et m be (-2 - -514)/(7/56). Determine f so that -m + 133*f + 18*f + 157*f - 4*f**2 - 52*f = 0.
32
Let y be (7 - 5) + 2380/700. Let -81/5 - 168/5*t**3 + y*t**2 + 162/5*t + 48/5*t**4 = 0. Calculate t.
-1, 3/4, 3
Let d(w) be the second derivative of w**9/12096 + w**8/960 + w**7/240 + w**6/180 + 49*w**3/2 - 24*w + 2. Let f(m) be the second derivative of d(m). Factor f(r).
r**2*(r + 1)*(r + 2)*(r + 4)/4
Let l = -9311 - -9313. Let f(i) be the first derivative of -5/3*i**3 + 5*i**l + 14 + 0*i. Determine v so that f(v) = 0.
0, 2
Determine s so that 0 + 272/3*s - 274/3*s**2 + 2/3*s**3 = 0.
0, 1, 136
Let l(d) = -2*d + 6. Let r(n) = 2*n - 5. Let u(c) = 6*l(c) + 7*r(c). Let o be u(7). Factor -8*w**2 + 5*w**3 - 17*w**2 - 36*w**4 + o*w + 41*w**4.
5*w*(w - 1)**2*(w + 3)
Let u(r) = -15*r**3 - 20*r + 27*r**2 + 4*r**3 - 7*r**2. Let s(n) = 12*n**3 - 20*n**2 + 20*n. Let x(g) = -6*s(g) - 7*u(g). Let x(p) = 0. What is p?
0, 2
Let w = 9343 + -9340. Let x = 55 - 55. Factor x - b - 4/3*b**2 - 1/3*b**w.
-b*(b + 1)*(b + 3)/3
Factor -3360/13*k**2 - 544/13 - 50/13*k**3 + 2712/13*k.
-2*(k + 68)*(5*k - 2)**2/13
Let -2304/7 - 4/7*q**2 + 192/7*q = 0. Calculate q.
24
Suppose 150 + 30 = 4*b. Let w = -32 + b. Factor 4*f**5 + 4*f**3 + 35*f**2 + w*f**4 - 5*f**4 - 35*f**2.
4*f**3*(f + 1)**2
Suppose -390/7*a - 69/7*a**2 - 3/7*a**3 + 0 = 0. What is a?
-13, -10, 0
Let x(p) = 15*p**2 - 123*p - 2172. Let l(f) = 13*f**2 - 124*f - 2174. Let r(c) = -6*l(c) + 5*x(c). Factor r(w).
-3*(w - 56)*(w + 13)
Let c(w) be the third derivative of -1/60*w**5 - 201*w**2 - 1/1344*w**8 + 0*w + 1/24*w**4 - 1/160*w**6 + 1/210*w**7 + 0 + 0*w**3. Find n such that c(n) = 0.
-1, 0, 1, 2
Let j(d) = -20*d**3 - 671*d**2 - 1971*d - 450. Let a(k) = 20*k**3 + 669*k**2 + 1969*k + 450. Let x(l) = 3*a(l) + 2*j(l). Suppose x(s) = 0. What is s?
-30, -3, -1/4
Factor 252944*k - 21*k**3 - 505779*k - 98*k**2 + 252955*k - k**4.
-k*(k - 1)*(k + 10)*(k + 12)
Let k(t) be the third derivative of 0*t**3 + 0 + 0*t**4 + 1/20*t**5 - 20*t + 4*t**2 + 1/480*t**6. Solve k(v) = 0 for v.
-12, 0
Let q(i) be the second derivative of -i - 21/20*i**5 - 81/2*i**3 + 4 + 81/2*i**2 + 45/4*i**4. Factor q(z).
-3*(z - 3)**2*(7*z - 3)
Let l(k) = 4*k**2 + 11*k + 3. Let v be l(-8). Suppose 333 - v - 35*u**3 + 55*u**2 - 177 - 5*u = 0. What is u?
-3/7, 1
Let z(p) be the first derivative of 2*p**5/55 - 16*p**3/33 + 32*p/11 - 129. Determine h, given that z(h) = 0.
-2, 2
Let s(a) be the first derivative of 3*a**4/28 + 62*a**3/7 + 183*a**2/14 - 3163. Let s(w) = 0. What is w?
-61, -1, 0
Let b(u) be the third derivative of u**6/72 - 11*u**5/4 + 1815*u**4/8 - 14*u**3 + u**2 - 48. Let z(i) be the first derivative of b(i). Let z(m) = 0. What is m?
33
Let l = -484 + 512. Suppose 4*q = -l*q - 6*q. Solve -1/2*p**2 + q + 1/2*p = 0 for p.
