185). Factor 25/6*o**u - 15/2 - g*o**3 - 5/2*o.
-5*(o - 3)**2*(o + 1)/6
Let k(y) be the third derivative of y**7/84 + 143*y**6/48 - y**5/8 - 2135*y**4/48 + 715*y**3/6 + 4*y**2 - 129*y. Determine u, given that k(u) = 0.
-143, -2, 1
Let f(d) be the third derivative of d**6/360 - 17*d**5/180 + 7*d**4/36 + 16*d**3/9 - 2154*d**2. Solve f(c) = 0 for c.
-1, 2, 16
Factor -1 - 3*s**2 - 49/4*s.
-(s + 4)*(12*s + 1)/4
Let b(r) be the third derivative of 1/75*r**6 - 1/120*r**8 - 33*r**2 + 0*r**5 + 0*r**4 + 0 + 4/175*r**7 + 0*r**3 + 0*r. Factor b(w).
-2*w**3*(w - 2)*(7*w + 2)/5
Let v(h) = -h**3 - h**2 + h - 18. Let x be v(0). Let p = 33 + x. Let 29*a**3 + 35*a + 0*a**2 - 25*a**2 - 24*a**3 - p = 0. Calculate a.
1, 3
Suppose 492*a - 235*a - 60 = 227*a. Let o(i) be the first derivative of 0*i + 14 - 98/5*i**5 + 21/2*i**4 + 4*i**a + 16*i**3. Factor o(l).
-2*l*(l - 1)*(7*l + 2)**2
Let j be (-1 - 2) + 5 + (-3)/(-1). Factor -20*w - 10*w**3 + 0 + 15 + j + 25*w**4 - 75*w**2.
5*(w - 2)*(w + 1)**2*(5*w - 2)
Solve -6203*y**4 - 2093087*y**3 - 1242507157 + 103*y**4 - 4307025547*y - 2*y**5 - 4112643*y**3 - 855037035 + 105743627*y - 2109937360*y**2 = 0.
-1016, -1
Let m be 6 + 1*0/(-4). Find p such that -13*p**5 - 24*p**5 - 7*p**2 - 54*p**3 - 53*p**4 + 25*p**5 + m*p = 0.
-3, -1, -2/3, 0, 1/4
Find g, given that -33*g**2 + g**4 + 15*g - 2*g**3 + 0*g**4 - 62*g + 56 + 25*g = 0.
-4, -2, 1, 7
Suppose 0 = 2*j + 312 - 308, -3*f + 5*j + 19 = 0. Let d(l) be the second derivative of 8 + 3*l**2 + 4/3*l**f + 1/6*l**4 - 2*l. Factor d(h).
2*(h + 1)*(h + 3)
Suppose -4173*b + 1280 + 8197*b - 4328*b - 4*b**2 = 0. What is b?
-80, 4
Let g = -101 - -96. Let n be (-1)/2*(-2014)/(-209) - g. Determine j, given that -n*j**3 + 12/11*j**2 + 16/11 - 24/11*j = 0.
2
Factor 0 - 5792/3*j + 4/3*j**3 - 5788/3*j**2.
4*j*(j - 1448)*(j + 1)/3
Suppose -b - 14 = -23. Let k be (4 - 24/b)*18. Suppose -30*g**3 + g**4 - 20*g**4 + 7*g**5 + k*g**3 = 0. What is g?
-2/7, 0, 3
Let z(m) = -2*m**3 - 30*m**2 + 2855*m + 140. Let b be z(-46). Find n such that -2*n**5 + 42*n**b + 112/3*n - 38/3*n**4 + 8 + 2*n**3 = 0.
-6, -1, -1/3, 2
Suppose 0 = -4*h + 2*v + 151 - 103, -2*v - 32 = 4*h. Factor 441 + 21*q + 1/4*q**h.
(q + 42)**2/4
Let s(i) be the third derivative of i**5/60 + 5*i**4/12 - 11*i**3/6 - 2*i**2 - 73. Factor s(d).
(d - 1)*(d + 11)
Factor -331*m**2 - 117*m**2 + 1052 - 1292*m - 4*m**3 + 1237 + 16 - 561.
-4*(m - 1)*(m + 4)*(m + 109)
Let q be (-84)/(-24)*12489/42. Let s = 1041 - q. Find k, given that -k**2 + 0*k + s*k**3 + 0 = 0.
0, 4
Suppose 4*y - 31*k - 88 = -27*k, -66 = -4*y + 3*k. Determine m so that -2/3*m**2 + y + 7/6*m = 0.
0, 7/4
Let r be (-728)/(-960) + 3615/(-5784). Factor -r*v**2 - 10082/15 + 284/15*v.
