+ 0*d**3 + 13*d**2 - 1/20*d**6 + 0*d + g*d**4 + 1/40*d**5. Factor p(a).
-3*a**2*(4*a - 1)/2
Suppose 16*s = 1250 + 622. Let c be (4 + s/(-36))*4. Suppose 12/5*w + 3/5*w**5 + 12/5*w**2 + 0 - 9/5*w**c - 6/5*w**4 = 0. What is w?
-1, 0, 2
Let i = 31222 - 156109/5. Suppose -2/5*h**2 + 2/5 + 1/5*h - i*h**3 = 0. Calculate h.
-2, -1, 1
Let x = -920 + 798. Let g be x/(-36) - (-61)/366. Determine c, given that 8/9*c - g*c**2 + 10/9*c**3 + 50/9*c**4 + 0 = 0.
-1, 0, 2/5
Let y(o) be the first derivative of -16*o**3/9 - 1322*o**2/3 - 220*o + 3354. Factor y(l).
-4*(l + 165)*(4*l + 1)/3
Suppose 0 = 144*b - 75*b. Let x(n) be the second derivative of 5/2*n**3 + b - n**4 - 11*n - 3/2*n**2. Let x(p) = 0. What is p?
1/4, 1
Suppose 120 = 18*w + 30. Factor -6*o**2 - 4*o - w*o**2 - o**3 + 36*o**2 - 8*o**2 - 12*o**2.
-o*(o - 4)*(o - 1)
Let f(y) be the second derivative of 0*y**2 + 0*y**3 + 1/42*y**7 + 1/30*y**6 - 78*y - 1/10*y**5 + 0 + 0*y**4. Suppose f(o) = 0. Calculate o.
-2, 0, 1
Factor 0 + 95/2*q**4 - 3/4*q**5 - 512*q**2 - 736*q**3 + 0*q.
-q**2*(q - 32)**2*(3*q + 2)/4
Let r(l) = -243*l**2 + 1460*l - 10. Let p be r(6). Determine f so that -45/2*f**3 - 25*f**p + 0 - 20/3*f - 25/6*f**4 = 0.
-4, -1, -2/5, 0
Let r = 40044/161 + 4590/23. Let p = r - 446. Factor 10/7*c**3 - 8/7*c + 0 - p*c**2.
2*c*(c - 2)*(5*c + 2)/7
Let j(v) be the first derivative of -201601*v**3/3 - 449*v**2/2 - v/4 - 245. Factor j(i).
-(898*i + 1)**2/4
Let v = -133 + 135. Suppose 3*i - 384 = -j, -2*i + 239 = -3*j - v*j. Solve -i*f**2 - 44*f**4 + 17*f**2 - 8 - 20*f + 72*f + 7*f**5 + 103*f**3 = 0 for f.
2/7, 1, 2
Suppose -1009*a + 1802 = 585 - 801. Factor -8/3*h**a - 6*h - 28/9 + 2/9*h**3.
2*(h - 14)*(h + 1)**2/9
Let k(a) be the third derivative of 5*a**8/1008 + 37*a**7/42 + 217*a**6/36 + 323*a**5/18 + 715*a**4/24 + 535*a**3/18 + 13*a**2 - 16*a. Factor k(h).
5*(h + 1)**4*(h + 107)/3
Let d(k) be the first derivative of -2*k**3/33 - 315*k**2/11 + 632*k/11 + 153. Factor d(l).
-2*(l - 1)*(l + 316)/11
Let p(u) be the first derivative of 4*u**3/3 - 1612*u**2 + 649636*u + 2669. Factor p(b).
4*(b - 403)**2
Let q(x) be the first derivative of -1/14*x**4 - 8/7*x + 4/7*x**2 + 2/21*x**3 - 60. Factor q(f).
-2*(f - 2)*(f - 1)*(f + 2)/7
Let o(i) be the second derivative of i**7/21 - 8*i**6/15 + i**5/2 + 19*i**4/3 + 8*i**3 + 1970*i. Solve o(h) = 0 for h.
-1, 0, 4, 6
Let a(h) = -5*h**2 + 335*h - 828. Let d(f) = f**2 - 66*f + 165. Let v(b) = -2*a(b) - 11*d(b). Factor v(w).
-(w - 53)*(w - 3)
Let w(o) be the second derivative of -1722*o**4 - 34 - 2/15*o**6 + 147928/3*o**3 + 124/5*o**5 - 2*o - 137842*o**2. Factor w(d).
-4*(d - 41)**3*(d - 1)
Let h be (3*5/5)/(-1 + 2). Suppose -3*y = f - 16, -h*f = 2*y + y - 24. Let 5*g**5 - 3*g**3 - 2149 - 10*g**f + 8*g**3 + 2149 = 0. Calculate g.
