Let m be (((-2470)/(-273) - 10) + (-5)/(-15)*2)*-7. Factor -125/2*a - 15/2*a**3 + 0 + 75/2*a**m + 1/2*a**4.
a*(a - 5)**3/2
Factor 3004/7*s - 22/7*s**2 - 1632/7.
-2*(s - 136)*(11*s - 6)/7
Let y(u) be the first derivative of -u**5/20 - 3*u**4 - 101*u**3/4 - 167*u**2/2 - 123*u - 79. Factor y(k).
-(k + 2)**2*(k + 3)*(k + 41)/4
Let a(f) be the first derivative of 5*f**3/3 - 215*f**2/2 - 1633. Let a(o) = 0. Calculate o.
0, 43
Let 5/2 + 7/4*t - 1/4*t**3 - t**2 = 0. Calculate t.
-5, -1, 2
Let y = 1289853 - 1289851. Factor -19/5 + 18/5*a + 1/5*a**y.
(a - 1)*(a + 19)/5
Let t(z) = z**3 + 1576*z**2 - 1583*z + 8. Let q(d) = d**3 - 1574*d**2 + 1582*d - 12. Let h(l) = 2*q(l) + 3*t(l). Factor h(f).
5*f*(f - 1)*(f + 317)
Let q(g) = 125*g + 24877. Let p be q(-199). Suppose 2/7*d**3 - 2/7*d - 4/7 + 4/7*d**p = 0. What is d?
-2, -1, 1
Suppose 12685*g**5 + 565*g**3 - 1475*g**2 + 215*g**4 - 2910*g - 6333*g**5 - 6347*g**5 + 3600 = 0. Calculate g.
-40, -3, 1, 2
Let f(o) = 4*o**2 - 20394*o + 26010106. Let h(k) = -3*k - 53. Let q(l) = f(l) + 2*h(l). Solve q(j) = 0 for j.
2550
Let z be (1 + 2)/3 + 3. Let o(c) = 19*c - 300. Let u be o(16). Let 2*p**5 - 15*p**4 + 19*p**4 - 22*p**3 + 12*p**2 + u*p**z = 0. Calculate p.
-6, 0, 1
Let q(p) be the first derivative of 1/4*p**4 - 172 + 0*p - 5/3*p**3 + 3*p**2. Solve q(s) = 0.
0, 2, 3
Let t(a) be the second derivative of 0 + 5/2*a**2 + 15*a**4 + 91*a - 25/2*a**3. Factor t(m).
5*(3*m - 1)*(12*m - 1)
Let j(f) be the third derivative of f**7/70 - 49*f**6/40 - 573*f**5/20 - 995*f**4/8 - 236*f**3 + 2967*f**2. Let j(b) = 0. Calculate b.
-8, -1, 59
Factor 0 - 1/3*k**3 + 44/3*k + 43/3*k**2.
-k*(k - 44)*(k + 1)/3
Let t(o) be the first derivative of 3*o**4/32 + 45*o**3/4 + 33*o**2 + 1376. Factor t(b).
3*b*(b + 2)*(b + 88)/8
Suppose 16*r = 9*r + 14. Suppose a - 12 = -0*a + 2*k, 1 = -r*a - k. Factor -2*d**3 + d**4 + d**3 + 8*d**4 + 124*d - 10*d**3 - 24 - 70*d**a.
(d - 2)**2*(d + 3)*(9*d - 2)
Let q(w) be the third derivative of w**6/180 - w**4/12 - 7*w**3 + 53*w**2. Let p(g) be the first derivative of q(g). Factor p(t).
2*(t - 1)*(t + 1)
Suppose -4*i = -5*j + 23, -j = -3*i + 2 - 0. Suppose 7*z - 77 = j. Factor 3*n**3 - z*n**2 - 7*n**3 + 3*n + 5*n + 12 - 4*n.
-4*(n - 1)*(n + 1)*(n + 3)
Let p(f) be the second derivative of -7*f**6/50 + 78*f**5/25 - 483*f**4/20 + 423*f**3/5 - 648*f**2/5 - 8*f + 384. Find m such that p(m) = 0.
6/7, 3, 8
Suppose 5*u - 622 = 4*a, -4*u - 5*a + 2*a = -510. Let g be 4/(-7) + 100/u. Factor -2/9*b**2 + 0 + g*b.
-2*b*(b - 1)/9
Suppose 0 = -3*h - 2*a + 2, -2*h + 6 = -a. Suppose 3*t = -h*t + 65. Find n, given that -t*n**5 + n**4 + 4*n**3 + 9*n**5 - 5*n**2 + 3*n**4 + n**2 = 0.