-2*(v - 71)**2/15
Let r be 60/14 + -4*1/14. Factor 55*i**4 + 9*i**2 - 64*i**r - 2*i - 6*i**3 + 8*i.
-3*i*(i - 1)*(i + 1)*(3*i + 2)
Suppose 2*x + 0*x = 3*j + 297, 4*x - 3*j - 597 = 0. Solve -x - 80*f**2 - 5*f**5 + 6*f**3 + 12*f**4 + f**5 + 62*f**3 - 384*f - 4*f**3 - 106 = 0.
-2, -1, 4
Let c = -9/3679 + 11055/7358. Suppose 6*t + 6 - c*t**2 - 3/2*t**3 = 0. Calculate t.
-2, -1, 2
Let g(i) be the third derivative of i**8/112 + 31*i**7/70 - 33*i**6/20 + i**5/10 + 65*i**4/8 - 33*i**3/2 - 1178*i**2. Suppose g(k) = 0. Calculate k.
-33, -1, 1
What is t in 5*t**4 + 60*t**3 + 30*t**3 + 196*t**2 + 15*t**2 + 189*t**2 + 210*t - 105*t**2 = 0?
-14, -3, -1, 0
Let n(c) be the third derivative of -c**6/480 + c**5/32 + 3*c**4/16 - 31*c**3/6 - 122*c**2. Let k(d) be the first derivative of n(d). Factor k(f).
-3*(f - 6)*(f + 1)/4
Let i(j) be the first derivative of -j**5/15 - 43*j**4/3 - 3698*j**3/3 + j**2 - 52*j + 113. Let l(r) be the second derivative of i(r). Solve l(u) = 0.
-43
Determine l, given that -1/2*l**5 + 0 + 5/2*l**3 - 3/2*l**4 + 3/2*l**2 - 2*l = 0.
-4, -1, 0, 1
Suppose 13*b = 14*b - 8*b. Let j(y) be the first derivative of 3/4*y**4 + b*y**2 + 1/2*y**6 + 16 - 6/5*y**5 + 0*y**3 + 0*y. Factor j(o).
3*o**3*(o - 1)**2
Let q be 0/1 + -1*70/(-5). Suppose -j + q = 8. Factor 6*i**2 - i**3 + 3*i**3 - 2*i + 0*i - j + 0*i**3.
2*(i - 1)*(i + 1)*(i + 3)
Let u(z) be the first derivative of -z**4/6 - 2*z**3/9 + 2*z**2/3 - 3818. Factor u(t).
-2*t*(t - 1)*(t + 2)/3
Suppose 8*w - 71*w = 63*w. Factor 1/8*l**2 + w - 3/4*l + 1/8*l**3.
l*(l - 2)*(l + 3)/8
Let u(m) be the first derivative of m**6/15 + 14*m**5/25 - m**4 - 224*m**3/15 - 96*m**2/5 - 6721. Solve u(f) = 0 for f.
-6, -4, -1, 0, 4
Factor -8/3*f + 8 - 2/3*f**2.
-2*(f - 2)*(f + 6)/3
Let b = -63 + 68. Suppose b*o - y = 124, -4*o - 2*y + 3*y + 99 = 0. Determine n so that 2*n - o + 47 - 2*n**3 + 2*n**2 - 24 = 0.
-1, 1
Suppose -4 = -h + 2. Let z be (3/(-12)*-4)/(2/h). Solve 15*l**4 - 6*l**3 + 4 - 12*l - 14*l**4 + z*l**2 + 10*l**2 = 0 for l.
1, 2
Let k = 423/92 - 77/23. Let x(o) be the first derivative of k*o**4 - 5*o**2 + 6*o**5 + 20 + 0*o - 25/3*o**3. Solve x(c) = 0 for c.
-2/3, -1/2, 0, 1
Let y be 8 + (30/40 - (14 + -4 + -2)). Let n(j) be the first derivative of 9/10*j**5 - 9/2*j + 5 - 21/2*j**2 - 8*j**3 - y*j**4. Determine k so that n(k) = 0.
-1, -1/3, 3
What is v in -5*v**2 + 233739 - 116361 - 116878 = 0?
-10, 10
Let r be ((-2)/42)/(((-2)/(-14))/((-468)/273)). Suppose r + 2/7*f**2 - 6/7*f = 0. What is f?
1, 2
Let h(a) = 2*a**2 - 610 - 25*a + a**2 + 0*a**2 + 621. Let b be h(8). Factor 2/11*u - 10/11*u**2 + 2/11 + 6/11*u**b.
2*(u - 1)**2*(3*u + 1)/11
Suppose o = 2*o, -8*j + 15 = -3*j + 4*o. Suppose 4*l + 4 = -d, 0 = -5*l + 3*l + d + 4. Find q such that -7/3*q**4 - 3*q**j + l*q - 2/3*q**2 + 0 = 0.
