Let n(b) = 7*b**4 - 14*b**3 - 180*b**2 - 35*b + 928. Let y(k) = 3*n(k) + 9*v(k). Factor y(q).
3*(q - 29)*(q - 2)*(q + 4)**2
Let z(x) = 6*x + 124. Let q be z(-19). Suppose q*t - 90 = -8*t. Suppose 0 + 1/7*m - 2/7*m**3 + 0*m**4 + 1/7*m**t + 0*m**2 = 0. Calculate m.
-1, 0, 1
Let p = 1/7 - -11/21. Let z = 1789063 + -1789059. Find q such that -p*q**z + 2/3*q**2 + 2/3*q - 2/3*q**3 + 0 = 0.
-1, 0, 1
Suppose 8 = 4*w - 4. Factor 6*c**2 - 2*c**2 - 288*c**w + 289*c**3 + 0*c**2 + 3*c.
c*(c + 1)*(c + 3)
Let a = 128/79 + -8099/5925. Let o = a + 2/25. Factor -1/2*h - 1/3 + o*h**2.
(h - 2)*(2*h + 1)/6
Solve -90134*j**2 + j**3 + 90009*j**2 - 395*j - 6*j**3 + 525 = 0 for j.
-21, -5, 1
Let z(j) be the second derivative of -j**7/5880 - j**6/2520 + j**5/84 - j**4/21 + 25*j**3/3 + 4*j + 2. Let w(t) be the second derivative of z(t). Factor w(b).
-(b - 2)*(b - 1)*(b + 4)/7
Let r be -4 + -2*(-3 + 4 - 4). Suppose -25*o**4 + 60*o**3 - 2 + 18 - 60*o + 5*o**r + 6 - 2 = 0. Calculate o.
-1, 2/5, 1, 2
Let d(n) be the second derivative of n**6/10 - 153*n**5/20 + 156*n**4 + 338*n**3 - 454*n. Determine v, given that d(v) = 0.
-1, 0, 26
Suppose 3*o - 142 + 129 = 2*r, 2*o + 2 = -4*r. Let h(i) be the second derivative of 11*i + 0 - 1/4*i**o - 1/24*i**4 - 1/2*i**2. Factor h(w).
-(w + 1)*(w + 2)/2
Let q(l) be the first derivative of -l**4/96 - l**3/6 - l**2 + 25*l + 100. Let n(a) be the first derivative of q(a). Factor n(o).
-(o + 4)**2/8
Suppose 0 = 10*u - 2 - 18. Suppose 0 = -4*v + 3 + 5. Factor 80 - 2*s**2 + s**u + 6*s**v + 2*s + 38*s.
5*(s + 4)**2
Suppose 37*m**4 - 18*m**3 - 112 - 45*m**4 + 72*m + 20*m**2 + 10*m**4 = 0. What is m?
-2, 2, 7
Let y(p) = p - 38. Let m be y(-6). Let z be (-5)/((-15)/6) - 0/m. Factor -6/7*b**z - 24/7*b + 0.
-6*b*(b + 4)/7
Let m = -22057 + 22062. Let y(v) be the third derivative of 0*v + 0*v**4 + 0 - 39*v**2 + 0*v**3 + 1/240*v**6 + 7/120*v**m. Determine a so that y(a) = 0.
-7, 0
Let h = 10/229 + 159/1603. Factor 1/7*y**2 - h*y**3 - 1/7*y**4 + 0*y + 1/7*y**5 + 0.
y**2*(y - 1)**2*(y + 1)/7
Let -448/13 + 220/13*u + 2/13*u**2 = 0. Calculate u.
-112, 2
Suppose 0 = 7*f - 2*f + 15, -5*h + 5*f = -55. Let s be 456/1026 + h/(-18). Factor 1/4*d**2 - 1/2*d + s.
d*(d - 2)/4
Let t be (-81)/15*-89*2/408. Let y = 3/68 + t. Suppose y - 6/5*w**2 + 6/5*w = 0. What is w?
-1, 2
Let s(w) = 19*w + 0*w - 14*w + w**2 - 34. Let a be s(-9). Factor -81/5 - 19/5*h**a + 99/5*h + 1/5*h**3.
(h - 9)**2*(h - 1)/5
Suppose -5*r = -13 + 3. Suppose 7*m - r*m - 4*i = 12, -3 = m + i. What is b in 6 - 21*b + 3*b**4 + 24*b**3 - 39*b**3 + m + 27*b**2 = 0?
1, 2
Let z(v) = -2*v**3 - 104*v**2 + 338*v + 412. Let q(g) = -g**3 - 105*g**2 + 328*g + 411. Let f(p) = 4*q(p) - 3*z(p). Suppose f(w) = 0. Calculate w.
