Let i(l) be the second derivative of -l**7/7560 + l**6/60 - 9*l**5/10 + 25*l**4/12 - 45*l. Let o(s) be the third derivative of i(s). Let o(q) = 0. Calculate q.
18
Let y(c) = 10*c - 213. Let m be y(22). Suppose 0 = m*q + 46 - 74. Suppose 3/7*u**q + 1/7*u**2 - 1/7*u**5 + 0 - 3/7*u**3 + 0*u = 0. What is u?
0, 1
Let c(u) be the first derivative of -1764*u - 4/3*u**3 - 99 - 84*u**2. Factor c(r).
-4*(r + 21)**2
Let t(u) be the first derivative of -u**3/18 - 439*u**2/12 + 220*u/3 + 4394. Factor t(l).
-(l - 1)*(l + 440)/6
Let r be 5*2 + -11 + 14. Suppose -25 - 14 = -r*d. Factor 0 - 6/7*b + 3/7*b**4 - 12/7*b**d + 15/7*b**2.
3*b*(b - 2)*(b - 1)**2/7
Let p(m) be the third derivative of -1/42*m**7 + 1 + 0*m + 5/6*m**4 - 5/6*m**3 + 1/6*m**6 + 181*m**2 - 1/2*m**5. Factor p(u).
-5*(u - 1)**4
Let j(a) = 4*a**2 + 456*a + 1284. Let w(b) = -4*b**2 - 457*b - 1275. Let v(p) = 5*j(p) + 4*w(p). Factor v(u).
4*(u + 3)*(u + 110)
Let q(a) be the second derivative of a**4/114 - a**3/57 - 6*a**2/19 - 9*a - 97. Factor q(g).
2*(g - 3)*(g + 2)/19
Let h be ((-4)/3*(-15)/(-360))/(50/(-100)). Factor 0 + 4/3*a + h*a**4 - 1/9*a**3 - 8/9*a**2.
a*(a - 2)**2*(a + 3)/9
Let q be 108/33 - 1832/(-2519). Determine s so that -14*s - 86/7*s**3 + 0 + 46*s**2 + 6/7*s**q = 0.
0, 1/3, 7
Suppose 4*l + 4*i = 84, -l = -3*i - i - 6. Suppose 0 = 5*z + 2*m - 21, 8*m = 2*z + 4*m + 6. Factor -83*b - 21*b**3 + 8*b + 30*b**2 + l*b**z.
-3*b*(b - 5)**2
Let q(l) be the first derivative of -l**5 + 45*l**4/2 + 100*l**3/3 - 45*l**2 - 95*l - 1187. Determine y, given that q(y) = 0.
-1, 1, 19
Let v = -596 + 396. Let g be 8/(-6)*(-5)/v*-12. Factor 4/5*s**2 + 0 - g*s - 2/5*s**3.
-2*s*(s - 1)**2/5
Let x be ((2 - 5) + 2)/(9/(-27)). Suppose -3*s**x + 0*s - 18*s**2 - 36*s - 2 + 9*s + 2 = 0. What is s?
-3, 0
Determine a so that 3623*a**2 + 5400 + 86*a**4 + 3*a**5 - 14*a**4 + 0*a**4 + 6660*a - 557*a**2 + 2075*a**3 - 1400*a**3 = 0.
-6, -5, -2
Let n(j) be the third derivative of j**5/90 + 71*j**4/8 + 319*j**3/18 + 861*j**2 - 1. Factor n(q).
(q + 319)*(2*q + 1)/3
Let j(c) be the second derivative of -1/5*c**5 - 8*c**2 + 2/21*c**7 - 2/5*c**6 + 7/3*c**4 + 42*c + 1 + 0*c**3. Determine q, given that j(q) = 0.
-1, 1, 2
Let c(m) = 2*m**4 + m**3 - m**2 - 2*m - 2. Let d(i) = -338*i**5 - 2310*i**4 - 6162*i**3 - 7990*i**2 - 5054*i - 1254. Let u(r) = -2*c(r) + d(r). Factor u(x).
-2*(x + 1)**3*(13*x + 25)**2
Let p be 270/(9/(-21)*(-28)/(-40)). Let n = p - -905. Suppose 2/17*g**4 + 10/17*g**3 + 0 - 4/17*g**n + 4/17*g**2 + 0*g = 0. Calculate g.
-1, -1/2, 0, 2
Let f(a) be the second derivative of -2/9*a**3 - 1/10*a**5 + 0 - 41*a - 1/90*a**6 - 1/4*a**4 + 0*a**2. Factor f(g).
-g*(g + 1)**2*(g + 4)/3
Let j = -81 + 69. Let s be j/15*20/(-4). Factor 4*m**4 - 4*m**3 + 32*m - s*m**2 - 67*m + 39*m.
