
-1, 1, 7
Find z such that 3/5*z**3 - 129/5*z + 126/5*z**2 + 0 = 0.
-43, 0, 1
Let j(c) = -c**2 + 4*c + 7. Let z be j(0). Factor -z - 77 - 76*s + 103*s**2 + 806 - 101*s**2.
2*(s - 19)**2
Find h such that 4/3*h - 3/2*h**4 - 7/6*h**5 + 0 + 13/3*h**3 + 6*h**2 = 0.
-2, -1, -2/7, 0, 2
Factor 3*l**4 - 539*l**3 + 223587*l**2 + 43*l - 43*l + 2177*l**3.
3*l**2*(l + 273)**2
Let u be 32 + -27 - (1 - 584). Suppose 0 = -u*s + 592*s. Solve s*x**2 + 0*x - 3/7*x**3 + 0 - 6/7*x**4 - 3/7*x**5 = 0 for x.
-1, 0
Suppose 0 = 6*y - 4*y + 3*m - 41, 0 = y + 2*m - 21. Let q(j) be the second derivative of y*j + 1/84*j**4 - 4/7*j**2 + 0 - 1/21*j**3. Factor q(x).
(x - 4)*(x + 2)/7
Let f(u) be the second derivative of 1/20*u**5 + 0 + 1/18*u**4 + 0*u**3 + 0*u**2 - 53*u + 1/42*u**7 - 4/45*u**6. Solve f(g) = 0 for g.
-1/3, 0, 1, 2
Let k(z) be the first derivative of z**3/2 + 51*z**2 + 945*z/2 - 1785. Let k(n) = 0. Calculate n.
-63, -5
Let t(x) = 23*x - 15. Let d be t(-1). Let p be -27 + 24 + d/(-6). Factor 2/3*w**2 + 8/3 + p*w.
2*(w + 1)*(w + 4)/3
Suppose -366*h = -185*h - 187*h. Let d(a) be the second derivative of 1/25*a**5 + 2/15*a**4 - 17*a + h + 0*a**2 + 2/15*a**3. Suppose d(m) = 0. Calculate m.
-1, 0
Suppose 48179 + 34699 = 57*c. Let j = c + -7269/5. Suppose -4/5*u + 4/5 + j*u**2 = 0. Calculate u.
2
Let a(z) be the third derivative of 1/450*z**6 - 1/10*z**4 + 3 + 1/75*z**5 - z**2 + 0*z + 20/3*z**3. Let m(g) be the first derivative of a(g). Factor m(u).
4*(u - 1)*(u + 3)/5
Let d(o) = 7*o**5 + 46*o**4 + 136*o**3 - 432*o**2 + 245*o - 2. Let a(g) = 2*g**5 - g**4 - g**3 + g - 1. Let f(c) = -2*a(c) + d(c). Factor f(q).
3*q*(q - 1)**2*(q + 9)**2
Let d(b) = -11*b**3 - 55*b**2 - 1501*b - 6125. Let t(f) = 15*f**3 + 55*f**2 + 1500*f + 6125. Let l(c) = 5*d(c) + 4*t(c). Find o, given that l(o) = 0.
-7, 25
Suppose 0*u - 3*u = -2*u. Suppose u = -3*c + 6*c - 6. Factor 2/3 + 1/3*q**c + q.
(q + 1)*(q + 2)/3
Let g(o) = -2*o**4 + o**3 + 3*o + 1. Let r(u) = -7*u**4 + 30*u**3 + 148*u**2 + 306*u + 175. Let y(m) = 20*g(m) - 5*r(m). Solve y(h) = 0 for h.
-19, -3, -1
Let r(o) = 2*o**3 - 9*o**2 + 5*o - 1. Let z be r(4). Factor -10*n**z - 5*n**4 + 4*n**4 + 19*n**3 - 4*n**3.
-n**3*(n - 5)
Let g(i) = -24 + 10*i**3 - 22*i**3 - 8*i**2 + 11*i**3 + 16*i. Let q be g(-10). Factor -8*o**4 - 16*o**4 + q*o**3 + 8*o**4 + 4*o**5.