-1, 4, 51
Let y = -167 + 195. What is d in 4*d**2 + 7*d - y*d - 12 + 5*d + 8*d = 0?
-1, 3
Let t = 1764 + -1761. Let i(p) be the second derivative of -1/15*p**5 - 1/45*p**6 + 1/18*p**4 + 0 + 0*p**2 + 7*p + 2/9*p**t. Factor i(u).
-2*u*(u - 1)*(u + 1)*(u + 2)/3
Suppose 3*d = 2*x - 55, 5*x = -5*d - 605 + 530. Solve -2/7*p**x - 104/7*p - 1352/7 = 0 for p.
-26
Factor 249/4*t**2 + 5475/4 - 3/4*t**3 - 2265/4*t.
-3*(t - 73)*(t - 5)**2/4
Let w(h) be the first derivative of h**6/10 + 6*h**5/5 + 13*h**4/4 + 3*h**3 + 48*h - 61. Let g(u) be the first derivative of w(u). Factor g(y).
3*y*(y + 1)**2*(y + 6)
Let b = -8291 - -41457/5. Let l(m) be the first derivative of -1/10*m**4 - b*m**2 - 8 + 0*m + 2/5*m**3. Factor l(r).
-2*r*(r - 2)*(r - 1)/5
Find t, given that 224/9 - 4/9*t**3 - 56/9*t**2 - 164/9*t = 0.
-8, -7, 1
Let w be (1 - 4)/((-3)/(-15)*-5). Suppose 1/2*g**3 - w + g**2 - 5/2*g = 0. Calculate g.
-3, -1, 2
Let b be (1/(-9)*3)/((-3)/189). Let n be 60/14 - 6/b. Solve -13*w + 6 + 4*w - 4*w**2 + 3*w**2 + n*w**2 = 0.
1, 2
Suppose 2*v + 20 = 6*v. Determine f, given that -15*f - f**v + 2*f**4 + 15*f = 0.
0, 2
Let n(j) be the third derivative of 0*j + j**2 + 0*j**4 + 0*j**5 + 1/672*j**8 + 0*j**3 - 1/210*j**7 + 55 + 1/240*j**6. Factor n(r).
r**3*(r - 1)**2/2
Let c(j) be the third derivative of j**8/1176 + 32*j**7/105 + 555*j**6/14 + 13500*j**5/7 - 140625*j**4/28 + 2592*j**2 + 2*j. Factor c(z).
2*z*(z - 1)*(z + 75)**3/7
Let k be -19 + 28 + (-5 + 1 - 2). Suppose -k*f = 5*o + 15, 2*f + 4*o = 5 - 17. Let 0*c**2 + f - 1/2*c**5 + 0*c + 1/4*c**3 - 1/4*c**4 = 0. What is c?
-1, 0, 1/2
Suppose -5*l = 62 + 163. Let h be 35/l*(-36)/42. Suppose h*u**3 + 4/3 + 0*u**2 - 2*u = 0. Calculate u.
-2, 1
Let p = -22/63 - -157/630. Let d = 3/5 + p. Factor 5/12 - d*m + 1/12*m**2.
(m - 5)*(m - 1)/12
Let x be (11/(-55))/(6/(-10))*6. Let o be (-147)/(-70)*32/28. Let 0 + 4/5*j - 4*j**3 + 16/5*j**5 - 12/5*j**4 + o*j**x = 0. What is j?
-1, -1/4, 0, 1
Factor 4*l + 1/2*l**4 + 0 + 7*l**2 + 7/2*l**3.
l*(l + 1)*(l + 2)*(l + 4)/2
Let u(f) = -30*f**2 - 74*f + 7. Let d be u(-7). Let x = 947 + d. Suppose 0*n + 3/4*n**3 - 1/2*n**4 - 3/4*n**5 + 1/2*n**x + 0 = 0. Calculate n.
-1, -2/3, 0, 1
Let d(g) be the first derivative of -4*g**3/21 - 1020*g**2/7 + 292*g + 4402. Factor d(r).
-4*(r - 1)*(r + 511)/7
Find q, given that 34*q**3 - 175 - 14*q**3 + 55*q**2 - 23*q**3 - 2*q**3 - 115*q = 0.
-1, 5, 7
What is c in 139*c**2 + 19*c - 12 + 161*c**2 - 304*c**2 = 0?
3/4, 4
Let -34/3*i**2 - 7/3*i**5 + 47/3*i + 44/3*i**4 - 10/3 - 40/3*i**3 = 0. Calculate i.
-1, 2/7, 1, 5
Let j = 873 - 7856/9. Factor -52/9*i + j*i**3 - 2*i**2 + 1/9*i**4 - 40/9.
