1, 1, 5
Let y(v) = 2*v**3 + v. Let l(k) = -25*k**3 - 15*k**2 - 15*k + 20. Let t(f) = -3*f - 102. Let w be t(-39). Let c(i) = w*y(i) + l(i). Find r such that c(r) = 0.
-1, 2
Suppose -4*z + r + 9 = -2*z, 2 = z + 2*r. Let h(q) = -9*q**3 - 24*q**2 - 29*q - 14. Let l(w) = -w**3 - w**2 - w - 1. Let f(v) = z*l(v) - h(v). Factor f(y).
5*(y + 1)**2*(y + 2)
Let z(q) = -14 - 109 - q**2 - 40 - 29*q - 4 + 2. Let d be z(-8). Suppose -3/2*j**2 + 3/2*j**4 + 7/4*j + 0 - 2*j**d + 1/4*j**5 = 0. Calculate j.
-7, -1, 0, 1
Let z(n) be the first derivative of -3/5*n**2 - 98 + 2/15*n**3 + 4/5*n. Factor z(j).
2*(j - 2)*(j - 1)/5
Let r(i) be the third derivative of -i**7/42 + 47*i**6/24 + 35*i**5/4 - 1735*i**4/24 + 490*i**3/3 - i**2 - 11*i + 20. Factor r(z).
-5*(z - 49)*(z - 1)**2*(z + 4)
Let j(v) = 26*v**2 + 1458*v + 115. Let m be j(-56). Let n(q) be the second derivative of 1/14*q**4 + 0 - 1/7*q**m - 13*q - 6/7*q**2. Factor n(b).
6*(b - 2)*(b + 1)/7
Suppose -118*b**3 - 26*b**3 + 39*b**4 + 237*b**2 - 172331 - 78*b**2 + 172331 - 54*b = 0. What is b?
0, 9/13, 1, 2
Let g be -15*((-8 + 2)*4 + 1). Let l be ((-184)/g)/((-16)/36). Factor 0*y + 2/5*y**3 - l*y**2 + 8/5.
2*(y - 2)**2*(y + 1)/5
Let n(h) be the third derivative of -h**6/200 - 11*h**5/100 + 19*h**4/10 - 32*h**3/5 - 60*h**2 + 15. Determine q so that n(q) = 0.
-16, 1, 4
Let j(n) be the third derivative of -27*n**7/70 + 189*n**6/5 - 738*n**5/5 + 244*n**4 - 216*n**3 + 815*n**2 - 2*n. Factor j(t).
-3*(t - 54)*(3*t - 2)**3
Let h(s) be the second derivative of -4232*s**2 + 184/3*s**3 - 1/3*s**4 + 0 + 50*s. Factor h(z).
-4*(z - 46)**2
Let w be (-2)/(-6)*-1 + 36386/339. Suppose 103*g - w*g + 12 = 0. Factor 0 + 0*b - 1/2*b**2 - 1/2*b**g.
-b**2*(b + 1)/2
Let o(b) be the first derivative of -b**4/28 + 65*b**3/21 - 122*b**2/7 + 820. Factor o(x).
-x*(x - 61)*(x - 4)/7
Let a(i) = i**2 + i - 9. Let l(m) = -2*m**4 - 15*m**3 + m**2 + 36*m - 41. Let o(u) = 3*a(u) - l(u). Solve o(b) = 0.
-7, -2, 1/2, 1
Let n = -1783250 + 19615776/11. Factor 58/11*r - 30/11 - 2/11*r**3 - n*r**2.
-2*(r - 1)**2*(r + 15)/11
Let c = 10924 - 21847/2. Let x = 83/2 + -165/4. Let x + 1/4*z**2 + c*z = 0. Calculate z.
-1
Let q = -227 + 547. Let p = q - 320. Factor 3/4*b**3 + 0 + 3/2*b**5 + p*b + 9/4*b**4 + 0*b**2.
3*b**3*(b + 1)*(2*b + 1)/4
Let b(y) be the first derivative of y**3 - 507*y**2 - 2040*y - 597. Solve b(g) = 0.
-2, 340
Let g = -13374 + 13379. Let y be (2/6)/(2/12). Solve -g*m**2 - 2*m + 266 - 267 + 4*m**y = 0 for m.
-1
Let u be 4/(-3)*6/(-4). Let f = 21 - u. Solve 0*t**3 + 12*t**5 + 4*t**2 - 24*t**5 + f*t**3 + t**3 - 4*t**4 - 8*t = 0.
-1, 0, 2/3, 1
Let l(w) = -3*w**2 - 72*w + 75. Let u(z) be the third derivative of -z**5/60 - z**4/24 + z**3/3 - z**2 + 18*z. Let i(m) = -l(m) + 6*u(m). What is d in i(d) = 0?