0, 1
Suppose -20*h + 7611 = 4351. Suppose -2*j - c = -329, -2*j - 2*j = 3*c - 661. Solve j - 4*q**5 - h = 0.
0
Let o = -63836 + 510689/8. Let 3/2*w**3 - 11/8*w**2 + 0 - o*w**4 + 0*w = 0. Calculate w.
0, 1, 11
Let x(y) = -15*y**2 - 480*y - 57125. Let v(h) = 52*h**2 + 1441*h + 171377. Let s(k) = -6*v(k) - 21*x(k). Factor s(p).
3*(p + 239)**2
Let r(s) be the third derivative of -s**6/630 + s**5/21 + 17*s**3/2 + 44*s**2 + 2*s. Let a(n) be the first derivative of r(n). Factor a(h).
-4*h*(h - 10)/7
Let c(f) = f**3 - 86*f**2 + 2736*f - 27004. Let s(l) = 2*l**3 - 171*l**2 + 5481*l - 54009. Let m(y) = 9*c(y) - 4*s(y). Factor m(i).
(i - 30)**3
Suppose -89*h + 219*h**2 - 18*h**4 - 15*h**4 - 60*h**3 - 37*h = 0. What is h?
-42/11, 0, 1
Let h(j) be the first derivative of -35*j**2/2 - 101*j + 26. Let z be h(-3). Determine t so that 2/3*t**3 - 2/3*t**4 + 14/3*t**2 - z - 2/3*t = 0.
-2, -1, 1, 3
Let z(i) be the first derivative of 4*i**6/9 - 14*i**5/5 - 131*i**4/6 + 460*i**3/3 - 836*i**2/3 + 112*i - 1321. Suppose z(u) = 0. What is u?
-6, 1/4, 2, 7
Let m(s) be the third derivative of -s**5/300 + s**4/15 + 13*s**3/6 - 4089*s**2. Factor m(n).
-(n - 13)*(n + 5)/5
Suppose 169*f + 668 - 2189 = 0. Determine s so that -f - 3/2*s**2 - 15/2*s = 0.
-3, -2
Solve 6*h + 2/3*h**2 - 140/3 = 0 for h.
-14, 5
Let u = -441/2 - -221. Let l(v) = -v**2 + 37*v + 362. Let a be l(-8). Factor u*n**a + 2*n + 3/2.
(n + 1)*(n + 3)/2
Let p(m) be the third derivative of 232*m**7/315 + 47*m**6/15 + 413*m**5/180 + m**4/3 - 2*m**3/9 + 3*m**2 + 18*m. Determine n so that p(n) = 0.
-2, -1/4, 2/29
Determine b, given that -1007/3*b**3 - 1250/3*b**2 - 56 + 1084/3*b - 15*b**4 = 0.
-21, -2, 2/9, 2/5
Suppose 58*s = 195*s + 356*s - 2958. Factor s*w**3 + 4 + 76/3*w**2 + 70/3*w.
2*(w + 1)*(w + 3)*(9*w + 2)/3
Let c(f) be the third derivative of 11/105*f**7 + 17/15*f**5 + 0*f**3 + 53/60*f**6 - 2/3*f**4 + 0 - 205*f**2 + f. Factor c(p).
2*p*(p + 1)*(p + 4)*(11*p - 2)
Let k(l) be the second derivative of l**4/54 + 5*l**3/3 + 434*l**2/9 + 70*l + 1. Factor k(h).
2*(h + 14)*(h + 31)/9
Let c(a) be the third derivative of -1/240*a**6 + 11/120*a**5 - 205*a**2 + 25/12*a**3 + 0 - 35/48*a**4 + 0*a. Factor c(n).
-(n - 5)**2*(n - 1)/2
Let w(q) = -32 + 12*q + 152*q**2 - 150*q**2 + 10 - 28. Let l be w(3). Suppose -4/3*n**l + 1/3*n**2 + 0*n + 0 + n**3 = 0. Calculate n.
-1/4, 0, 1
Let q(n) be the third derivative of n**9/2520 - n**8/5040 + n**5/4 + 15*n**2 + 3. Let d(l) be the third derivative of q(l). Solve d(f) = 0 for f.
0, 1/6
Let d(t) = -t**3 - 31*t**2 + 11*t - 7. Suppose -5*u = 3*p + 50, 2*u + 4*p + 9 = -25. Let a(z) = -15*z**2 + 6*z - 3. Let r(s) = u*a(s) + 3*d(s). Factor r(m).
-3*m*(m - 3)*(m - 1)
Determine p so that 0 - 560/3*p**2 + 44/3*p**3 + 1600/3*p - 1/3*p**4 = 0.
