
Suppose -3*y - 7*y = -100. Suppose y = -s + 13. Factor 2*j + 5*j**s + 8*j - 17*j + 2*j.
5*j*(j - 1)*(j + 1)
Let v(d) be the first derivative of -3*d**4 - 224*d**3/3 + 6*d**2 + 224*d + 1718. Determine j, given that v(j) = 0.
-56/3, -1, 1
Let b(z) be the third derivative of z**6/10 - 448*z**5/15 + 593*z**4/6 - 296*z**3/3 + 2*z**2 - 1099. Let b(q) = 0. What is q?
1/3, 1, 148
Let y(s) = 5*s**2 - 131*s + 28. Let j be y(26). Let d(h) be the second derivative of 0 + 4*h + 0*h**j - 1/18*h**3 - 1/72*h**4. Suppose d(r) = 0. What is r?
-2, 0
Let l(s) be the first derivative of 2*s**2 - 2/15*s**3 + 315 - 32/5*s. Factor l(f).
-2*(f - 8)*(f - 2)/5
Let c(o) = 8*o**2 - 1171*o - 7168. Let z(k) = -3*k**2 + 6*k - 2. Let m(w) = c(w) + z(w). Factor m(n).
5*(n - 239)*(n + 6)
Factor 40*q**2 + 629*q**3 + 639*q**3 - 1263*q**3 + 35*q.
5*q*(q + 1)*(q + 7)
Suppose 10 = s + 2*u, -5*s + 14*u + 70 = 19*u. Factor 13*c**4 - 12*c**3 + 15*c**4 + 4 + s*c**2 + 2*c**3 - 26*c**4 - 14*c.
2*(c - 2)*(c - 1)**3
Let g = 527 - 506. Let j(i) be the second derivative of 0 + 0*i**3 + 1/168*i**7 + g*i + 0*i**4 - 1/20*i**6 + 0*i**2 + 9/80*i**5. Factor j(l).
l**3*(l - 3)**2/4
Let b(l) be the second derivative of 5*l**4/12 - 25*l**3/3 - 595*l**2/2 + 39*l + 14. Determine i so that b(i) = 0.
-7, 17
Suppose -w + y = -3*w + 8, -w + 2*y + 4 = 0. Let d = -249 + 251. Factor -w*v**d + 1/2*v**3 + 0 + 8*v.
v*(v - 4)**2/2
Let s(f) be the first derivative of f**4/12 + 11*f**3/2 + 201*f + 58. Let z(v) be the first derivative of s(v). Let z(c) = 0. What is c?
-33, 0
Suppose -902289/5 + 2403/5*u**4 + 12/5*u**5 + 159792/5*u**3 + 697470*u**2 - 2747268/5*u = 0. What is u?
-67, -1/4, 1
Let r(o) be the first derivative of 4*o**3/3 + 1348*o**2 - 4968. Find v such that r(v) = 0.
-674, 0
Let x be (-20)/6*((-21)/(-14) - 0). Let w be -4*x/(-30) + 34/6. Let -3/2*s**w - 3/2*s + 6*s**2 + 0 - 9*s**3 + 6*s**4 = 0. Calculate s.
0, 1
Let i = -387506 + 387614. Factor 54*s - 9*s**2 - i + 1/2*s**3.
(s - 6)**3/2
Let k(v) be the first derivative of v**3/3 + 3*v**2 - 14*v - 8. Let j be k(-8). What is s in -s**4 - 1 - 5 + 7 - 4*s + j*s**3 + 2*s = 0?
-1, 1
Suppose 91*y - 89*y + 3*q = -2273, 5685 = -5*y - 5*q. Let z = -5666/5 - y. What is f in 2/5*f**2 - z*f + 72/5 = 0?
6
Let c(v) be the second derivative of -235/12*v**4 + 0 + 4*v - 1/4*v**5 - 2875/6*v**3 - 2645/2*v**2. Let c(p) = 0. What is p?
-23, -1
Let w(i) be the second derivative of -i**6/24 - i**5/6 - 5*i**4/24 + 83*i**2/2 + 35*i. Let m(s) be the first derivative of w(s). Factor m(o).
-5*o*(o + 1)**2
Let 48*l**2 + 82*l**2 - 50 - 60*l**3 + 60*l - 39 + 18 - 64 + 5*l**4 = 0. Calculate l.
-1, 1, 3, 9
Let d be ((-6)/9)/(8/420). Let q be (d/14)/(-1 + (-5)/(-6)). Factor 7*g**2 + 3*g**2 + 10*g**3 - q*g**3.
-5*g**2*(g - 2)
Suppose 0 = 2408*l + 2240*l - 154*l - 269640. Determine x so that -1/2*x**2 - 1800 - l*x = 0.
