3)/4
Let r = 2513224 - 2513222. Let a = 2 + 1. Factor -4/7*i**r + 0*i**a + 2/7*i**5 - 2/7*i + 0 + 4/7*i**4.
2*i*(i - 1)*(i + 1)**3/7
Let c(j) be the first derivative of -j**3 - 12*j**2 + 1035*j - 507. Suppose c(v) = 0. What is v?
-23, 15
Let t be -14034*120/(-1152) + (-35)/(-56). Determine p so that -9/2*p**4 - 1035/2*p**2 - 1500 + t*p + 159/2*p**3 = 0.
8/3, 5
Let i(k) be the second derivative of k**6/6 + 4*k**5 - 455*k**4/12 - 565*k**3/3 - 300*k**2 + 434*k - 1. Factor i(j).
5*(j - 6)*(j + 1)**2*(j + 20)
Let s be (1 + -8 + (-1298)/(-22) + -48)*64/6. Let b be (-1 - (-9)/5)*5. Solve 4096/9 + s*a**2 + 1/9*a**b + 32/9*a**3 + 2048/9*a = 0 for a.
-8
Let a(y) = -225*y**2 - 73830*y - 70. Let b(x) = 13*x**2 + 4343*x + 4. Let d(c) = 2*a(c) + 35*b(c). Factor d(i).
5*i*(i + 869)
Let l(x) be the first derivative of -x**6/3 - 74*x**5/15 - 122*x**4/9 + 1688*x**3/27 + 1120*x**2/9 - 3200*x/9 + 528. Determine p, given that l(p) = 0.
-20/3, -2, 1, 2
Let i(t) be the second derivative of 0*t**3 + 1 - 3/10*t**6 + 1/28*t**7 + 0*t**2 + 0*t**4 + 50*t + 3/5*t**5. Find j, given that i(j) = 0.
0, 2, 4
Determine r, given that -460*r - 830*r**2 + 1643*r**2 - 818*r**2 + 940 = 0.
-94, 2
Suppose -3 = -6*m - 3. Suppose -5*n + 6*n - 4 = m. Suppose 2*o**2 - 4*o**3 + 4*o + o**n + 5*o**4 - 8*o**4 + 0*o**4 = 0. What is o?
-2, -1, 0, 1
Suppose -9747/4*k - 345/4*k**3 - 3/4*k**4 - 10089/4*k**2 + 0 = 0. What is k?
-57, -1, 0
Let w be ((-26)/429)/((-32)/88). Let l(f) be the first derivative of -1/10*f**5 - 13 - w*f**3 - 3/4*f**2 + f + 3/8*f**4. Determine n, given that l(n) = 0.
-1, 1, 2
Factor 0 - 2/9*v**5 + 32/3*v**4 - 1058/9*v + 736/3*v**2 - 1244/9*v**3.
-2*v*(v - 23)**2*(v - 1)**2/9
Let h(f) be the first derivative of 16*f - 25 - 3*f**2 + 2/3*f**3 - 1/18*f**4. Let i(v) be the first derivative of h(v). Factor i(l).
-2*(l - 3)**2/3
Let n(g) be the first derivative of -g**6/900 + 13*g**5/450 + 7*g**4/90 + 35*g**2 + 2*g + 142. Let o(v) be the second derivative of n(v). Factor o(a).
-2*a*(a - 14)*(a + 1)/15
Let v(q) be the second derivative of -1/12*q**4 + 1/90*q**6 - 2/3*q**2 + 0 - 4/9*q**3 + 1/30*q**5 + 94*q. Solve v(h) = 0.
-2, -1, 2
Suppose -40*d - 29378 - 1582 = 0. Let s = 778 + d. Find z such that 9/5*z**3 + 3/5*z + 0 + 9/5*z**2 + 3/5*z**s = 0.
-1, 0
Suppose -4*j - 2*r = -8, j - 1 - 1 = 5*r. Let k = -10/29201 - -233738/379613. Determine m so that k*m**j + 0 - 2/13*m**3 - 8/13*m = 0.
