6*z**2 - 24/5*z**3 + 0*z - 1/300*z**5. Find h such that b(h) = 0.
-12
Let v(i) be the third derivative of i**2 - 23/300*i**5 - 13/60*i**4 + 4/15*i**3 - 1/150*i**6 + 0 - 96*i. Factor v(d).
-(d + 2)*(d + 4)*(4*d - 1)/5
Suppose 197*l + 9357 + 2571 = 268*l. Suppose -4/5 - 114/5*z - l*z**2 - 392/5*z**3 = 0. What is z?
-2, -1/14
Let u = 1519 + -626. Determine k so that 684*k**2 - u*k + 529*k**3 + 1001*k + 302*k**3 - 798*k**4 + 147*k**5 = 0.
-2/7, 0, 3
Let b(s) be the first derivative of 2*s**3/15 + 2*s**2/5 - 2165. Factor b(w).
2*w*(w + 2)/5
Suppose 8*p = -25*p + 7128. Let n = 650/3 - p. Let 2/3 + 2/3*h**4 - 4/3*h**2 + 2/3*h**5 + n*h - 4/3*h**3 = 0. What is h?
-1, 1
Let p be 25/(-2) + (-2112)/48 + 58. Factor -3/2*r**3 + 1/4*r**4 + p*r - 1/4*r**2 + 0.
r*(r - 6)*(r - 1)*(r + 1)/4
Let w = 83 - 80. Let c(p) be the third derivative of 0*p**5 + 0*p**7 - p**2 + 0*p**w + 1/108*p**4 + 0 + 1/1512*p**8 - 1/270*p**6 + 0*p. Solve c(v) = 0.
-1, 0, 1
Let k be -35 - -42 - ((-3)/(-10))/(90/(-840)). Factor 1/5*n**4 + k*n + 63/5*n**2 + 0 + 3*n**3.
n*(n + 1)*(n + 7)**2/5
Let u = -159 + 162. Factor -142*c + 287*c + c**u - 3*c**2 - 143*c.
c*(c - 2)*(c - 1)
Let j be 4275/285 + 15/(-1). Let o(b) be the first derivative of 0*b + 2*b**2 - 2/3*b**6 + 8 + 8/5*b**5 + j*b**4 - 8/3*b**3. Factor o(i).
-4*i*(i - 1)**3*(i + 1)
Let u(b) be the first derivative of -b**3/9 + 37*b**2/3 - 489. Find f, given that u(f) = 0.
0, 74
Let l = 68 + -65. Suppose -l*i - 57*i**2 + 0*i - 10 + 58*i**2 = 0. Calculate i.
-2, 5
Suppose 6*r - 51 = 15. Let i(q) be the first derivative of -4/11*q + r - 2/3*q**3 - 13/11*q**2. Factor i(b).
-2*(b + 1)*(11*b + 2)/11
Let d be (-810)/(-2295) + (-584)/(-272). What is g in -d*g**2 + 15/2 - 5*g = 0?
-3, 1
Let x(u) be the second derivative of u**4/36 + 35*u**3/18 - 49*u**2 - 444*u + 2. Let x(o) = 0. What is o?
-42, 7
Let j(b) be the second derivative of -b**9/7560 + b**7/1260 - 2*b**4/3 - b**3/6 + 9*b + 1. Let g(x) be the third derivative of j(x). Factor g(k).
-2*k**2*(k - 1)*(k + 1)
Let b(f) = -67*f**3 - 136*f**2 - 16*f. Let o = -278 + 287. Let a(l) = -135*l**3 - 273*l**2 - 33*l. Let p(t) = o*b(t) - 4*a(t). Factor p(m).
-3*m*(m + 2)*(21*m + 2)
Let x be 6 - ((-9)/(-72) + 848/(-2688)). Factor 16/7*v**2 + 4 + x*v + 2/21*v**3.
2*(v + 1)*(v + 2)*(v + 21)/21
Let f(s) = -s**4 - s**3 - 2*s. Suppose 18*v - 19*v - 1 = 0. Let y(t) = -3*t**4 + 6*t**3 - 20*t**2 + 12*t. Let d(i) = v*y(i) + 2*f(i). Let d(w) = 0. Calculate w.
0, 2, 4
Let r(a) = -4*a**3 + 132*a**2 - 684*a - 7226. Let l(g) = -20*g**3 + 660*g**2 - 3420*g - 36132. Let b(k) = -3*l(k) + 16*r(k). Factor b(u).
-4*(u - 19)**2*(u + 5)
Let n(q) be the third derivative of q**5/20 + 7*q**4 - 57*q**3/2 + 3*q**2 - 82. Let n(c) = 0. Calculate c.