4*o**3*(o - 2)**2
Let y be 6419/1441 + 18/33. Let v(a) be the first derivative of -1/57*a**6 - 4/95*a**y + 0*a + 10 + 1/19*a**2 + 4/57*a**3 + 0*a**4. Factor v(r).
-2*r*(r - 1)*(r + 1)**3/19
Let b = 1126053 - 1126043. Determine s so that 8/9*s**2 + b*s**4 - 8/9*s + 106/9*s**3 + 0 = 0.
-1, -2/5, 0, 2/9
Let c = -14906 - -14911. Let o(q) = -q - 1. Let m be o(-1). Determine h, given that -27/2*h**3 - 3/2*h**c + m*h + 0*h**2 + 0 + 9*h**4 = 0.
0, 3
Let i(b) be the first derivative of -b**4 + 366*b**2 + 728*b - 5320. Solve i(x) = 0 for x.
-13, -1, 14
Let h(k) be the first derivative of -4*k**3/3 + 1440*k**2 + 2884*k - 825. Let h(a) = 0. What is a?
-1, 721
What is g in 2/9*g**5 - 250/9*g**4 + 1516/9*g**2 + 250/3 - 2006/9*g - 4/3*g**3 = 0?
-3, 1, 125
Suppose 31*r - 17109 - 16929 = 0. Suppose -r*y + 1095*y + 12 = 0. Factor 0 - y*t - 4/3*t**2.
-4*t*(t + 3)/3
Suppose 12 + 4 = 8*r. Factor -f + 732*f**r - 729*f**2 + f.
3*f**2
Let p be ((-5)/(-4))/((-3)/12)*3. Let w be (p/(-9) + -3)/((-1)/3). Determine x so that -x**3 + 4*x**3 - 24 - 28*x + x**2 + x**2 + x**w - 8*x**2 = 0.
-2, 3
Suppose 17820*p**4 - 12150*p**5 - 10224*p**3 - 1184/3*p + 8608/3*p**2 + 64/3 = 0. What is p?
2/9, 2/5
Let j(u) be the first derivative of u**5/15 + 19*u**4/3 + 74*u**3/3 - 7*u**2/2 - 2*u + 20. Let k(c) be the second derivative of j(c). Factor k(m).
4*(m + 1)*(m + 37)
Let l(a) be the second derivative of 37/15*a**2 - 47*a - 38/45*a**3 + 0 + 1/90*a**4. Suppose l(v) = 0. What is v?
1, 37
Let f(v) be the second derivative of 10*v**3 + 55/12*v**4 - 3*v + 1/4*v**5 - 3 - 1/2*v**6 + 10*v**2 - 5/42*v**7. Factor f(l).
-5*(l - 2)*(l + 1)**3*(l + 2)
Suppose 15 = -0*o + 5*o. Suppose 40 - 8*v**o - 86*v + 10*v - 128*v**2 - 4*v**3 = 0. What is v?
-10, -1, 1/3
Factor -3648 + 0*f**2 + 160*f + 6*f**2 - 66*f - 150*f - 2*f**2.
4*(f - 38)*(f + 24)
Determine x, given that 10176*x - 10239*x - 309*x**4 + 30*x**5 - 159*x**2 + 413*x**3 + 304*x**3 = 0.
-1/5, 0, 1/2, 3, 7
Let y(b) be the third derivative of 3*b - 2/45*b**5 + 0 - 16/9*b**3 - 1/30*b**6 + 2/315*b**7 + 15*b**2 + 2/3*b**4. Factor y(s).
4*(s - 2)**2*(s - 1)*(s + 2)/3
Let k(p) be the first derivative of -4*p**6/3 - 138*p**5/5 + 59*p**4/2 + 58*p**3 - 55*p**2 - 36*p + 3879. Solve k(o) = 0.
-18, -1, -1/4, 1
Suppose -215*w = -49*w + 38*w - 9384. Let q(d) be the first derivative of w - 1/16*d**4 + 1/4*d**3 - 1/4*d**2 + 0*d. Determine a, given that q(a) = 0.