0, 2
Let f be (-3 - 15/(-10))*4/(-2). Let h be ((-3)/6)/((3/(-10))/f). Let -5*n**2 - 17*n**3 - h*n**5 + 15*n**2 + 32*n**3 = 0. What is n?
-1, 0, 2
Let m = 119372 + -119370. Factor 6/5*i + 0 + 2/5*i**m.
2*i*(i + 3)/5
Solve -7/2*a**4 - 5*a**3 + 0*a**2 + 0*a - 1/2*a**5 + 0 = 0 for a.
-5, -2, 0
Let y = -195235 - -3709627/19. Determine l, given that -36/19*l + 36/19*l**3 - 2/19*l**4 - 160/19*l**2 + y = 0.
-1, 1, 9
Determine s so that 8/11*s - 2/11*s**4 - 294/11*s**2 - 104/11*s**3 + 392/11 = 0.
-49, -2, 1
Factor 9528*w + 171*w**2 - 69*w**2 - 48*w**2 - 3808 - 29*w**2 - 45*w**2.
-4*(w - 476)*(5*w - 2)
Suppose 51 + 6 = 19*y. Factor -n**4 - 8*n**2 - 4*n + 7*n**5 - 4*n + 5*n**4 - 9*n**5 + 6*n**y.
-2*n*(n - 2)**2*(n + 1)**2
Let a(v) be the second derivative of -v**4/12 - 937*v**3/3 - 877969*v**2/2 - 2*v + 369. Suppose a(k) = 0. What is k?
-937
Suppose 0 = 5*a - 15, -165 = 2*z + 2*a + 9. Let o be ((-12)/z)/((-12)/(-30)). Factor o*j**2 + 3 + 2*j.
(j + 3)**2/3
Factor 0 - 166/3*t + 27*t**2 + 1/3*t**3.
t*(t - 2)*(t + 83)/3
Let w(s) be the second derivative of s**5/10 - 343*s**4/6 + 1360*s**3/3 - 1356*s**2 + 2431*s. Find h such that w(h) = 0.
2, 339
Suppose -30*j = -5037 + 4977. Factor -24/7*x + 3/7*x**3 + 36/7 - 3/7*x**j.
3*(x - 2)**2*(x + 3)/7
Let a be (-10*(-37)/(-1110))/(7/(-24)). Let w = 167 + -1167/7. Factor 2*k**4 + 30/7*k**3 + 26/7*k**2 + 0 + a*k + w*k**5.
2*k*(k + 1)**3*(k + 4)/7
Let g(v) be the third derivative of v**6/480 + v**5/30 - v**4/6 - 16*v**3/3 + 7154*v**2. Suppose g(t) = 0. Calculate t.
-8, -4, 4
Suppose 5*h = 5*q + 65, 4*q = -10*h + q - 13. Factor -11/2 + 1/4*t**h + 9/4*t.
(t - 2)*(t + 11)/4
Factor -417*x**2 + 58256 - 12887 + 13845*x + 18*x**3 - 13*x**3 - 2*x**3.
3*(x - 71)**2*(x + 3)
Factor -2/13*g**2 + 0 - 604/13*g.
-2*g*(g + 302)/13
Let s(p) = -p**2 + 2*p - 2. Let z(k) = -2 - 14 - 3 + 10*k**2 + 0*k - 3*k**2 - 8*k. Let g(a) = 4*s(a) + z(a). Factor g(x).
3*(x - 3)*(x + 3)
Let y(j) be the third derivative of j**6/300 - 19*j**5/150 - j**4/60 + 19*j**3/15 + 1198*j**2. Solve y(u) = 0 for u.
-1, 1, 19
Let l = 895/26904 - -5/472. Let m(o) be the second derivative of 1/285*o**6 - 1/190*o**5 + 0 - 8*o + 0*o**2 - l*