-60
Let s be (7/((-42)/(-64))*3*(-14)/(-8))/6. Determine x, given that s*x**4 + 0 + 13/3*x**5 - 3*x**3 - 28/3*x**2 - 4/3*x = 0.
-2, -1, -2/13, 0, 1
Let b(x) be the second derivative of 41*x**5/30 + 55*x**4/3 + 224*x**3/3 + 32*x**2/3 + 1103*x. Let b(m) = 0. Calculate m.
-4, -2/41
Let b(c) = c**3 - 297*c**2 - 293*c - 1490. Let r be b(298). Let 2/5*i**5 - 2/5*i**2 + 2/5*i**4 + 12/5*i + r - 14/5*i**3 = 0. Calculate i.
-3, -1, 0, 1, 2
Find y such that 574/5*y - 64/5*y**3 - 484/5*y**2 + 16/5*y**4 + 2/5*y**5 + 196 = 0.
-7, -1, 2, 5
Let z(m) be the third derivative of -2*m**7/21 - 13*m**6/24 + 85*m**5/12 + 295*m**4/12 + 20*m**3 - 80*m**2 + 6*m. Find v, given that z(v) = 0.
-6, -1, -1/4, 4
Let f(y) be the second derivative of -y**6/30 + y**5/20 + 17*y**4/12 - 7*y**3/2 - 18*y**2 + 1529*y. Solve f(k) = 0.
-4, -1, 3
Let i(r) be the third derivative of 0*r + 0 + 49*r**2 + 1/6*r**6 + 1/5*r**5 + 0*r**4 - 1/84*r**8 + 0*r**3 + 2/105*r**7. Let i(z) = 0. What is z?
-1, 0, 3
Determine a, given that -59*a**4 - 20*a**2 + 684*a**3 + 201*a**2 - 426*a**3 - 6*a - 374*a**3 = 0.
-3, 0, 2/59, 1
Let l = 11/610 - 24533/610. Let s = l - -1819/45. Factor -1/9 - s*p - 1/9*p**2.
-(p + 1)**2/9
Let i = -185 + 239. Factor -3*o**4 + i*o**3 - 18*o**4 - 3213*o**2 + 3153*o**2 + 3*o**5 + 24*o.
3*o*(o - 2)**3*(o - 1)
Let u(z) be the second derivative of 130/3*z**3 + 5/6*z**6 + 0 + 85/2*z**4 + 43/4*z**5 - 100*z**2 + 5*z. Factor u(d).
5*(d + 2)**2*(d + 5)*(5*d - 2)
Let m(q) be the first derivative of q**5 + 115*q**4/4 + 100*q**3/3 - 110*q**2 + 947. Determine z, given that m(z) = 0.
-22, -2, 0, 1
Let o(a) = -4*a**3 + 36*a**2 - 196*a. Let b(n) = -9*n**3 + 70*n**2 - 390*n. Let c(m) = -2*b(m) + 5*o(m). Factor c(v).
-2*v*(v - 10)**2
Let y = 3524/793 - 4669/1586. Suppose -7/4*a + y + 1/4*a**2 = 0. Calculate a.
1, 6
Let g(p) = -128*p**4 - 1827*p**3 - 5445*p**2 - 3*p. Let m(o) = -169*o**4 - 1826*o**3 - 5445*o**2 - 4*o. Let b(x) = 4*g(x) - 3*m(x). Factor b(y).
-5*y**2*(y + 3)*(y + 363)
Let k(y) be the first derivative of -4*y**3/9 - 5972*y**2/3 + 8849. Suppose k(w) = 0. Calculate w.
-2986, 0
Suppose 20*o - 11*o = -5364. Let l = -594 - o. Factor -2*v + 3/7*v**l + 8/7.
(v - 4)*(3*v - 2)/7
Let a be (2/(-10))/(43/(-2795)). Suppose 30*u = -a*u + 86. Let -24/7 + 44/7*x + 4/7*x**3 - 24/7*x**u = 0. What is x?
1, 2, 3
Let u = -8/641 - -5184/4487. Let b(k) be the first derivative of -1/21*k**3 - 13 - 5/7*k**2 + 1/28*k**4 - u*k. Solve b(y) = 0 for y.
-2, -1, 4
Let j = 4/265 - -494/2385. Let s(i) be the first derivative of j*i**3 + 2/3*i**2 + 2/3*i + 31. Factor s(z).
2*(z + 1)**2/3
Suppose 5*w - 4 = 2*s, -3*w = 942*s - 946*s + 6. Determine q, given that 2/3*q**w - 2/3 + 0*q = 0.
