)/6
Suppose 31 = 37*v - 80. Let j be -4 + 4 + -2 - -6. Factor -13*h**3 - 17*h**4 - 10*h - 37*h**j - 55*h**2 - 52*h**v + 34*h**4.
-5*h*(h + 1)*(h + 2)*(4*h + 1)
Let v(c) = -13*c**3 + 109*c**2 - 80*c - 52. Let n(q) = 18*q**3 - 164*q**2 + 120*q + 80. Let g(h) = 5*n(h) + 8*v(h). Suppose g(a) = 0. Calculate a.
-2/7, 2
Let v(n) be the first derivative of n**8/8400 - n**7/2100 - n**6/1800 + n**5/300 - 7*n**3/3 - 16. Let k(q) be the third derivative of v(q). Factor k(p).
p*(p - 2)*(p - 1)*(p + 1)/5
Let t = -577 + 587. Suppose -7*j = -10 + t. Factor 0*o + 2/3*o**4 + j - 2/3*o**2 + 0*o**3.
2*o**2*(o - 1)*(o + 1)/3
Let x(i) = -37*i**2 + 96*i - 524. Let u(b) = -5*b**2 + 14*b - 75. Let p(n) = 15*u(n) - 2*x(n). Find r, given that p(r) = 0.
7, 11
Let f = 1367338 - 1367336. Factor 1/9*u**2 - f + 1/3*u.
(u - 3)*(u + 6)/9
Let b = 6389 + -6384. Let t(s) be the first derivative of -12/5*s**4 + 31/15*s**3 + 16/25*s**b - 2/5*s - 2 + 3/10*s**2. Suppose t(k) = 0. What is k?
-1/4, 1/4, 1, 2
Let f(r) be the third derivative of 9/40*r**5 - 39*r**2 - 7/36*r**4 + 0*r + 0 + 1/12*r**3 - 1/10*r**6 + 4/315*r**7. Let f(g) = 0. Calculate g.
1/4, 1, 3
Let w(t) = -365*t**3 - 137*t**2 + 145*t + 1937. Let q(l) = -43*l**3 - 17*l**2 + 18*l + 242. Let u(f) = 17*q(f) - 2*w(f). Factor u(d).
-(d - 4)*(d + 4)*(d + 15)
Let a(d) be the third derivative of -d**2 + 1/1344*d**8 + 0*d**4 + 25 - 1/96*d**6 - 1/210*d**7 + 0*d**3 + 0*d + 0*d**5. Factor a(j).
j**3*(j - 5)*(j + 1)/4
Suppose -706*l + 3030*l + 272707 - 272706 + 1350244*l**2 = 0. What is l?
-1/1162
Let o(i) be the second derivative of 0*i**2 + 1/15*i**6 - 1/2*i**3 - 1/3*i**4 - 3*i - 11 + 1/4*i**5. Factor o(s).
s*(s - 1)*(s + 3)*(2*s + 1)
Let x(j) = j**2 + 5*j - 145. Let r be x(10). Suppose r*w - 20 = -2*n, -8 = -2*w + 6*n - 11*n. Solve 2/3*u**5 - 4/3*u**3 + 0 + 0*u + 2/3*u**w + 0*u**2 = 0.
-2, 0, 1
Solve 1027 - p**2 - 1048 + 20*p + 2*p**2 = 0 for p.
-21, 1
Let k(c) be the first derivative of c**4/20 + 4*c**3/15 - 6*c**2 - 288*c/5 + 2754. Suppose k(x) = 0. What is x?
-6, 8
Let f = 867741 + -867739. Factor -34/9*v - 2/9*v**3 + 16/9*v**f + 20/9.
-2*(v - 5)*(v - 2)*(v - 1)/9
Let j(x) be the third derivative of -x**6/200 + 249*x**5/100 - 72*x**4 + 4266*x**3/5 + 243*x**2 + 2*x - 1. Factor j(g).
-3*(g - 237)*(g - 6)**2/5
Let c be 38324/1820 + 2/(-35). Suppose -7*l - c*l = -4*l. Factor 0*t + 6/13*t**4 + 0 - 8/13*t**2 + l*t**3 - 2/13*t**5.
-2*t**2*(t - 2)**2*(t + 1)/13
What is x in 9*x**4 - 62*x - 67*x + 2*x**5 - 13*x**3 + 217*x - 74*x - 3*x**5 - 9*x**2 = 0?
-1, 0, 1, 2, 7
Let h be -6*(-9)/(-24)*38/(-76). Let a(v) = v**2 - 8*v - 9. Let k be a(9). Find s, given that 3/8*s - h*s**2 + k = 0.
0, 1/3
Let d(s) = -5*s**3 - 96*s**2 - 93*s - 42. Let q(l) = 3*l**2 + 2. Let z(a) = -3*d(a) - 24*q(a). Factor z(h).