0, 1
Let r(x) = -82*x - 1680. Let f be r(0). Let u = f - -1684. Solve -2/3*n**2 - u + 14/3*n = 0.
1, 6
Let p(u) = -u**3 + u**2 + 33*u - 2. Let c be p(6). Let d be (69/(-15) + 5)/(c/50). Determine r, given that -45/4*r + 75/4*r**2 - 35/4*r**3 + d*r**4 + 0 = 0.
0, 1, 3
Factor 158/9*r + 2/9*r**2 + 308/9.
2*(r + 2)*(r + 77)/9
Let c(y) be the second derivative of 1/10*y**4 + 1/50*y**5 + 1/5*y**2 - 18*y + 1/5*y**3 - 5. Factor c(h).
2*(h + 1)**3/5
Let b = -8849/3 - -2981. Let 0*h + 0*h**2 - b*h**4 + 20/3*h**3 + 0 + 6*h**5 = 0. Calculate h.
0, 2/9, 5
Let j(k) be the second derivative of k**4/60 - 41*k**3/5 + 15129*k**2/10 + 656*k. Factor j(l).
(l - 123)**2/5
Let n(g) = -2*g - 19*g - 12*g + 12*g. Let i be n(0). What is u in 1/2*u**3 - 1/6*u**4 + i + 1/6*u - 1/2*u**2 = 0?
0, 1
Let t(l) be the second derivative of -1/3*l**2 + 1/18*l**4 + 118*l + 0 + 0*l**3. Suppose t(r) = 0. What is r?
-1, 1
Suppose 19 = 13*z - 7. Suppose 5*m - 2 = -z*x, -8 + 11 = -m + 3*x. Factor m - 1/5*o**5 + 1/5*o**4 + 1/5*o**3 + 0*o - 1/5*o**2.
-o**2*(o - 1)**2*(o + 1)/5
Let i(r) = 38*r**3 - 130*r**2 - 478*r + 591. Let v(k) = 11*k**3 - 44*k**2 - 159*k + 198. Let g(a) = 6*i(a) - 21*v(a). Find j, given that g(j) = 0.
-4, 1, 51
Let i = -39365/6 + 1574213/240. Let w = -13/16 - i. Factor -16/5 + 4*v**3 - w*v**5 + 4/5*v**4 - 4/5*v**2 - 32/5*v.
-4*(v - 2)**2*(v + 1)**3/5
Suppose 12*q + 2 - 38 = 0. Factor -5*y**3 - 69*y**2 + 456 - 7*y**3 - 360*y + 11*y**q - 2*y**3 - 24.
-3*(y - 1)*(y + 12)**2
Let l(z) be the first derivative of -32/3*z**3 + 0*z**2 + 0*z - 294*z**6 - 92*z**4 - 280*z**5 + 3. Factor l(r).
-4*r**2*(7*r + 2)**2*(9*r + 2)
Factor 408*v**3 + 4068*v**2 + 471 + 8168*v + 4*v**4 - v**4 - 5*v**4 + 4985 + 262*v**3.
-2*(v - 341)*(v + 2)**3
Suppose -c = 0, n - 111*c + 106*c + 315 = 0. Let k be n/(-60)*(-6)/(-14). Let 3/2*o**5 - k*o**4 + 0*o + 0*o**2 + 3/4*o**3 + 0 = 0. Calculate o.
0, 1/2, 1
Suppose 0 = -7*m - 0 - 14. Let d(n) = -6*n**5 + 16*n**4 + 62*n**3 + 48*n**2 + 2*n. Let g(r) = r**5 - 2*r**4 + r**3 - r. Let h(a) = m*g(a) - d(a). Factor h(l).
4*l**2*(l - 6)*(l + 1)*(l + 2)
What is y in 111556/3 - 2/3*y**5 - 53116/3*y**3 + 219776/3*y**2 - 220*y**4 - 92518*y = 0?
-167, 1, 2
Let o = -135 + 145. Suppose -22 = -6*v - o. Suppose -27*t**3 + 23*t**v + 6*t - 36 + 24*t - 6*t + 13*t**4 - t**5 - 4*t**4 = 0. Calculate t.
-1, 2, 3
Suppose -2*y - 24*g - 8 = -28*g, -3*y + 5*g = 8. Determine x, given that -44*x**2 + 30 - 13*x + 2 + 0 + 5*x**3 + y = 0.
-1, 4/5, 9
Let f be (-3)/5 - ((-1)/(-5))/((-60)/2220). Factor -8/5*g**3 + 2 - f*g**2 + 32/5*g.
-2*(g - 1)*(g + 5)*(4*g + 1)/5
Suppose -2*x - x + 2684 = -i, 4476 = 5*x - i. Solve -4*u**4 - 70*u + 85*u**3 - x*u - 664*u**2 + 27*u**3 - 714*u - 900 = 0.