-57, 1
Let l(u) be the first derivative of u**6/360 - u**5/20 + u**4/3 - 26*u**3 - 78. Let q(i) be the third derivative of l(i). Factor q(w).
(w - 4)*(w - 2)
Let t = -12183299304 + 278961004098282/22897. Let a = 2/3271 - t. Find f, given that 26/7*f - a + 6/7*f**2 = 0.
-5, 2/3
Let f(d) be the first derivative of -d**5/20 - d**4/4 - d**3/4 + 93. Determine c, given that f(c) = 0.
-3, -1, 0
Let g(d) be the third derivative of -2*d**7/315 + d**6/60 + 2*d**5/15 - 7*d**4/36 - 2*d**3/3 - 2220*d**2. Solve g(s) = 0.
-2, -1/2, 1, 3
Suppose 8*d - 20 = -2*d. Suppose 4*c**3 - 49 - 26 - 21 - 2*c - 4*c**4 + 40*c**d - 14*c = 0. Calculate c.
-2, 2, 3
Factor -4/11*c**2 + 0 - 16/11*c + 2/11*c**3.
2*c*(c - 4)*(c + 2)/11
Let y = -52 + 592. Suppose -516 - y = -6*s. Factor 2*x**2 + 178*x**3 - 2*x**4 + 2*x**2 - s*x**3.
-2*x**2*(x - 2)*(x + 1)
Let z(o) = 9*o - 315. Let m be z(35). Let w(h) be the third derivative of -1/21*h**4 + 0*h - 24*h**2 + m*h**3 + 1/42*h**5 + 0. Factor w(g).
2*g*(5*g - 4)/7
Let -144/5 - 8/5*w**3 + 72/5*w**2 + 16/5*w + 1/5*w**5 - 9/5*w**4 = 0. What is w?
-2, 2, 9
Let a(t) be the second derivative of t**7/84 - t**6/20 - 11*t**5/20 + 15*t**4/4 - 9*t**3/4 - 135*t**2/4 + t - 1167. Suppose a(h) = 0. Calculate h.
-5, -1, 3
Let t(s) be the second derivative of -27*s**5/10 + 167*s**4/2 - 578*s**3/3 + 104*s**2 - 52*s - 9. Suppose t(g) = 0. Calculate g.
2/9, 1, 52/3
Let a = -3553399/200 - -17767. Let f(n) be the third derivative of 0*n - 2/5*n**3 + 0*n**4 + 0 + a*n**6 + 3/100*n**5 + 4*n**2. Factor f(w).
3*(w - 1)*(w + 2)**2/5
Let h(d) be the first derivative of 5*d**4/4 - 920*d**3/3 + 915*d**2/2 - 1025. Factor h(w).
5*w*(w - 183)*(w - 1)
Let c(x) = 2*x**3 + 10*x**2 + 3. Let j be c(-5). Suppose -j*u + 33 = 24. Factor -12*p**2 - u*p**2 - 7*p**2 - 8 + 24*p**2.
2*(p - 2)*(p + 2)
Let p(u) be the second derivative of -19 + 13/36*u**4 + 1/60*u**5 + 2*u + 0*u**2 + 7/3*u**3. Solve p(x) = 0.
-7, -6, 0
Let n(k) be the second derivative of -k**4/66 - 31*k**3/11 - 92*k**2/11 + 3368*k. Factor n(l).
-2*(l + 1)*(l + 92)/11
Determine s, given that -80/11*s - 2/11*s**2 + 658/11 = 0.
-47, 7
Suppose 17 = -4*b - 5*a + 58, 2*a - 10 = 0. Suppose b*c - 12 = 0, -k + c = -0*k. Factor 2 - k*h**2 - 5 - 14*h + 20*h.
-3*(h - 1)**2
Suppose 0 = -2*i - 5*m - 6 + 1162, -5*m = -20. Let -480*f + 82 + 968*f - i*f - 2*f**2 = 0. Calculate f.
-41, 1
Factor -7072/7*d - 6251648/7 - 2/7*d**2.
-2*(d + 1768)**2/7
Suppose 37*g - 72*g + 175 = 0. Let l(z) be the second derivative of -2/21*z**4 + 0*z**2 - 1/7*z**g - 2/147*z**7 - 8/105*z**6 + 0*z**3 + 0 - 6*z. Factor l(m).
-4*m**2*(m + 1)**2*(m + 2)/7
Let q(l) be the second derivative of -l**5/140 + 25*l**4/42 + 496*l**3/21 + 2112*l**2/7 - l - 520. Determine i, given that q(i) = 0.
-8, 66
Factor -36*z - 46*z**3 - 45*z**3 - 46*z**3 + 6*z**2 + 138*z**3 + 3*z**2.
z*(z - 3)*(z + 12)
Let q be 90563/(-10505) + -4 + 11. Let x = -4/191 - q. Determine g, given that x*g - 8/5 - 2/5*g**3 + 2/5*g**2 = 0.
