c(b) = -5*b**3 + 62*b**2 - 192. Let r(o) = -13*c(o) + 6*z(o). Determine s, given that r(s) = 0.
-50, 0
Let n(z) be the first derivative of 3*z**5/80 - 13*z**4/32 + z**3/2 - 3*z**2 - 4*z - 20. Let f(s) be the second derivative of n(s). Find g, given that f(g) = 0.
1/3, 4
Let v(q) be the third derivative of -q**7/350 + 23*q**6/100 - 98*q**5/25 + 148*q**4/5 - 576*q**3/5 + 2764*q**2. Determine b, given that v(b) = 0.
2, 4, 36
Let f(d) be the first derivative of -2/5*d**2 + 0*d + 2/15*d**3 + 1/10*d**4 + 145. Suppose f(s) = 0. What is s?
-2, 0, 1
Let a be (-235)/(-188) - 87556/(-48). Factor a - 296/3*l + 4/3*l**2.
4*(l - 37)**2/3
Suppose -3*i - 130 = 86. Let z be ((-352)/i - 4)*(-1)/(-2). Solve -8/9*s - 16/9*s**3 + 20/9*s**2 + 0 + z*s**4 = 0.
0, 1, 2
Suppose 0 + 2/3*n**2 + 46*n = 0. What is n?
-69, 0
Let d = 178 - 119. Factor 14*n**2 - 2*n - 4*n + 2*n**4 - d*n**3 - 52*n**3 + 101*n**3.
2*n*(n - 3)*(n - 1)**2
Let k(w) be the third derivative of -1/9*w**4 + 0 + 0*w - 7/360*w**5 - 1/3*w**3 - 1/720*w**6 + 146*w**2. Factor k(z).
-(z + 2)**2*(z + 3)/6
Let x(w) = -3880*w + 7762. Let q be x(2). Factor -21/8*i + 15/4 + 3/8*i**q.
3*(i - 5)*(i - 2)/8
Suppose -7*n + 639 = -733. Let 284*f**2 - 100*f**5 - 106 - 96*f - 73 + 35 + n*f**3 + 0*f**5 - 140*f**4 = 0. Calculate f.
-6/5, -1, 1
Let d = 373603 + -373568. Factor 100/3 + d*t + 5/3*t**2.
5*(t + 1)*(t + 20)/3
Let b(p) be the second derivative of 0*p**3 - 20 + 2*p - 18/35*p**5 - 4/21*p**4 - 2/7*p**6 - 1/21*p**7 + 0*p**2. Factor b(z).
-2*z**2*(z + 2)**2*(7*z + 2)/7
Let v be (((-68)/32)/17)/(4/(-24)). Let r(g) be the first derivative of 1/2*g - 10 + v*g**3 + 7/8*g**2 + 5/16*g**4 + 1/20*g**5. Factor r(x).
(x + 1)**3*(x + 2)/4
Let t = -1571765 - -7858827/5. Factor -24/5*y - 72/5 - t*y**2.
-2*(y + 6)**2/5
Factor -44/5*g**3 - 9/5*g - 4/5 + 46/5*g**2 + g**5 + 6/5*g**4.
(g - 1)**3*(g + 4)*(5*g + 1)/5
Let g(c) be the second derivative of -c**7/483 + 16*c**6/345 - 3*c**5/10 - 9*c**4/23 + 252*c**3/23 - 648*c**2/23 - 1304*c. Find j, given that g(j) = 0.
-3, 1, 6
Let l(i) be the first derivative of -2*i**3/9 - 220*i**2/3 - 4155. Suppose l(o) = 0. Calculate o.
-220, 0
Factor 17774*d**2 + 8659*d**2 - 4503*d**2 + 11087997*d + 15624715640 + 5*d**3 + 20973663*d.
5*(d + 1462)**3
Let d(l) be the first derivative of 5/2*l**4 - 17*l**2 - 2*l**3 - 20*l + 2/5*l**5 - 69. Factor d(a).
2*(a - 2)*(a + 1)**2*(a + 5)
Let d(s) = -7*s**2 + 780*s - 1577. Let j(h) = 10*h**2 - 1171*h + 2365. Let w(r) = 7*d(r) + 5*j(r). Factor w(v).
(v - 393)*(v - 2)
Let o(g) be the first derivative of -g**6/21 + g**4 + 8*g**3/7 - 13*g**2/7 - 24*g/7 + 4341. Determine a, given that o(a) = 0.
-3, -1, 1, 4
Let w = 580 - 48. What is m in 72 - 30*m**4 + w*m**3 + 67*m**2 + 128*m**4 - 456*m + 487*m**2 = 0?