1, 21
Let t(a) be the first derivative of 2*a**5/105 - 29*a**4/21 - 750. Factor t(h).
2*h**3*(h - 58)/21
Let x(m) be the first derivative of 7*m**5/170 + 8*m**4/51 + 11*m**3/51 + 2*m**2/17 + 137*m + 147. Let q(h) be the first derivative of x(h). Factor q(z).
2*(z + 1)**2*(7*z + 2)/17
Determine q, given that 20*q - 375 + 1/3*q**2 = 0.
-75, 15
Let q(u) = 27*u**4 - 243*u**3 + 201*u**2 - 45*u + 30. Let i(r) = -7*r**4 + 61*r**3 - 50*r**2 + 12*r - 8. Let k(l) = -15*i(l) - 4*q(l). Factor k(n).
-3*n**2*(n - 18)*(n - 1)
Suppose 52 = 5*p - 2*z - z, -5*z + 4 = 3*p. Suppose 5*k - 7 - p = 0. Factor 7*i + 5*i + 4*i**3 + 10*i**k - 12*i**2 - 4 - 10*i**3.
4*(i - 1)**3
Determine u so that 30/13 + 64/13*u**2 + 20/13*u**3 + 2/13*u**4 + 76/13*u = 0.
-5, -3, -1
Let l(v) = -v. Let i be l(-2). Suppose -4*y = r - 11, 4 = i*y + r - 1. Factor -9 - y*n**2 - 19*n + 60*n - 29*n.
-3*(n - 3)*(n - 1)
Let b(o) be the first derivative of 3*o**4/4 - 11*o**3/3 - 19*o**2/2 - 5*o - 2413. Determine t so that b(t) = 0.
-1, -1/3, 5
Let p = 2/18481 + 18477/36962. Factor 97/2*t**2 + p*t**4 - 72*t + 32 - 9*t**3.
(t - 8)**2*(t - 1)**2/2
Let n(p) be the third derivative of p**8/1176 - 31*p**7/735 + p**6/15 + 2*p**5/7 + 2102*p**2. Suppose n(g) = 0. Calculate g.
-1, 0, 2, 30
Let d(l) = 18*l**3 - 340*l**2 - 696*l - 56. Let m(h) = -4*h**3 + 68*h**2 + 140*h + 12. Let k(g) = 3*d(g) + 14*m(g). Let k(w) = 0. Calculate w.
-32, -2, 0
Factor -4*g**2 - 293764 + 5688*g - 1575*g - 1945*g.
-4*(g - 271)**2
Suppose -2*r + 3*r = -2, -4*g + 336 = -2*r. Let i = g - 81. Solve 16*m - 4 + 6*m**2 - 8*m**i + 22 = 0 for m.
-1, 9
Factor -240*t**2 - 2*t**3 - 772 + 123*t**2 - 20 + 618*t + 5*t**3.
3*(t - 33)*(t - 4)*(t - 2)
Suppose 97969/5 + 626/5*w + 1/5*w**2 = 0. Calculate w.
-313
Let d be (3*(-40)/(-30))/((-707)/(-808)). Factor d*l + 12/7 + 5/7*l**2.
(l + 6)*(5*l + 2)/7
Let h(x) be the first derivative of -8*x**5/5 + 19*x**4/2 + 678*x**3 - 7975*x**2 - 4114*x - 177. Find a such that h(a) = 0.
-17, -1/4, 11
Let u(a) = -53*a**3 + 4561*a**2 - 31008*a + 43972. Let y(t) = -11*t**3 + 912*t**2 - 6201*t + 8794. Let j(d) = -3*u(d) + 14*y(d). Factor j(b).
5*(b - 176)*(b - 5)*(b - 2)
Let -64*n**2 + 856*n**3 - 414*n**2 - 447*n**2 - 4*n**4 + 73*n**2 + 0*n**4 = 0. Calculate n.
0, 1, 213
Let z(t) be the third derivative of t**8/840 + 671*t**7/525 - 50*t**2 - 9. Factor z(v).
2*v**4*(v + 671)/5
Let k(v) = 4*v**2 - 8*v - 9. Let a(w) = 2*w**2 - 1. Suppose -x + 4*x + 3 = 0. Let p(b) = x*k(b) + 3*a(b). Find u such that p(u) = 0.
-3, -1
Suppose -4*h + p = -16, 4 = 2*h - 2*p + 2. Suppose 4*u - 7 = -h*d + 4, d = -u + 2. Factor 0*r**2 - 10*r**d - 70*r**4 + 2*r**5 + 66*r**4 + 12*r**2.
