a(w) be the second derivative of -w**7/2100 - w**6/450 + w**5/300 + w**4/30 - 25*w**3/6 + 8*w. Let h(l) be the second derivative of a(l). Factor h(m).
-2*(m - 1)*(m + 1)*(m + 2)/5
Let i(q) be the first derivative of -q**7/168 - q**6/36 + 5*q**5/24 + 5*q**4/4 + 5*q**3 + 88. Let n(u) be the third derivative of i(u). Factor n(c).
-5*(c - 2)*(c + 1)*(c + 3)
Let l(x) = 19*x**2 + 18*x + 32. Let d(m) = 0*m + 8*m - 5*m**2 + 0*m - 12*m - 8. Let u(v) = 22*d(v) + 6*l(v). Suppose u(y) = 0. Calculate y.
-4, -1
Let b = -3790/219 - -2115/73. Factor b*s**2 + 4/3 - 22/3*s - 25/6*s**3.
-(s - 2)*(5*s - 2)**2/6
Let 2*c**5 + 54*c + 156*c**3 + 153*c**3 - 57*c**2 - c**5 - 5*c**4 + 14*c**4 - 316*c**3 = 0. Calculate c.
-9, -3, 0, 1, 2
Suppose -5*n - 13 = 2*a, -9*a + n = -5*a + 15. Let g be 18/a - -2 - 1005/(-402). Factor -1/4*t**2 + 0*t - 1/4*t**5 + g - 3/4*t**4 - 3/4*t**3.
-t**2*(t + 1)**3/4
Let a(l) = -l + 6. Let q be a(3). Suppose -q*u + 1 + 11 = 0. Factor -g**u - 3*g - 2*g**2 + 0*g + 4*g - g**5 + 3*g**4.
-g*(g - 1)**3*(g + 1)
Let u(b) be the second derivative of b**4/24 - b**3/2 + 2*b**2 - 393*b. Suppose u(o) = 0. What is o?
2, 4
Let s(f) = f**2 - 4*f. Suppose -6*m - 2*n + 356 = -2*m, 3*m + 2*n = 267. Let z = m + -94. Let l(h) = -3*h**2 + 8*h. Let q(c) = z*s(c) - 3*l(c). Factor q(i).
4*i*(i - 1)
Let t(j) be the second derivative of -343*j**6/15 - 245*j**5 + 378*j**4 - 664*j**3/3 + 64*j**2 + 21*j + 17. Factor t(c).
-2*(c + 8)*(7*c - 2)**3
Let n(u) be the second derivative of 8*u**6/15 + 309*u**5/5 + 227*u**4 + 902*u**3/3 + 150*u**2 + 721*u - 1. Suppose n(l) = 0. What is l?
-75, -1, -1/4
Let r(w) = -5 - 5*w + 6*w**2 - 4 - 1. Let m(d) = d**2 - d - 2. Let g(c) = -5*m(c) + r(c). Find h such that g(h) = 0.
0
Factor -145*o - 21 + 199*o + o**2 - 4*o**2 - 174.
-3*(o - 13)*(o - 5)
Determine g so that 123 - 469*g**3 + 489*g + 357*g**2 + 242*g**3 + 218*g**3 = 0.
-1, -1/3, 41
Let s(j) = -30*j**2 - 465*j + 5. Let f(g) = -13*g**2 - 232*g + 2. Let d(r) = -5*f(r) + 2*s(r). Factor d(u).
5*u*(u + 46)
Factor 2*d**2 - 532618 + 746840 + 2*d**2 - 4496*d + 1049154.
4*(d - 562)**2
Solve -30*t + 0 - 2/5*t**3 + 8*t**2 = 0 for t.
0, 5, 15
Let o = -164543 + 329087/2. What is n in o*n**2 + 2*n - 1/2*n**3 - 2 = 0?
-2, 1, 2
Factor 17732890625*k + 34884375/2*k**2 + 27042658203125/4 + 7625*k**3 + 5/4*k**4.
5*(k + 1525)**4/4
Suppose 0 = 4*p - 3*w - 30, -3*p = -3*w - 30 + 9. Let q(n) be the second derivative of -10*n**2 + p*n + 0*n**3 + 0 + 5/12*n**4. Factor q(y).
5*(y - 2)*(y + 2)
Let a(c) be the first derivative of 0*c**2 + 4*c**3 - 3/4*c**4 + 1 + 0*c. Factor a(s).
-3*s**2*(s - 4)
Let t be ((-24)/(-2046))/((-104)/(-1612)). Suppose -4/11*i**3 - 1/11*i**4 + 0 - 5/11*i**2 - t*i = 0. What is i?