-2, 1, 2
Suppose 0 = -8*y - 567 + 359. Let w(m) = m**3 + 28*m**2 + 53*m + 31. Let x be w(y). Factor 40/3*t**2 + 0 - 2/3*t**x - 16/3*t - 12*t**3 + 14/3*t**4.
-2*t*(t - 2)**3*(t - 1)/3
Let f(k) be the second derivative of 3*k**5/160 - 191*k**4/32 - 193*k**3/8 - 4169*k. Factor f(c).
3*c*(c - 193)*(c + 2)/8
Let z(t) = 2*t**2 + 14*t - 13. Let k be z(-8). Factor 27*n + 144*n**2 + 177*n**k - 16*n**3 + 31*n**3.
3*n*(8*n + 3)**2
Determine d so that 6/11*d**2 + 336*d + 3690/11 = 0.
-615, -1
Suppose 3*x + r + 0 = 1, 5*r = -25. Suppose 15 = 5*n - 4*m - 4, 0 = 2*n + 4*m - x. Solve -9/2*c**2 + 3/2*c**n - 3/2*c + 9/2 = 0 for c.
-1, 1, 3
Let p = 286427990064/125511010625 - 12/81131875. Let b = 4/1105 + p. Factor 2*i + 10/21 + b*i**2 + 8/21*i**3.
2*(i + 5)*(2*i + 1)**2/21
Let x(y) be the first derivative of -y**4/96 - y**3/24 + 3*y**2/16 + 36*y + 55. Let m(u) be the first derivative of x(u). Factor m(t).
-(t - 1)*(t + 3)/8
Let u = -58300 - -291528/5. What is w in 2 - 6/5*w**2 + u*w = 0?
-1/3, 5
Let b = 421 - 424. Let q(i) = 5*i**3 - 45*i**2 + 109*i - 72. Let j(t) = 10*t**3 - 90*t**2 + 216*t - 143. Let z(d) = b*j(d) + 7*q(d). Solve z(s) = 0 for s.
1, 3, 5
Suppose -11*f = -9*f - 198. Let x be 2/(-3)*-4*f/66. Find k, given that 2*k**5 - 4*k**4 - 2*k**3 + 0*k**3 + x*k**2 + 9*k**3 - 9*k**3 = 0.
-1, 0, 1, 2
Let s(q) = 19*q**5 - 41*q**4 - 15*q**3 + 41*q**2 - 10*q. Let m(d) = d**5 + d**4 - d**2. Let h = 310 - 309. Let b(z) = h*s(z) + 6*m(z). Let b(p) = 0. What is p?
-1, 0, 2/5, 1
Suppose 4/13*i**3 - 408/13*i**4 - 2/13*i**5 + 816/13*i**2 - 2/13*i - 408/13 = 0. Calculate i.
-204, -1, 1
Let h(n) be the first derivative of 92 + 1/15*n**5 + 0*n - 1/6*n**2 + 1/12*n**4 - 1/9*n**3. Factor h(y).
y*(y - 1)*(y + 1)**2/3
Suppose 5*b = 5*w + 15, -6*b = 4*w - 11*b + 8. Let c be ((42/4)/w)/((-45)/6). Factor -c*p**3 + 0*p - 9/5*p**2 + 0.
-p**2*(p + 9)/5
Let q = 278030 - 278028. Factor -8/7 + 20/7*c**q - 12/7*c.
4*(c - 1)*(5*c + 2)/7
Factor -303/4*w**2 + 101 + 49/2*w**3 + 1/4*w**4 + w.
(w - 2)**2*(w + 1)*(w + 101)/4
Let l be 1*(-9)/(-3) - 2*22. Let x = 43 + l. Suppose -66*f + 71 - 4*f**3 + 15*f**x + 41*f**2 - 6*f**3 - 107 = 0. What is f?
-2/5, 3
Let x(t) = -4*t**2 + 4464*t - 4364. Let f(s) = -s**2 + 1488*s - 1451. Let n(b) = 8*f(b) - 3*x(b). Factor n(a).
4*(a - 371)*(a - 1)
Let z = -11831/9 - -11909/9. Determine k so that -40/3*k + z*k**2 + 22/3*k**3 - 8/3 = 0.
-2, -2/11, 1
Let k(b) be the second derivative of -b**7/126 + 9*b**5/10 - 6*b**4 + 27*b**3/2 - 6*b - 62. Suppose k(h) = 0. Calculate h.
-9, 0, 3
Factor -367 - 263 - 5*c**3 - 26*c**2 + 126*c*