-1, -2/7, 0
Suppose 5*a + 138 - 338 = 0. Suppose a = 12*h + 8*h. Factor 0*t - 3/5*t**3 + 0*t**h + 0.
-3*t**3/5
Let r(y) = 2*y**2 - 62*y + 510. Let j(n) = -4*n**2 + 123*n - 1019. Let g = -47 - -45. Let k(l) = g*j(l) - 5*r(l). Determine o, given that k(o) = 0.
16
Let v(r) = -12*r**3 + 886*r**2 - 136816*r + 6885922. Let y(q) = -q**3 - 2*q**2 - q + 2. Let h(f) = 2*v(f) - 20*y(f). Solve h(l) = 0 for l.
151
Let x(g) be the second derivative of -g**8/105 + g**7/42 + g**6/15 + 2*g**3/3 - g**2/2 + 48*g. Let v(z) be the second derivative of x(z). Factor v(a).
-4*a**2*(a - 2)*(4*a + 3)
Let m(k) be the second derivative of k**6/1620 - 8*k**5/135 + 64*k**4/27 + 23*k**3/3 + k - 61. Let u(l) be the second derivative of m(l). Factor u(x).
2*(x - 16)**2/9
Let f(q) be the third derivative of 26*q**2 - 2 + 0*q + 7/60*q**5 + 3/2*q**3 + 1/120*q**6 + 5/8*q**4. Suppose f(j) = 0. What is j?
-3, -1
Let v(l) be the first derivative of -l**3 - 285*l**2 - 27075*l + 1897. Find t such that v(t) = 0.
-95
Let i = 115925 - 115923. What is q in -1/9*q**i - q**3 + 0 + 1/9*q - 11/9*q**4 - 4/9*q**5 = 0?
-1, 0, 1/4
Let s(t) be the second derivative of -1/78*t**4 - 144/13*t**2 + 8/13*t**3 + 2 - 7*t. Factor s(m).
-2*(m - 12)**2/13
Factor 17*b**2 + 381*b + 320 - 17*b + 23*b**2 - 4*b**3.
-4*(b - 16)*(b + 1)*(b + 5)
Let w(x) = -36*x + 146. Let n be w(4). Suppose -3*z + z = 0, -n*z - 9 = -3*g. Factor -g + 21/2*j - 21/2*j**3 + 3*j**2.
-3*(j - 1)*(j + 1)*(7*j - 2)/2
Let z be 956/1195*(-1 + 2 + -5)/(23 + -24). Factor 0*t + 0 - z*t**4 - 8/5*t**2 + 4*t**3 + 4/5*t**5.
4*t**2*(t - 2)*(t - 1)**2/5
Let j(h) be the third derivative of -11/36*h**5 + 0*h**3 + 0 - 5/6*h**4 + 1/72*h**6 - 124*h**2 + 0*h. What is r in j(r) = 0?
-1, 0, 12
Let w(i) = -7*i**5 - 4*i**4 - 29*i**3 - 32*i**2 - 8. Let s(j) = j**5 + j**2 + 1. Let m(h) = -8*s(h) - w(h). Suppose m(r) = 0. What is r?
-3, -1, 0, 8
Suppose -104 = -7*q + 211. Suppose 8*h + 13 = q. Find y such that -15*y**h + 2*y**5 - 13*y**3 - 14*y**3 - 3*y - 5*y**5 - 3*y - 21*y**2 = 0.
-2, -1, 0
Factor -1298/9*u - 1168/9 - 128/9*u**2 + 2/9*u**3.
2*(u - 73)*(u + 1)*(u + 8)/9
Let z be (1 - 4/3) + 49 + -36 + -12. Factor z*j + 5/3*j**2 + 0 + 1/3*j**4 + 4/3*j**3.
j*(j + 1)**2*(j + 2)/3
Let p be (20/5)/((-36)/(-7551)). Let t = -837 + p. Suppose -32/3*c - 4/3*c**t + 12 = 0. What is c?
-9, 1
Let l(v) be the first derivative of 2*v**5/25 - 611*v**4/10 + 82824*v**3/5 - 8364816*v**2/5 - 16979328*v/5 - 707. Factor l(o).
2*(o - 204)**3*(o + 1)/5
Let r be 7316/25389 - (-4)/(-18). Let y = r - -128/819. Factor 0*z + 0 + y*z**2.
2*z**2/9
Let c(i) be the second derivative of -5*i**5/11 + 40*i**4/33 - 23*i**3/22 + 9*i**2/22 + 3244*i. Factor c(t).
-(t - 1)*(10*t - 3)**2/11
Let l(q) be the first derivative of q**5 + 325*q**4/2 - 1340*q**