-2, -1, 0
Let a(s) be the first derivative of s**9/1008 - s**8/560 - s**7/70 + s**6/30 + 9*s**3 + s**2/2 - 31. Let w(k) be the third derivative of a(k). Factor w(t).
3*t**2*(t - 2)*(t - 1)*(t + 2)
Let a(q) be the first derivative of 3*q**4/4 - 1049*q**3 + 6285*q**2/2 - 3141*q - 6753. What is g in a(g) = 0?
1, 1047
Let n = -465 - -467. Determine v so that 19*v**2 + 108 - 30*v**3 + 145*v**n + 0*v**4 - 180*v - 53*v**2 + 3*v**4 = 0.
2, 3
Suppose -52*k = -320*k + 804. Factor 0 + 9747/5*y**k - 684/5*y**2 + 12/5*y.
3*y*(57*y - 2)**2/5
Let h(l) be the second derivative of -l**7/3780 - l**6/360 + 11*l**4/4 + 3*l + 14. Let f(i) be the third derivative of h(i). Let f(u) = 0. What is u?
-3, 0
Let h be 20 + -4 - (6 + (-44)/4). Suppose -a + 5*a = 20, -3*d - 3*a = -h. Factor 9/7*b**4 - 3/7*b + 15/7*b**3 + 3/7*b**d + 0.
3*b*(b + 1)**2*(3*b - 1)/7
Suppose -28*n + 8*n = 10*n + 52*n. Let n*a + 1/2*a**3 + 0 + 5/2*a**2 = 0. Calculate a.
-5, 0
Let r(s) = 113*s**2 - 20*s + 19. Let x be r(1). Factor 22*k**2 + 12*k**4 - x*k**3 + 4*k**2 - 5*k**2 + 15*k**2.
4*k**2*(k - 9)*(3*k - 1)
Let t(q) be the third derivative of -q**7/1050 - 23*q**6/600 - 4*q**5/15 - 19*q**4/30 + 151*q**2. Suppose t(x) = 0. Calculate x.
-19, -2, 0
Suppose -3*i = 5*u - 47, 3*i = u + 14 + 9. Suppose i*y + 2*y = 55. Factor 10*z**5 - 15*z**y - 12*z**3 + 17*z**3.
-5*z**3*(z - 1)*(z + 1)
Let r(h) be the second derivative of h**7/42 - 3*h**5/20 - h**4/6 - 20*h. Find u such that r(u) = 0.
-1, 0, 2
Let h(k) be the first derivative of -k**5/360 - k**4/36 + k**3/3 + k**2 + 19*k - 147. Let t(q) be the second derivative of h(q). Find u, given that t(u) = 0.
-6, 2
Let q(c) be the first derivative of -c**6/1260 - c**5/14 + c**3/3 + c**2 - 73. Let k(p) be the third derivative of q(p). Suppose k(m) = 0. What is m?
-30, 0
Factor -16*p + 33984*p**2 + 378 - 33981*p**2 + 97*p + 132.
3*(p + 10)*(p + 17)
Let s(o) be the second derivative of o**6/8 + 6*o**5/5 + 3*o**4/4 + 254*o. Let s(t) = 0. What is t?
-6, -2/5, 0
Let n(r) be the second derivative of -r**7/560 + r**6/240 + 23*r**3/2 - 60*r + 2. Let d(u) be the second derivative of n(u). Factor d(v).
-3*v**2*(v - 1)/2
Suppose 5*c - 50 = c + 3*j, c - 4*j - 19 = 0. Suppose -u - 7 + c = 0. Factor -6*t**2 - 5*t**3 - 7*t**2 - 2*t - 2*t**3 - u*t**3.
-t*(t + 1)*(11*t + 2)
Suppose -9*s + 3*s = -42. Solve -i + s*i - 2*i**3 + 8*i - 6*i = 0 for i.
-2, 0, 2
Let p(k) be the third derivative of -1/80*k**6 - 1/28*k**7 + 0*k**4 + 0*k**3 + 0 - 1/56*k**8 + 62*k**2 + 0*k**5 + 0*k. Factor p(m).
-3*m**3*(m + 1)*(4*m + 1)/2
Let w = -338 - -339. Let b(u) = -u**4 + u**3 - u**2 + u. Let f(d) = 4*d**4 - d**3 + 7*d**2 - 17*d - 9. Let g(h) = w*f(h) + 5*b(h). Find k such that g(k) = 0.
-1, 3
Let -48*o + 54*o - 8*o**3 + 788*o**4 - 799*o**4 - 16*o**3 + 29*o**2 = 0. What is o?
-3, -2/11, 0, 1
Factor -288/5*s**2 - 1782/5*s - 540 + 2/5*s**3.