-3, 2/7
Let k(d) be the third derivative of d**5/6 - 89*d**4/72 - d**3/6 - 609*d**2 + d. Suppose k(b) = 0. What is b?
-1/30, 3
Solve 8*v - 14/5*v**3 - 96/5 + 36/5*v**2 - 3/5*v**4 + 1/5*v**5 = 0.
-3, -2, 2, 4
Let t(w) be the third derivative of -25*w**6/6 + w**5/5 + 971*w**2. Factor t(k).
-4*k**2*(125*k - 3)
Let b(k) be the third derivative of k**7/140 + k**6/4 + 67*k**5/20 + 85*k**4/4 + 225*k**3/4 - 698*k**2. Factor b(u).
3*(u + 1)*(u + 5)**2*(u + 9)/2
Let u(m) = 2*m**3 + 4*m**2 - 2*m + 2. Let l(p) = 3*p**3 + 4*p**2 - p + 2. Let d = -278 - -275. Let f(j) = d*l(j) + 4*u(j). Suppose f(i) = 0. Calculate i.
1, 2
Suppose 310/7*q - 628/7 + 2/7*q**2 = 0. Calculate q.
-157, 2
Let k(g) be the first derivative of -20*g**3/3 - 275*g**2/2 + 295*g + 189. Suppose k(w) = 0. Calculate w.
-59/4, 1
Let h(g) = 1060*g + 37103. Let d be h(-35). Suppose 7/4*a**d + 1/4*a**5 + 5/4*a**4 - 1/4*a**2 - 2*a - 1 = 0. Calculate a.
-2, -1, 1
Let c(t) be the second derivative of -1/63*t**7 + 22 + 0*t**3 + 2197/18*t**4 + 13/15*t**6 - 169/10*t**5 + 0*t**2 - 7*t. Solve c(h) = 0 for h.
0, 13
Let i(f) be the third derivative of 0*f**4 - 1/1680*f**8 + 0*f - 8/15*f**3 - 62*f**2 + 1/150*f**6 + 0 + 4/75*f**5 - 1/350*f**7. Determine p so that i(p) = 0.
-2, 1, 2
Let x(j) = 4*j**2 - 6*j + 2. Let t be x(2). Suppose t*u + 4*u = u. Factor u - 2 - 4*d + 3 - d**2 - 5.
-(d + 2)**2
Let g(n) = 2*n**2 + 2*n - 4. Let j(c) = -7*c**2 - 395*c - 372. Let s(d) = -4*g(d) - j(d). Factor s(x).
-(x - 388)*(x + 1)
Let u(c) be the first derivative of -c**4/36 + 13*c**3/18 - 6*c**2 + 182*c + 173. Let x(p) be the first derivative of u(p). Solve x(f) = 0 for f.
4, 9
Let j be 10192/364 + 106/(-4). Factor 1/2*y**2 + 2*y + j.
(y + 1)*(y + 3)/2
Let g(k) = -5*k**3 + 42*k**2 - 86*k + 17. Let u be g(5). Factor 88/5*a - 24/5*a**3 + u + 0*a**2 + 4/5*a**4.
4*(a - 5)*(a - 3)*(a + 1)**2/5
Suppose 0 = 27*m + m - 2912. Suppose -2*u + m - 98 = 0. Factor -3/5*i**u + 0*i + 0 + 0*i**2 + 3/5*i**4.
3*i**3*(i - 1)/5
Suppose 2/9*a**3 + 0 + 2/9*a**2 - 8/3*a = 0. What is a?
-4, 0, 3
Let o = 6725 - 33623/5. Let f(a) = a + 5. Let t be f(-5). Suppose -2/5*h**2 - o*h + t = 0. Calculate h.
-1, 0
Let r(f) be the first derivative of 5/3*f**3 + 0*f - 15/2*f**2 - 52. Factor r(z).
5*z*(z - 3)
Suppose -11*h = 50 + 104. Let w be 247/91 + h/(-49). Suppose -4/3*f**4 + 0 + 0*f + 4/3*f**5 + 4/3*f**2 - 4/3*f**w = 0. What is f?
-1, 0, 1
Let k(w) = w**3 + 1. Let f(a) = -13 - 680*a + 9 - 8 - 15*a**3 + 692*a. Suppose 0 = -5*r - 15, 4*z - 3*r = r + 16. Let h(l) = z*f(l) + 12*k(l). Factor h(i).
-3*i*(i - 2)*(i + 2)
Let c(o) be the first derivative of o**6/51 - 372*o**5/85 + 369*o**4/34 - 368*o**3/51 + 660. Factor c(w).
2*w**2*(w - 184)*(w - 1)**2/17
Suppose 43*r = 1092 - 468 - 495. Solve 0 - 2304/5*m + 192/5*m**2 - 4/5*m**r = 0 for m.