-1, 0, 1
Let g(z) be the first derivative of -z**5/90 - 53*z**4/18 - 2809*z**3/9 - 4*z**2 - 3*z + 73. Let k(q) be the second derivative of g(q). Solve k(l) = 0.
-53
Solve 290/9*b**3 - 124/9*b**2 - 272/9*b**4 + 16/9*b + 10*b**5 + 0 = 0.
0, 2/9, 4/5, 1
Let a be 216/48*12/1. Determine r so that -36*r**5 - a*r**5 + 55*r**5 + 95*r**4 + 10*r + 5*r**2 - 75*r**3 = 0.
-2/7, 0, 1
Let s(o) be the second derivative of -o**7/14 - 33*o**6/5 - 144*o**5/5 - 95*o**4/2 - 63*o**3/2 - 2098*o. Determine m so that s(m) = 0.
-63, -1, 0
Suppose -5*s + 3 + 7 = -l, -3*l = -s - 12. Let g be (-1554)/(-504) + l*(-1)/6. Determine i, given that g + 3*i + 3/4*i**2 = 0.
-3, -1
Let o(h) = -h**3 - 6*h**2 + 5*h - 16. Let b be o(-7). Let q be (1/2)/(b/(-12)). Factor -20*x**2 - 30*x**3 + 10*x**3 + 13*x**q + 20*x + 12*x**3.
5*x*(x - 2)**2
Let n(z) be the first derivative of -5*z**5 + 415*z**4/4 - 1430*z**3/3 + 280*z**2 + 480*z - 314. Determine c so that n(c) = 0.
-2/5, 1, 4, 12
Let c(z) be the third derivative of -z**5/105 + 1669*z**4/84 + 835*z**3/21 + 84*z**2 + 15. Determine j, given that c(j) = 0.
-1/2, 835
Let r(d) = d**4 - 2*d**2 - 2*d. Let p(x) = 22*x**4 - 127*x**3 - 17*x**2 + 125*x - 6. Let k(u) = -2*p(u) + 2*r(u). Find j, given that k(j) = 0.
-1, 1/21, 1, 6
Let y(i) be the third derivative of 5*i**2 - 1/40*i**5 - 1 + 0*i**3 + 0*i - 1/16*i**4. Factor y(b).
-3*b*(b + 1)/2
Let o be (3/12 + (-5)/(-4))*8/6. Find x such that -4*x + 2/3*x**3 + 16/3 - 2*x**o = 0.
-2, 1, 4
Let d = 348775/2 - 174386. Determine v, given that d*v**2 - 9/4*v**3 + 0 + 4*v + 1/4*v**4 = 0.
-1, 0, 2, 8
Let w = -978 + 995. Suppose 7*l - 18 = w. Solve -13/3*v**3 + 2*v**4 + 0 - 4/3*v + 4*v**2 - 1/3*v**l = 0 for v.
0, 1, 2
Let r be (21/(7/(-1)))/((-3)/357). Let b = r + -1063/3. Factor b*p - 7*p**2 + 2/3*p**3 + 4/3 + 7/3*p**4.
(p - 1)**2*(p + 2)*(7*p + 2)/3
Suppose -79 = -5*z - 5*g - 64, -3 = -g. Factor 0*q**3 + z*q - 2/3 + 4/3*q**2 - 2/3*q**4.
-2*(q - 1)**2*(q + 1)**2/3
Let x(t) be the first derivative of -1/6*t**3 - 9/2*t**2 + 35 - 81/2*t. Suppose x(d) = 0. What is d?
-9
Let w be 592/(-1566)*(297/(-22) - -15). Let g = -1/87 - w. Suppose g*r**2 - 4/9 - 8/9*r = 0. Calculate r.
-2/5, 2
Let c = -2190/203 + 462/29. Let c*f - 4/7 - 80/7*f**2 = 0. What is f?
1/5, 1/4
Let c be (-2)/(-14)*(-678797)/(-3958). Find g, given that -51/2*g**2 - 8 - 1/2*g**4 - 19/2*g**3 - c*g = 0.
-16, -1
Let c be 5/(-2)*15/(-225)*18. Factor 0*d**4 - 17 + 38*d**2 - 24*d - 31 + 24*d**c + 3*d**4 + 7*d**2.
3*(d - 1)*(d + 1)*(d + 4)**2
Let h(t) be the third derivative of 1/210*t**5 + 190*t**2 + 0*t + 9/28*t**4 - 58/21*t**3 + 0. Suppose h(c) = 0. Calculate c.
-29, 2
Find d, given that -1/3*d**3 - 8/9 + 4/3*d + 2/9*d**2 = 0.
-2, 2/3, 2
Factor -2/3*h**2 - 92/21*h + 2.
-2*(h + 7)*(7*h - 3)/21
Suppose -2/11*f**5 + 128/11*f - 52/11*f**2 + 16/11*f**4 - 26/11*f**3 - 64/11 = 0. What is f?