2*r**2*(r - 3)*(r - 1)*(r + 2)
Let j(t) be the third derivative of -t**8/504 + 2*t**6/45 + t**5/15 - 7*t**4/36 - 2*t**3/3 + 10900*t**2. Find r, given that j(r) = 0.
-2, -1, 1, 3
Let f(l) be the second derivative of -l**7/1400 - 11*l**6/600 - l**5/20 + l**3/6 + 2*l**2 + 70*l. Let w(i) be the second derivative of f(i). Factor w(u).
-3*u*(u + 1)*(u + 10)/5
Let w(k) be the first derivative of -2/15*k**3 - 16/5*k - 6/5*k**2 + 88. Factor w(t).
-2*(t + 2)*(t + 4)/5
Let x be (-56)/(-12) + 6/(-9). Let a(k) = k**3 + 14*k**2 + 4. Let p be a(-14). Let p*z**2 + z**2 - 8*z + 4*z**2 - 5*z**2 + x = 0. What is z?
1
Let m = -3662 - -3667. Let s(k) be the second derivative of 0*k**2 + 0*k**3 + 0 - 1/28*k**7 + 3/40*k**m - 10*k + 1/20*k**6 - 1/8*k**4. Factor s(j).
-3*j**2*(j - 1)**2*(j + 1)/2
Suppose 0*o + 5*o = 2*m + 60, 3*o - 10 = -4*m. Suppose 4*s - o = -2. Factor 3*i - 3*i**4 + i**2 - 6*i**3 + 2*i**5 - 3 + i**5 + 5*i**s + 0.
3*(i - 1)**3*(i + 1)**2
Factor 16740*q - 9162 - 1497 - 1653 - 8640*q**2 + 172*q**5 + 175*q**5 - 343*q**5 + 2040*q**3 - 200*q**4.
4*(q - 38)*(q - 3)**4
Let z = -18146 - -18151. Let b(d) be the third derivative of -5/8*d**4 - 3/2*d**3 + 0 - 1/120*d**6 - 7/60*d**z - 15*d**2 + 0*d. Factor b(p).
-(p + 1)*(p + 3)**2
Let s(u) = 38*u**3 - 54*u**2 + 80*u + 971. Let a(i) = -7*i**3 + 11*i**2 - 16*i - 194. Let g(v) = 11*a(v) + 2*s(v). Find y such that g(y) = 0.
-3, 8
Let r(u) be the first derivative of -u**4 + 512*u**3/3 - 7930*u**2 - 33800*u - 1807. Find z such that r(z) = 0.
-2, 65
Let d(w) be the third derivative of -w**6/180 + 23*w**5/15 - 205*w**4/3 + 11800*w**3/9 - 8970*w**2. Factor d(x).
-2*(x - 118)*(x - 10)**2/3
Let l be (330/(-30))/(1/(-161)) + 5. Suppose -3*p = l - 1785. Solve 11/4*f**2 + 0 - 5/2*f - 1/4*f**p = 0.
0, 1, 10
Let a be (-5 - -1) + -4 + (27 - 1). Let q be 1 - 0 - (1034/55 - a). Factor 0*b + 1/5*b**2 - q.
(b - 1)*(b + 1)/5
Suppose 0 = -183*r - 15*r. Let n(b) be the first derivative of 1/14*b**4 + 4/21*b**3 + 0*b**2 + r*b + 23. Factor n(y).
2*y**2*(y + 2)/7
Suppose 0 = 3*m - 5*t - 482, -3*m + 114*t - 111*t + 474 = 0. Let q be 11/m*288/12. Factor 3/7 + 18/7*x**2 - q*x + 3/7*x**4 - 12/7*x**3.
3*(x - 1)**4/7
Suppose -230*r - 55 = 113*r - 741. Let 1/2*l**r + 2025/2 - 45*l = 0. Calculate l.
45
Let w be (((-290)/(-435))/(2/(-126))*16/(-6))/22. Find o such that 442/11*o + 676/11 + 2/11*o**3 + w*o**2 = 0.
-13, -2
Factor 0 - 1/4*x**4 - 2*x**3 - 9/2*x - 21/4*x**2.
-x*(x + 2)*(x + 3)**2/4
Suppose -2*k = -4*i + 12, 3*i - 3*k + k - 8 = 0. Factor 1295 + 5754 - 2149 - 276*d**2 + 4620*d + i*d**3.
4*(d - 35)**2*(d + 1)
Determine v so that -516*v - 156*v**2 + v**3 + 240*v - 220*v - 576 - v**4 - 22*v**3 = 0.
-9, -4
Let r(i) be the third derivative of i**6/120 - 97*i**5/20 + 289*i**4/12 - i**2 - 83*i. Find s such that r(s) = 0.
0, 2, 289
Let y(u) be the second derivat