3*(h + 1)*(h + 13)*(5*h + 2)
Let q(s) be the second derivative of s**5/20 + 3*s**4/8 + 3*s**2/2 - 3*s + 24. Let b(c) be the first derivative of q(c). Suppose b(g) = 0. Calculate g.
-3, 0
Let z(u) = 2*u**3 + 44*u**2 - 963*u - 10095. Let y(h) = -3*h**3 - 46*h**2 + 962*h + 10090. Let a(f) = -3*y(f) - 2*z(f). Factor a(d).
5*(d - 14)*(d + 12)**2
Let z(w) be the second derivative of w**5/160 + w**4/16 - 55*w**3/48 + 2005*w. Factor z(k).
k*(k - 5)*(k + 11)/8
Let u(l) = 2*l**3 + 8*l**2 - 46*l - 124. Let a(h) = 4*h**3 + 18*h**2 - 92*h - 250. Let f(r) = 2*a(r) - 5*u(r). Determine d, given that f(d) = 0.
-4, -3, 5
Factor j**3 - 2*j**3 + 3238258*j - 6486451*j + 17595*j**2 + 8069823585 - 4*j**3 - 17390742*j.
-5*(j - 1173)**3
Let v = 14773/18 - 821. Let b = v + 97/90. Suppose -14/5*k**2 + 0 + 8/5*k**4 + b*k - 2*k**3 = 0. Calculate k.
-1, 0, 1/4, 2
Factor -96*q - 286/3*q**2 + 2/3*q**3 + 0.
2*q*(q - 144)*(q + 1)/3
Let g be -1*3 - (975/(-135) + (-8)/(-36)). Let b(x) be the first derivative of 1/6*x**g - x**2 + 0*x**3 + 19 + 4/3*x. Solve b(j) = 0.
-2, 1
Let k(r) = -r**2 + 306*r + 1549. Let b(m) = -103. Let s(c) = 15*b(c) + 5*k(c). Factor s(z).
-5*(z - 310)*(z + 4)
Let t be -3 - (-2611)/693 - (-25)/15*54/(-165). Factor t*u**2 - 2/9*u - 8/3.
2*(u - 4)*(u + 3)/9
Determine r, given that 250*r + 8*r**3 - 6*r**3 - 784 - 6*r**3 + 6*r**3 - 70*r + 102*r**2 = 0.
-49, -4, 2
What is a in 229*a**3 + 390*a**3 - 1035*a**3 + 3*a**4 - 21632*a**2 - 5*a**4 = 0?
-104, 0
Let w(g) be the first derivative of -g**6/6 + 2*g**5 + 51*g**4/2 + 272*g**3/3 + 283*g**2/2 + 102*g - 5319. Suppose w(r) = 0. Calculate r.
-3, -2, -1, 17
Suppose 13*j - 29*j = 0. Determine z so that -32*z - 614*z**3 + 646*z**3 - 4*z**4 + j*z**2 + 4*z**2 = 0.
-1, 0, 1, 8
Suppose 6 = 126*i - 123*i. Solve 15*v**3 + 3 + 9*v**i - 10 - 27*v + 3*v**4 + 7 = 0 for v.
-3, 0, 1
Factor 0 - 196/3*l**2 + 9604/3*l + 1/3*l**3.
l*(l - 98)**2/3
Factor -82668 + 7240*f**2 - 3*f**3 - 25678*f + 3019*f - 7750*f**2.
-3*(f + 4)*(f + 83)**2
Let t(b) be the second derivative of 18*b - 1/6*b**4 + 0*b**2 + 1 + 4/3*b**3. Suppose t(w) = 0. Calculate w.
0, 4
Let v(y) = 4*y**2 - 401*y - 384. Let i(p) = -3*p**2 + 399*p + 388. Let o(z) = 3*i(z) + 2*v(z). Suppose o(k) = 0. Calculate k.
-1, 396
Let n = -461 - -464. Suppose 0 = n*h + 5*c - 31, 2*h - 34*c - 19 = -37*c. Let 2/9 - 2/9*q**h + 0*q = 0. What is q?
-1, 1
Let p be ((-15)/(-55))/((-18)/(-22)). Factor -1/6*z**2 + 1/2*z**3 - 1/6*z**4 + p - 1/2*z.
-(z - 2)*(z - 1)**2*(z + 1)/6
Solve 36*g**4 - 16*g**5 + 1809*g + 31 + 2*g**5 + 489*g**3 + 2*g**5 - 328*g**2 - 451 - 1862*g**2 = 0.
-7, 1/2, 4, 5
Let g(q) be the first derivative of 5*q**4/4 + 15*q**3 + 35*q**2 + 13441. Solve g(p) = 0 for p.