-2, 1, 4
Let i(h) be the first derivative of 15*h**6/2 - 264*h**5/5 + 327*h**4/4 + 40*h**3 - 186*h**2 + 144*h + 645. Find a such that i(a) = 0.
-1, 2/3, 1, 6/5, 4
Let u = -36 + 40. Let b(s) = 51*s - 9. Let j be b(u). Determine i, given that 19 + j*i**2 + 15*i**3 - 21*i**4 - 135*i - 56 - 17 = 0.
-3, -2/7, 1, 3
Let u be 7/28*(-1 + (11 - 2)). Factor 10 + 6*i + 47*i - 5*i**3 + 128*i**2 - 242*i**u + 128*i**2.
-(i - 5)*(i + 2)*(5*i + 1)
Let p be (-3)/(59 + -67 - 26/(-4)). Let q(i) be the first derivative of -p*i**2 - 14/3*i**3 + 0*i - 15. Let q(c) = 0. What is c?
-2/7, 0
Let v(a) be the second derivative of -a**7/42 + a**6/8 - a**5/4 + 5*a**4/24 + 21*a**2/2 - 66*a. Let o(r) be the first derivative of v(r). Factor o(d).
-5*d*(d - 1)**3
Let z = -16798 - -16801. Let q(p) be the third derivative of -13/24*p**4 + 0 + 1/30*p**6 - 2/3*p**z + 0*p + 13/60*p**5 - 14*p**2. Find w, given that q(w) = 0.
-4, -1/4, 1
Let d(l) = -9*l**4 + 22*l**3 - 13*l**2 - 15*l - 3. Let k(j) = 16*j**4 - 46*j**3 + 24*j**2 + 31*j + 5. Let o(a) = -5*d(a) - 3*k(a). Find s, given that o(s) = 0.
-2/3, 0, 1, 9
Let x(u) be the first derivative of u**7/3360 - u**6/480 - u**5/120 + u**4/8 - u**3/3 - 27*u + 246. Let p(j) be the third derivative of x(j). Factor p(t).
(t - 3)*(t - 2)*(t + 2)/4
Let t be (-60)/40*(-243)/108. Let t - 27/8*x**2 + 3/8*x - 3/8*x**3 = 0. What is x?
-9, -1, 1
Let l be ((-54)/(-30))/((-1)/(-10)). Suppose 0 = p - 3, w + p = -4*p + l. Factor 35*r**5 - 2*r**3 - 68*r**4 + 12*r**w + 113*r**4.
5*r**3*(r + 1)*(7*r + 2)
Factor 0*p + 0*p**2 - 117/8*p**3 + 0 + 3/8*p**4.
3*p**3*(p - 39)/8
Let j(l) = -48680*l**2 + 5185*l - 520. Let o(g) = 1803*g**2 - 192*g + 19. Let b(m) = -2*j(m) - 55*o(m). Factor b(u).
-5*(19*u - 1)**2
Let c(b) be the third derivative of -b**7/14 - 877*b**6/40 + 53*b**5/2 + 44*b**4 + b**2 + 965*b. Find p such that c(p) = 0.
-176, -2/5, 0, 1
Let f(x) = -2*x**3 - 54*x**2 - 340*x - 284. Let i(b) = -6*b**3 - 161*b**2 - 1019*b - 853. Suppose 2 = -3*c - 10. Let o(z) = c*i(z) + 11*f(z). Factor o(a).
2*(a + 1)*(a + 12)**2
Let d be -11*1 + ((-5)/6 - (-15779)/1302). Solve d*f**3 + 16/7*f**2 + 36/7 + 6*f = 0 for f.
-3, -2
Let n(m) = 2*m**5 + 2*m**4 + 2*m**3 - m + 1. Let y(r) = 9*r**5 + 18*r**4 - 156*r**3 + 666*r**2 - 1057*r + 544. Let q(z) = 4*n(z) - y(z). Factor q(h).
-(h - 3)**3*(h - 1)*(h + 20)
Let o(u) = -24*u**3 + 4866*u**2 - 6458*u + 2146. Let x(m) = -m**3 + m - 1. Let s(w) = o(w) - 6*x(w). Factor s(r).
-2*(r - 269)*(3*r - 2)**2
Let n = 720 + -581. Factor -10 + n*j**2 - 60*j**2 - 5*j - 25*j**3 - 39*j**2.
-5*(j - 1)**2*(5*j + 2)
Let t be 51 - (-23)/(2530/(-4125)). Solve 3/2*y**3 + 0 + t*y**2 + 21*y = 0.
-7, -2, 0
Let y(q) be the first derivative of -q**4/10 - 892*q**3/15 + 447*q**2/5 - 971. What is 