-1, 15
Let g(k) = k**2 + 6*k + 4. Let r be g(-6). Suppose 2*f = -2*y + 64, -40 = -4*f + y + 78. Solve 4*d + 15*d - 60*d**2 - 5*d**r + 21*d + f*d**3 = 0.
0, 2
Let o be 274/(-660) + (-29)/(-58) - 38/(-209). What is k in 2/15*k**2 - 2/5 + o*k = 0?
-3, 1
Let i(z) be the second derivative of z**4/15 - 812*z**3/15 + 82418*z**2/5 - 853*z. Factor i(s).
4*(s - 203)**2/5
Factor -79704/11*l**4 - 2250/11 - 103930/11*l**2 - 25800/11*l - 11664/11*l**5 - 165996/11*l**3.
-2*(l + 3)**2*(18*l + 5)**3/11
Let t(y) = y**3 + 6*y**2 - 45*y - 48. Let w be t(5). Let i(p) be the second derivative of 1/2*p**3 + 0*p**w + 0*p**4 + 26*p - 3/20*p**5 + 0. Solve i(f) = 0.
-1, 0, 1
Let i = 1/2118 - -933/17650. Let f = i - -56/75. Solve 2/5*t - 2/5*t**3 - 4/5*t**2 + f = 0.
-2, -1, 1
Let f(n) = -202*n**3 + 1469*n**2 - 3449*n - 1058. Let q(i) = 40*i**3 - 294*i**2 + 690*i + 212. Let s(a) = -6*f(a) - 31*q(a). Determine o, given that s(o) = 0.
-2/7, 4, 7
Let c(y) be the third derivative of y**7/2520 + y**6/24 + 15*y**5/8 - 91*y**4/24 + 10*y**2 + y. Let g(m) be the second derivative of c(m). Solve g(j) = 0.
-15
Let h(g) be the third derivative of g**6/420 - 32*g**5/105 + 391*g**4/84 + 152*g**3/7 - 65*g**2 - g - 6. Factor h(a).
2*(a - 57)*(a - 8)*(a + 1)/7
Let i(o) be the third derivative of 4*o**2 + 16 - 7/60*o**5 + 0*o**3 + 0*o - 1/12*o**4 - 1/70*o**7 - 1/15*o**6. Find a, given that i(a) = 0.
-1, -2/3, 0
Let n(p) = -6*p + 49. Let q be n(7). Let w be 1 + q + 124/(-20). Solve -w*m**5 + 0 - 4/5*m**3 + 0*m**2 + 12/5*m**4 + 0*m = 0.
0, 2/3
Let b(g) be the second derivative of -g**7/945 - g**6/108 - 2*g**5/135 - 78*g**2 - 31*g - 2. Let o(f) be the first derivative of b(f). Factor o(p).
-2*p**2*(p + 1)*(p + 4)/9
Factor -1/5*l**5 + 0*l**2 - 462/5*l**4 - 53361/5*l**3 + 0 + 0*l.
-l**3*(l + 231)**2/5
Determine u, given that -16/11 - 422/11*u**2 + 260/11*u**3 + 178/11*u = 0.
8/65, 1/2, 1
Solve 31*s - 4*s**3 + 14 + 6*s**2 + 658 - 59*s**2 - 15*s - 115*s**2 = 0 for s.
-42, -2, 2
Let v(q) be the third derivative of 0 + 29/48*q**4 + 116*q**2 + 0*q + 1/120*q**5 - 5/2*q**3. Factor v(l).
(l - 1)*(l + 30)/2
Let g(s) = 2*s**3 + 60*s**2 - s - 1. Let z(j) = -1 + 1 - 63*j + 62*j - 1 + 0. Let v(i) = -g(i) + z(i). Factor v(r).
-2*r**2*(r + 30)
Let j(x) = 741*x**2 - 6*x + 8. Let n(k) = k - 1. Let h(v) = -5*j(v) - 40*n(v). Suppose h(l) = 0. What is l?
-2/741, 0
Let x(r) be the third derivative of 2*r**3 - 9 + 0*r - 1/3*r**4 + 10*r**2 - 1/1080*r**6 + 1/36*r**5. Factor x(l).
-(l - 6)**2*(l - 3)/9
Let k = 2/1376911 + 4130723/6884555. Factor 3/5*n + 18/5 - k*n**2.
-3*(n - 3)*(n + 2)/5
Let z be (-26)/39*3 + (1 + 17)/3. Let f(h) be the first derivative of -1/18*h**3 + 1/4*h**2 + 7 + 1/6*h - 1/8*h**z. Factor f(d).
-(d - 1)*(d + 1)*(3*d + 1)/6
Let a(r) be the second deriva