0, 4, 20
Let f(q) be the second derivative of -q**6/45 + 13*q**5/10 - 37*q**4/6 + 109*q**3/9 - 12*q**2 - 5241*q. Factor f(r).
-2*(r - 36)*(r - 1)**3/3
Suppose 0 = -3*w - 12, 0 = -3*o - 0*w - 2*w - 11. Let n be 1 - -7 - (o - -5). What is i in -i**4 - 2*i - n*i**2 + 5*i + 2 - 3*i**3 + 3*i**2 = 0?
-2, -1, 1
Let u = 1760 + 775. Let x = 2538 - u. Suppose -2/13*c**x + 0 - 12/13*c - 10/13*c**2 = 0. Calculate c.
-3, -2, 0
Let y(u) be the first derivative of 42*u**2 + 36*u + 1 + 61/3*u**3 + 7/2*u**4 + 1/5*u**5. Factor y(l).
(l + 1)**2*(l + 6)**2
Let m = -547 - -19. Let i = m + 12152/23. Solve 0*g + i - 2/23*g**2 = 0 for g.
-2, 2
Let h(j) be the first derivative of 3*j**4/28 + 6*j**3/7 - 144*j**2/7 - 1920*j/7 - 865. Find s, given that h(s) = 0.
-8, 10
Suppose 60 = -s + 62. Let t = 689/3 - 229. Determine a, given that -a + 1/3*a**s + t = 0.
1, 2
Let t(z) be the third derivative of -z**8/112 - 12*z**7/35 - 29*z**6/10 - 69*z**5/10 + 117*z**4/8 + 81*z**3 - 3*z**2 + z - 59. Let t(x) = 0. What is x?
-18, -3, -1, 1
Let v(m) = -m**3 + m**2 - 2*m - 4. Let c(h) = -4*h**3 - 24*h**2 + 114*h - 186. Let l(r) = c(r) - 6*v(r). Determine j, given that l(j) = 0.
3, 9
Let l(w) = 5*w**2 - 2*w**2 + 4*w - 3*w - 2*w**2 + 1. Let k be l(-2). Solve -24 - 16 + 169*x - 360*x - 2430*x**2 - 3645*x**k - 349*x = 0.
-2/9
Let x(z) be the third derivative of -1/54*z**4 - 1/315*z**7 - z**2 - 7/270*z**5 + 0*z**3 + 0 - 97*z - 2/135*z**6. Suppose x(j) = 0. What is j?
-1, -2/3, 0
Let u = 14 + -19. Let n be ((-6)/u)/(28/105). Find x such that n*x**4 + 0 - 6*x**3 - 6*x**2 + 0*x = 0.
-2/3, 0, 2
Factor -172/15*b - 178/5 + 2/15*b**2.
2*(b - 89)*(b + 3)/15
Let t = -429 - -471. Let v be 70/t - (-5)/(-3). Factor 8/5*c**2 + 6/5*c + 2/5*c**3 + v.
2*c*(c + 1)*(c + 3)/5
Let t(l) be the first derivative of 8*l**2 + 253 + 1/30*l**3 + 640*l. Determine y so that t(y) = 0.
-80
Determine m so that 540*m - 378 - 184*m**3 + 280*m**4 + 378 - 5*m**5 - 351*m**3 - 280*m**2 = 0.
-1, 0, 1, 2, 54
Suppose -38*f + 18*f + 1820 = 0. Let f*r**2 - 29*r**2 + 35*r**2 + 51*r**2 + 29*r**2 + r**4 - 616*r + 784 - 22*r**3 = 0. What is r?
4, 7
Factor 118/9*u**2 + 10/3*u**3 + 2/9*u**4 + 0 + 10*u.
2*u*(u + 1)*(u + 5)*(u + 9)/9
Let b be ((-20)/15)/(6/(-81)*6). Let l be 690/207 + b*2/(-27). Factor l*h**2 - 4/9 - 8/3*h.
4*(h - 1)*(7*h + 1)/9
Let q(t) be the third derivative of t**6/1620 - t**4/12 + 15*t**3/2 - 7*t**2. Let g(l) be the first derivative of q(l). Factor g(d).
2*(d - 3)*(d + 3)/9
Let x(m) = -46*m**3 + 12718*m**2 - 26864868*m + 18948593814. Let b(h) = 2*h**3 - h**2 + 6*h - 1. Let w(p) = 44*b(p) + 2*x(p). Suppose w(t) = 0. What is t?
2116
Let h = 171 + -169. Solve -50*x**h - 48*x - 5*x**5 + 5*x**4 + 25*x**3 + 5*x**4 + 28*x + 40 = 0 for