(i - 5)*(i + 2)**3/9
Let t(i) be the first derivative of -1/10*i**5 + 2/27*i**3 + 0*i**2 - 4*i - 2 - 7/54*i**4. Let v(a) be the first derivative of t(a). Factor v(g).
-2*g*(g + 1)*(9*g - 2)/9
Let k(t) be the first derivative of t**3/3 - 5*t**2/2 - 14*t - 37. Let n be k(8). Let -54*j + n + 2*j**3 + 12*j**2 + 24*j + 6 = 0. Calculate j.
-8, 1
Solve 165984*o**4 - 12*o**2 - 399*o**2 - 165981*o**4 + 408*o**3 = 0.
-137, 0, 1
Let j(g) be the first derivative of g**5/10 + 3*g**4 - 17*g**3/2 + 13*g**2/2 - 554. Factor j(h).
h*(h - 1)**2*(h + 26)/2
Let j(k) be the first derivative of -k**5/30 + k**4 - 12*k**3 - 16*k**2 + 13. Let n(i) be the second derivative of j(i). Factor n(b).
-2*(b - 6)**2
Solve 527/3*d + 2023/3 + 41/3*d**2 + 1/3*d**3 = 0 for d.
-17, -7
Let f(i) be the first derivative of -7*i**5/15 - 143*i**4/6 - 2752*i**3/9 + 581*i**2 - 147*i - 1107. Let f(k) = 0. Calculate k.
-21, 1/7, 1
Let p be (-14)/42 + 52/3. Suppose 4*x - 27 = x. Determine t, given that 3 + 27*t**3 + p*t + 45*t**2 + 4*t + 9*t - x*t = 0.
-1, -1/3
Suppose -l + 12 = t + 6, 5*t + l = 10. Let a be ((-182)/(-18) - 10)*(t + 1). Let 2/9 + 4/9*g + a*g**2 = 0. Calculate g.
-1
Let r = -36317 + 36319. Let t(d) be the first derivative of -3/4*d - 11 - 3/8*d**r + 3/16*d**4 + 1/4*d**3. Factor t(v).
3*(v - 1)*(v + 1)**2/4
Let i(c) be the second derivative of -c**6/120 - 11*c**5/80 - 17*c**4/48 + 11*c**3/24 + 9*c**2/4 + 488*c. Find t, given that i(t) = 0.
-9, -2, -1, 1
Let w be ((-17)/3570)/(2/(-116)) - 75/(-375). Let r be -6 + 5 + 23/(-63)*-3. Find l, given that 0 + w*l**3 + r*l**4 + 2/3*l**2 + 2/7*l = 0.
-3, -1, 0
Factor -25/2*w + 750 - 5/2*w**2.
-5*(w - 15)*(w + 20)/2
Let h(r) = 11*r**2 + 100*r - 39. Let w = 473 - 477. Let b(l) = 21*l**2 + 200*l - 79. Let x(y) = w*b(y) + 9*h(y). Factor x(m).
5*(m + 7)*(3*m - 1)
Let n(l) be the first derivative of -l**4/6 - 284*l**3/9 - 3185*l**2/3 - 39208*l/3 + 8702. Factor n(p).
-2*(p + 13)**2*(p + 116)/3
Let u(f) be the second derivative of 0 - 136*f + 17/6*f**3 - 1/24*f**4 - 289/4*f**2. Suppose u(r) = 0. What is r?
17
Let g(f) be the third derivative of -f**8/2016 - 2*f**7/315 - 5*f**6/144 - 19*f**5/180 - 7*f**4/36 - 2*f**3/9 + f**2 - 112*f. Solve g(y) = 0.
-2, -1
Let y(k) be the third derivative of k**5/150 - 226*k**4/5 + 612912*k**3/5 - 96*k**2 - 8*k. Find x, given that y(x) = 0.
1356
Let i = -79 + 83. Factor 11*b**4 - 4*b**3 - b**3 - b**i - 5*b**4.
5*b**3*(b - 1)
Let l(t) = -2*t**2 + 11*t. Let c(p) = -6*p**2 + 32*p. Suppose -33*w = -34*w + 8. Let r(u) = w*l(u) - 3*c(u). Factor r(d).
2*d*(d - 4)
Let m(v) be the second derivative of v**5/60 + v**4/24 - v**3 - 123*v**2 - 79*v - 1. Let q(p) be the first derivative of m(p). Determine l, given that q(l) = 0.
-3, 2
Suppose -87 = 4*o + 5*q, -3*q - 547 = o - 492. Factor 0 + 3/5*r**o - 21/5*r.
3*r*(r - 7)/5
Suppose u - 5*p = -7, 11*p - 35 = 6*p. Let j(o) be the first derivative of -2/7*o**4 -