-1, 1
Suppose 466 = -169*l + 782 + 191. Let -336*p**2 + 1024/11*p - 96/11 - 686/11*p**4 + 4704/11*p**l = 0. What is p?
2/7, 6
Find d, given that -578*d**2 - 25 - 932*d + 288*d - 2156*d + 33 + 490*d = 0.
-4, 1/289
Let t(a) = a**2 - 11*a + 12. Suppose -11*q + 80 = -3*q. Let n be t(q). Solve 50/3 + 2/3*r**n - 20/3*r = 0 for r.
5
Suppose -3*y + 4*b = -37, 5*y = 4*b - 15 + 90. Find d, given that -2*d - y*d + 9*d**2 + 3*d**3 - 6*d**2 - 21*d**2 = 0.
-1, 0, 7
Let n(u) be the second derivative of 7/4*u**4 + 0*u**2 + 11/20*u**5 - 3/10*u**6 + 1/42*u**7 + 0*u**3 - 59*u + 0. Let n(m) = 0. Calculate m.
-1, 0, 3, 7
Suppose -982/7*x - 984/7*x**2 + 2/7 = 0. What is x?
-1, 1/492
Let b = -95 + 98. Suppose 2*n = -5*a + 8, 6*a - 10*a = 3*n - 12. Factor -3/7*j**b - 6/7*j**2 + a - 3/7*j.
-3*j*(j + 1)**2/7
Let a(s) = -2*s**3 - 4*s**2 - 6*s - 2. Let y be a(-1). Let -7*d**2 + 4*d**3 - 301*d + 317*d + 6*d**y + 17*d**2 = 0. What is d?
-2, 0
Suppose -1/7*n**2 + 954/7 - 953/7*n = 0. What is n?
-954, 1
Let c(t) = -16*t**3 - 3*t**2 + 3*t - 1. Let h be c(2). Let m = h + 137. Find o such that 4*o**5 - 16*o + 12*o**3 - o**m - 3 + 3 + 17*o**2 - 16*o**4 = 0.
-1, 0, 1, 2
Let b = -104 - -77. Let q be (b/(-15) - 0)*35/42. Solve -3/2*u - q*u**2 + 0 = 0.
-1, 0
Let m = 604 + -509. Let c be -5 - ((-3)/15 + (-466)/m). Solve c*b**2 + 2/19*b - 4/19 = 0 for b.
-2, 1
Factor -2385*s**2 - 223315500 + 3/2*s**3 + 1264050*s.
3*(s - 530)**3/2
Factor 144/5 - 48/5*k**2 - 48/5*k + 3/5*k**4 + 12/5*k**3.
3*(k - 2)**2*(k + 2)*(k + 6)/5
Let g be 78/12*2/3 + -4. Let n(a) be the first derivative of g*a - 1/9*a**3 + 7 + 0*a**2. Suppose n(q) = 0. What is q?
-1, 1
Let d(o) be the first derivative of 30 + 2/5*o**5 + 26/3*o**3 + 8*o - 3*o**4 - 12*o**2. Factor d(q).
2*(q - 2)**2*(q - 1)**2
Let a be (((-28)/8)/7)/(25/(-2850)). Suppose 48*k + 36 = a*k. Find s, given that -40/7*s**3 - 288/7*s**2 - 864/7*s - 864/7 - 2/7*s**k = 0.
-6, -2
Let x be (-16)/(-2) - (-520)/(-26). Let m be 10*-3*x/72. Factor -12/7*c**2 + 0 + 15/7*c**4 + 3/7*c**m + 18/7*c**3 - 24/7*c.
3*c*(c - 1)*(c + 2)**3/7
Let x(f) be the first derivative of f**6/33 - 2*f**5/11 - 7*f**4/11 + 24*f**3/11 + 72*f**2/11 + 1595. Suppose x(z) = 0. What is z?
-2, 0, 3, 6
Let l(m) = 12*m**2 - 3*m + 3. Let z be l(2). Suppose -y - 5*i + 35 = 2*y, z = 5*y + 5*i. Factor 6*a**2 + 3*a**4 - 4*a**3 - y*a**4 - 10*a + 6*a**3 + 4.
-2*(a - 1)**3*(a + 2)
Let z = 14 + -51. Let c = z - -40. Factor 248*b**3 - 278*b**c + 25*b**4 - 5*b**5 + 43*b - 3*b - 20*b**2.
-5*b*(b - 2)**3*(b + 1)
Let w(h) be the third derivative of -60*h**2 + 0*h**3 + 0*h - 1/30*h**4 + 0 + 17/150*h**5. Solve w(d) = 0 for d.
0, 2/17
Let x(z) be the third derivative of z**8/504 - z**6/45 - 20*z**2 + z. Factor x(r).
2*r**3*(r - 2)