4*m*(m - 1)**2*(m + 1)
Let c(x) be the third derivative of x**5/20 - 15*x**4/4 + 112*x**3 + 2*x**2 - 20*x + 5. Let c(z) = 0. What is z?
14, 16
Factor -884*u**2 - 264*u + 90*u + 86*u + 84*u - 3*u**3 + 7*u**3 + 884.
4*(u - 221)*(u - 1)*(u + 1)
Factor 540/7*n**2 + 78 + 3/7*n**3 - 1089/7*n.
3*(n - 1)**2*(n + 182)/7
Let r = -10340/57567 + 18/619. Let i = r - -256/465. Let 0 - 8/5*y**2 + i*y**3 + 6/5*y = 0. Calculate y.
0, 1, 3
Let u(l) = 9*l**2 - 74 - 2*l**3 + l + 2*l + l**3 + 53. Let v be u(9). Suppose t - 2*t**3 - v*t + 7*t**3 = 0. What is t?
-1, 0, 1
Let j be 493/435 - -14 - 15. Determine y, given that -j*y**2 + 0 - 6/5*y = 0.
-9, 0
Let t = 9396 + -9391. Let z(f) be the second derivative of 1/6*f**4 + 0*f**2 + 3/40*f**t - 17*f + 1/12*f**3 + 0. What is b in z(b) = 0?
-1, -1/3, 0
Factor 75 - 1/2*d**2 + 73/2*d.
-(d - 75)*(d + 2)/2
Suppose 100/7*w**4 + 0 - 52/7*w**2 + 40/7*w**3 + 8/7*w = 0. Calculate w.
-1, 0, 1/5, 2/5
Let a(h) = -14*h + 28. Let n be a(2). Let v(j) be the third derivative of 0*j**6 + 0*j - 4*j**2 - 2/735*j**7 + 1/35*j**5 + 1/21*j**4 + n*j**3 + 0. Factor v(b).
-4*b*(b - 2)*(b + 1)**2/7
Let m(b) be the second derivative of -b**7/21 - b**6/5 + 7*b**5/2 + 25*b**4/2 - 250*b**3/3 + 2004*b. Let m(q) = 0. What is q?
-5, 0, 2, 5
Let p be (1 - 40)*10*1/108. Let r = 1/18 - p. Suppose 0 + 2/3*m + 7/3*m**4 + 16/3*m**3 + r*m**2 = 0. Calculate m.
-1, -2/7, 0
Let s(w) = 8*w**2 - 8*w - 10. Let t(l) = -728*l**2 - 15*l - 20 + 376*l**2 + 367*l**2. Let z be 1 + -2*1 + -2. Let y(o) = z*t(o) + 5*s(o). Factor y(j).
-5*(j - 2)*(j + 1)
Let k(m) be the second derivative of -m**8/23520 + m**7/2940 + m**6/630 + 23*m**4/12 + m**2/2 + 64*m. Let a(j) be the third derivative of k(j). Factor a(v).
-2*v*(v - 4)*(v + 1)/7
Let s = 37 - 41. Let b be 4 - 8 - -4 - s. Let o(f) = -18*f**3 - 30*f**2 - 14*f - 2. Let x(i) = -i**3 - i**2 - i - 1. Let d(g) = b*x(g) - o(g). Factor d(v).
2*(v + 1)**2*(7*v - 1)
Suppose 2*j - 2*k = k - 9, k = -5*j - 31. Let n be ((-16)/j)/((-136)/(-204)). Suppose 63/4*r**3 - 21/4*r**5 - 3/2*r**n - 3*r - 6*r**2 + 0 = 0. What is r?
-2, -2/7, 0, 1
Let g(q) be the second derivative of -q**4/6 - 12*q**3 - 224*q**2 - 313*q. Determine y, given that g(y) = 0.
-28, -8
Let d(a) = -a**2 - 339*a - 5165. Let u be d(-16). Let l(n) be the first derivative of -4/3*n**u + 4*n - 2*n**2 + 22 + n**4. What is m in l(m) = 0?
-1, 1
Let f be -4 + (167 - -3) - (-8)/(-2). Suppose -f = 3*p - 12*p. Let -12*l + 4*l**2 - 8*l**3 - l**4 + 36*l + 3*l**4 - p - 4*l**4 = 0. Calculate l.
-3, 1
Factor 136080*k**2 + 1035921 + 7130092 + 1512*k**3 + 1760750 + 1404*k**3 + 2116800*k + 1049237.
4*(9*k + 140)**3
Let q(o) be the first derivative of -405/2*o**2 - 105*o**3 - o**5 + 0*o - 113 + 85/4*o**4. Factor q(y).