2*(s - 150)*(s + 3)**2/5
Let c(z) = 20*z**3 + 104*z**2 + 236*z + 144. Let u(s) = 1131*s + 7*s**3 - 16 + 35*s**2 + 64 - 1052*s. Let t(p) = -3*c(p) + 8*u(p). Factor t(x).
-4*(x + 1)*(x + 3)*(x + 4)
Let q(t) be the third derivative of 5*t**8/336 + t**7/14 - 7*t**6/4 + 49*t**5/6 - 145*t**4/8 + 45*t**3/2 - 705*t**2. Factor q(d).
5*(d - 3)*(d - 1)**3*(d + 9)
Let l(y) be the second derivative of y**5/50 - 2297*y**4/10 + 5276209*y**3/5 - 12119452073*y**2/5 + 4261*y. Let l(t) = 0. Calculate t.
2297
Let n = -160/9 + 401/18. Suppose b - 86 = 14*u, 2*b + 17*u - 16*u + 2 = 0. Solve -15/4 - n*f - 3/4*f**b = 0.
-5, -1
Let g(k) be the third derivative of 1/27*k**4 + 0*k + 1/270*k**5 + 0 + 65*k**2 + 1/9*k**3. Suppose g(y) = 0. What is y?
-3, -1
Let w(c) be the second derivative of 1/18*c**4 + 0 - 20*c + 8/9*c**3 + 5*c**2. Factor w(b).
2*(b + 3)*(b + 5)/3
Let n(g) be the third derivative of -g**6/120 + 11*g**5/60 + 25*g**4/24 + 13*g**3/6 + 8213*g**2. Solve n(k) = 0.
-1, 13
Let p(g) be the second derivative of -g**4/32 - 153*g**3/4 - 70227*g**2/4 + 6*g - 187. Suppose p(m) = 0. Calculate m.
-306
Let i be 522/(-348) - (-18)/4. Let n = -899 - -9897/11. Solve 8/11*f**2 - n*f + 0 + 10/11*f**4 + 26/11*f**i = 0.
-2, -1, 0, 2/5
Let j(v) be the second derivative of v**6/90 - 9*v**5/10 + 223*v**4/12 + 868*v**3/9 - 392*v**2 - 7*v + 57. Find a, given that j(a) = 0.
-3, 1, 28
Let q(b) be the second derivative of 5/42*b**3 - 1/420*b**5 - 31/2*b**2 + 5*b + 0 + 1/42*b**4. Let x(y) be the first derivative of q(y). Factor x(w).
-(w - 5)*(w + 1)/7
Let u = -56704 + 396932/7. Let u + 18/7*v**2 + 2/7*v**4 - 2*v - 10/7*v**3 = 0. What is v?
1, 2
Let r(t) be the third derivative of 51*t + 0 + 0*t**3 + 2/3*t**4 + t**2 + 4/15*t**5 + 1/30*t**6. Factor r(f).
4*f*(f + 2)**2
Let r(h) = 2*h - h**3 - 2*h. Let l(i) = 3716*i**3 - 1241*i**3 - 1250*i**3 - 5*i**4 - 1263*i**3. Let m(k) = l(k) - 3*r(k). Factor m(p).
-5*p**3*(p + 7)
Let j = -49565/2 + 24784. Suppose 0 = u - 0*u. Factor 3/2*b**2 + j*b + u.
3*b*(b + 1)/2
Find y, given that 2/17*y**4 + 2396/17*y + 2400/17*y**2 + 798/17 + 804/17*y**3 = 0.
-399, -1
Solve -11/2*k**4 - 79*k + 12 + 143/2*k**2 + k**3 = 0 for k.
-4, 2/11, 1, 3
Let w be 40396/(-222178) + (2 + 50/(-88) - (3 - 2)). Suppose 5/2*d**3 + w + 3/4*d**4 + 3/2*d + 3*d**2 = 0. What is d?
-1, -1/3
Let c(b) = -11*b**2 + 65*b - 75. Let o(k) = 5*k**2 - 32*k + 37. Let r(f) = 6*c(f) + 13*o(f). Let g(j) = j + 1. Let l(w) = 2*g(w) - r(w). Factor l(v).
(v - 1)*(v + 29)
Let i = -346 + 563. Let t = i - 213. Factor 3 + 21/4*o**t - 12*o + 75/4*o**2 - 3/4*o**5 - 57/4*o**3.
-3*(o - 2)**2*(o - 1)**3/4
Let l(v) = -20*v**2 + 59*v + 81. Let y(f) = 10*f**2 - 29*f - 41. Let a(h) = 4*l(h) + 9*y(h). 