0, 24
Let g(r) = 4*r - 111. Let o be g(30). Suppose 5*i - 38 = -4*x - o, -5*x + 25 = 4*i. Solve 5/2*q - 25/4*q**2 + 0 - 5/4*q**4 + i*q**3 = 0 for q.
0, 1, 2
Let m(b) be the third derivative of -b**5/510 - 35*b**4/102 - 23*b**3/17 - 1126*b**2. Find k, given that m(k) = 0.
-69, -1
Let s(v) be the third derivative of v**6/120 - 103*v**5/180 + 4*v**4 - 94*v**3/9 - 2*v**2 + 354*v - 2. Suppose s(n) = 0. What is n?
1, 2, 94/3
Let d(v) be the first derivative of 3*v**4/8 - 59*v**3 - 2607*v**2/4 - 1125*v + 5621. Factor d(x).
3*(x - 125)*(x + 1)*(x + 6)/2
Let w(b) be the first derivative of 2*b**5/5 + 5*b**4 + 46*b**3/3 + 14*b**2 - 889. Find n such that w(n) = 0.
-7, -2, -1, 0
Suppose 0 = -3*m - 3*j - 264, 3*m + 104 = 2*m + 3*j. Let z = m + 99. Find n, given that 90*n + 122 - 2*n**2 + 283 + z*n**2 = 0.
-9
Let m(o) = o**2 + 47*o + 316. Let j be m(-8). Determine q so that 4*q + 25*q**j - 4*q**2 - 9*q**3 - 3*q**5 - 23*q**4 + 6*q**3 + 4*q**5 = 0.
-2, 0, 1
Let q(g) be the first derivative of -4*g**3/3 + 108*g**2 - 212*g + 143. Find i, given that q(i) = 0.
1, 53
Let x(j) be the third derivative of 68*j**2 + 2/3*j**3 + 1/72*j**4 - 1/180*j**5 + 0 + 0*j. Solve x(o) = 0 for o.
-3, 4
Factor -2*n + 0 - 28/3*n**2.
-2*n*(14*n + 3)/3
Suppose 25*p - 34*p + 87 = 3*x, 45 = 4*p - 5*x. Let i(f) be the second derivative of 25/6*f**3 - 22*f + 5/12*f**4 + 0 + p*f**2. Factor i(s).
5*(s + 1)*(s + 4)
Let -253*k + 0*k**2 - 4*k**2 + 952 + 361*k = 0. Calculate k.
-7, 34
Let o(u) be the second derivative of -u**7/10 + 17*u**6/25 + 39*u**5/50 - 22*u**4/5 - 83*u**3/10 - 3*u**2 + 2048*u. Let o(x) = 0. Calculate x.
-1, -1/7, 2, 5
Let a(i) be the second derivative of 2/3*i**4 - 2/3*i**3 + 1 - 4*i**2 + 7*i + 1/5*i**5. Factor a(x).
4*(x - 1)*(x + 1)*(x + 2)
Let l = 28357/37900 + 17/9475. Suppose 1/2*v**4 + 3/4*v**5 - l*v + 7/2*v**2 + 0 - 4*v**3 = 0. What is v?
-3, 0, 1/3, 1
Let p = -17407 + 261107/15. Let u(f) be the third derivative of 0*f - 1/150*f**6 + 0 - 17/30*f**4 - 16*f**2 + 16/15*f**3 + p*f**5. Factor u(m).
-4*(m - 8)*(m - 1)**2/5
Let g(d) = -3*d**2 + 70*d + 95. Let c be g(24). Factor -16*w**2 + c*w**2 - 14*w**2 - 6*w**2 - 14*w**2 - 18*w.
-3*w*(w + 6)
Let p(z) be the third derivative of -z**6/72 + 13*z**5/12 - 845*z**4/24 - 61*z**3/3 - z**2 + 13*z. Let b(d) be the first derivative of p(d). Solve b(l) = 0.
13
Let d(o) = o - 6. Let w be d(-3). Let g be 8*(45/(-10))/w. Determine i so that 5*i**g - 8*i**2 + 3*i**2 - 5*i**3 + 4*i**5 + i**5 = 0.
-1, 0, 1
Solve 18/7*c**3 + 334/7*c**2 - 456/7 - 176/7*c - 2/7*c**5 - 38/7*c**4 = 0.
-19, -3, -1, 2
Determine j so that -86/3 - 1/3*j**2 - 29*j = 0.
-86, -1
Factor -20/3*g**2 + 2/3*g**4 - 16/3*g - 2/3*g**3 + 0.
2*g*(g - 4)*(g + 1)*(g + 2)/3
Let l(i) = 1