-5*y*(y - 9)**2*(y + 1)
Factor 1/6*u**3 + 43/6*u**2 + 46/3 - 68/3*u.
(u - 2)*(u - 1)*(u + 46)/6
Let n(j) be the third derivative of -j**7/630 - j**6/40 - j**5/9 - 799*j**2. Determine v so that n(v) = 0.
-5, -4, 0
Let r(q) be the first derivative of -q**3/3 + 173*q**2 - 29929*q + 3156. Factor r(n).
-(n - 173)**2
Let t(m) be the third derivative of -m**5/300 + 1331*m**4/60 - 1771561*m**3/30 - 2123*m**2. Factor t(v).
-(v - 1331)**2/5
Let t be (-191140)/(-950) - 198 - -1*2/(0 - 1). Factor 2/5*d**2 - t*d + 4/5.
2*(d - 2)*(d - 1)/5
Let c(d) be the third derivative of d**6/90 - 115*d**5/3 + 383*d**4/2 - 3446*d**3/9 + d**2 + 4399*d. Solve c(a) = 0.
1, 1723
Suppose -80/3*y**3 - 78*y**4 - 54*y**5 + 0*y - 8/3*y**2 + 0 = 0. What is y?
-1, -2/9, 0
Let w be ((-3)/13)/((-176344)/1456 - -121). Let 2/11*u**w - 180/11*u + 4050/11 = 0. What is u?
45
Suppose 1265 = -5*i - 175. Let u be i*(-1)/138*3 + -6. Find p such that 2/23*p**2 - u*p - 8/23 = 0.
-1, 4
Suppose 5*j + 9 = -5*r - 31, -3*r - 56 = -5*j. Factor 6 - 117/5*d + 18/5*d**j + 3/5*d**5 - 102/5*d**3 + 168/5*d**2.
3*(d - 1)**4*(d + 10)/5
Let b be (-825)/2100 - (3 - (-153)/(-36)). Determine v, given that -2/7 + 2/7*v**5 - 6/7*v + b*v**4 - 4/7*v**2 + 4/7*v**3 = 0.
-1, 1
Let p(t) be the third derivative of -4*t**7/1785 - 19*t**6/255 + t**5/2 - 49*t**4/51 + 44*t**3/51 - 9*t**2 - t - 5. Find x such that p(x) = 0.
-22, 1/2, 2
Let v be (2 + -1)/(4*2/2752). Suppose -99 = 5*j - v. Let 2*r**3 + r**5 + r**3 + j*r**4 - 52*r**4 - r**2 = 0. What is r?
0, 1
Let v(t) be the third derivative of 49*t**5/120 + 91*t**4/4 + 507*t**3 + 35*t**2 - 3*t. Let v(n) = 0. What is n?
-78/7
Let d be ((-124)/(-78) + (-368)/(-4784))/(35/6). Determine t so that -8/7 - 30/7*t**2 + 26/7*t - d*t**4 + 2*t**3 = 0.
1, 4
Let z(r) be the second derivative of 7*r**5/10 - 3*r**4/8 - r**3 - 61*r**2 + 3*r - 3. Let q(k) be the first derivative of z(k). Factor q(o).
3*(2*o - 1)*(7*o + 2)
Let s(c) = 40*c + 559. Let l be s(-14). Let q be (1 - (-8 + 13))/l. Factor 0*b**3 + 0*b + 2/5 + 2/5*b**q - 4/5*b**2.
2*(b - 1)**2*(b + 1)**2/5
Let g(n) be the third derivative of 0 + 1/20*n**6 - 2/5*n**5 - 1/8*n**4 - 1/112*n**8 + 2*n**3 + 45*n**2 + 2/35*n**7 + 0*n. Find w, given that g(w) = 0.
-1, 1, 4
What is r in 3/2*r**3 - 63*r - 17/2*r**2 - 20 = 0?
-4, -1/3, 10
Find q such that -172/23*q**2 + 0 - 32/23*q + 22/23*q**3 = 0.
-2/11, 0, 8
Let -20/3*j**4 + 0*j + 320/3*j**2 + 0 + 32/3*j**3 - 2/3*j**5 = 0. Calculate j.
-10, -4, 0, 4
Let d(m) = 76*m**3 + 22824*m**2 - 3617772*m + 28. Let h(i) = -8*i**3 - 2536*i**2 + 401974*i - 3. Let n(v) = 3*d(v) + 28*h(v). Find k, given that n(k) = 0.
0, 317
Suppose -2*b - 5*t = 60, 0 = 5*t + 1446 - 1386. Find j such that 2/7*j**3 + 24/7*j - 16/7*j**2 + b = 0.
0, 2, 6
Let m(c) be the fi