-7, -2, 0
Suppose -w - 81 = -4*g, 4*w - 3*w = 5*g - 100. Suppose g*m = -0*m. Determine s, given that -s + m - 1/4*s**2 = 0.
-4, 0
Factor 5090/11*q + 2546/11 + 2542/11*q**2 - 2/11*q**3.
-2*(q - 1273)*(q + 1)**2/11
Let v = 130/211 - -373/422. Suppose 3/2 - 1/10*n**3 - v*n**2 + 1/10*n = 0. What is n?
-15, -1, 1
Let f(p) be the first derivative of 4/3*p**3 + 36*p**2 + 46 + 324*p. Factor f(c).
4*(c + 9)**2
Let s be (-5 + -4)*(-80)/180. Suppose s*y + 5*l + 8 = 0, 3*y + 5*l - 47 = -58. What is h in -2*h**4 - 22/7*h**y + 0*h - 2/7*h**5 - 10/7*h**2 + 0 = 0?
-5, -1, 0
Suppose 10*k = 21 + 19. Let v(f) = -f**2 + 10*f - 19. Let s be v(k). Factor 10 - m - 3*m + 20*m**2 - m - 40 - s*m**3.
-5*(m - 3)*(m - 2)*(m + 1)
Suppose 7*m = -0*m + 1673. Let k = m - 239. Factor k + 3*z**2 + 0*z + 3/2*z**3.
3*z**2*(z + 2)/2
Let w be (1*7 - 325/50)*(-6)/(-15). Let x(k) be the second derivative of 2*k - w*k**2 - 1/15*k**3 + 1/50*k**5 + 0 + 1/30*k**4. Factor x(a).
2*(a - 1)*(a + 1)**2/5
Let g = 1/11357 + 22705/102213. Let p(n) be the second derivative of -2/3*n**2 - g*n**4 - 48*n + 0 - n**3. Let p(r) = 0. What is r?
-2, -1/4
Solve 75/2*q**3 + 330*q - 5/2*q**4 - 185*q**2 - 180 = 0.
1, 2, 6
Let v(x) be the first derivative of 4*x**5/3 - 140*x**4/3 + 515*x**3/3 - 1135*x**2/6 + 250*x/3 + 743. What is q in v(q) = 0?
1/2, 2, 25
Let u be 32 + -36 + ((-20542)/(-38))/(-1). Let o = u - -545. Suppose -90/19*l**4 - o - 226/19*l**2 + 276/19*l**3 + 72/19*l = 0. Calculate l.
1/3, 2/5, 2
Let r be (96/126)/(284/994). Suppose -2/3*b**4 - 2/3*b**5 + 2/3*b**2 + r + 10/3*b**3 - 16/3*b = 0. What is b?
-2, 1
Let y(c) = 14*c**2 + 19*c - 6. Let b(r) be the third derivative of r**5/4 + 3*r**4/4 - r**3 + 65*r**2 + r. Let o(h) = -2*b(h) + 3*y(h). Factor o(t).
3*(t + 2)*(4*t - 1)
Let w = 974526952733/3717 + -262181049. Let s = -4/531 - w. Solve -s - 4/7*v**2 - 16/7*v = 0 for v.
-3, -1
Let 52*a - 25/4*a**2 - 144 + 1/4*a**3 = 0. Calculate a.
8, 9
Let h(t) = t**2 + 20*t + 69. Let z be h(-16). Find l such that -2*l**3 + 20*l**2 + 20 - 34*l + z - 9 = 0.
1, 8
Suppose 0 = 258*s - 255*s, 4*s = -2*n + 4. Let -14/19*c + 36/19*c**n - 2/19 = 0. What is c?
-1/9, 1/2
Let m be -1*10/6*(0 + -3). Suppose m*a - 590 = o, -a + o + 472 = 3*a. Factor 6 - a*n + 109*n + 9*n**3 - 5*n**2 - 2*n**2 + n**2.
3*(n - 1)*(n + 1)*(3*n - 2)
Suppose -3*f + 20 = 4*o, -19*o + 36 = -15*o - f. Find g, given that 3 + 38*g**2 + 447*g**3 + 453*g**3 - o - 13*g - 28*g**4 + 5*g**5 - 5 - 892*g**3 = 0.
-1, -2/5, 1, 5
Let q(o) = 5*o - 14. Let l be q(2). Let w be (10/(-3))/(l/24). Factor -2*c**2 + 21*c - 41*c - 7*c**3 + w*c - 5*c**4.
-c**2*(c + 1)*(5*c + 2)
Let o(k) = -k**3 + 85*k**2 - 1682*k + 962. Let d be o(30). Factor 7/3*u - 5/3*u**d + 2.
-(u - 2)*(5*u + 3)/3
Suppose -170*z + 286 = -39 - 15. Let j(w) be the first derivativ