0, 1, 2
Let k(s) be the third derivative of s**8/13440 - s**7/2240 + s**6/1440 + 77*s**3/6 - 12*s**2 - 2*s. Let a(h) be the first derivative of k(h). Factor a(y).
y**2*(y - 2)*(y - 1)/8
Let y(t) be the first derivative of 0*t + 2/15*t**3 + 84 - 16/5*t**2. Factor y(j).
2*j*(j - 16)/5
Let p be (-58)/(-14) - ((-504)/(-98) + -4). Let a = 219/86 + -2/43. Factor 0 + 1/2*n - 1/2*n**p - a*n**4 + 5/2*n**2.
-n*(n - 1)*(n + 1)*(5*n + 1)/2
Let a(k) = k**2 + 6*k - 35. Let r be a(4). Factor -36*z**3 + 165*z**2 + 4 - r*z + z - 169*z**4 + 56*z - 16*z**3.
-(z - 1)*(z + 1)*(13*z + 2)**2
Let g(w) be the first derivative of w**3/6 + 1149*w**2/2 + 1320201*w/2 + 3642. Factor g(q).
(q + 1149)**2/2
Let v(f) = f**3 - 3*f**2 - f + 3. Let x(z) = 9*z**3 - 186*z**2 + 3009*z - 17532. Let s(k) = 6*v(k) - x(k). Determine u, given that s(u) = 0.
15, 26
Let l(b) be the third derivative of b**8/336 + b**7/5 + 49*b**6/15 + 76*b**5/5 - 66*b**4 - 720*b**3 - 11858*b**2. What is c in l(c) = 0?
-30, -6, -2, 2
Let j be (-42)/18*3 - (4 + 0). Let o be ((-4)/85)/(((-176)/(-200))/j). Determine b so that 4/17 + 8/17*b**2 + 2/17*b**3 + o*b = 0.
-2, -1
Factor -21/4 - 1/4*j**2 + 5/2*j.
-(j - 7)*(j - 3)/4
Suppose 0*w**2 + 0 + 249/2*w**4 - 27/2*w**5 + 0*w - 27*w**3 = 0. What is w?
0, 2/9, 9
Suppose -25*w = 1891 + 384. Let b be 0 - (6 - (-560)/w). Suppose 0*n**2 + 2/13 - 4/13*n**3 - b*n**4 + 4/13*n = 0. Calculate n.
-1, 1
Suppose 0 = -r - g + 3, 6*g + 277 = -r + 285. Suppose 32/7*f + 4/7*f**r + 4 = 0. What is f?
-7, -1
Let s(d) be the first derivative of -5*d**3/9 + 4140*d**2 - 10283760*d + 10617. Factor s(w).
-5*(w - 2484)**2/3
Let h be 5/(25/(-6))*(-4935)/(-8883) - -2. Find w, given that 2/3 + 2/3*w - h*w**2 = 0.
-1/2, 1
What is t in 0 - 18/7*t**2 + 10/7*t**4 + 0*t + 4/7*t**5 - 12/7*t**3 = 0?
-3, -1, 0, 3/2
Factor -1074/7 + 6/7*l**2 - 1068/7*l.
6*(l - 179)*(l + 1)/7
Let d(r) be the second derivative of 11/36*r**4 + 0 + 3/4*r**2 - 2/3*r**3 + 71*r + 1/180*r**6 - 1/15*r**5. Suppose d(o) = 0. Calculate o.
1, 3
Let x(j) be the second derivative of 3*j**5/20 + 145*j**4/4 + 72*j**3 - 35*j + 66. Factor x(r).
3*r*(r + 1)*(r + 144)
Let f(b) = 5*b**2 + 240*b + 2880. Let d(n) = 1200*n + 17292 + 25*n**2 - 1367 - 1525. Let u(x) = 2*d(x) - 11*f(x). Factor u(l).
-5*(l + 24)**2
Let x be 58/(-899) - (-30)/465. Suppose 0 - 18/7*n**2 - 2/7*n**5 + x*n - 30/7*n**3 - 2*n**4 = 0. Calculate n.
-3, -1, 0
Let u(a) be the third derivative of -a**8/3696 - a**7/770 + 7*a**6/660 + 4*a**5/55 + 4*a**4/33 + 2*a**2 - 515. Solve u(n) = 0.
-4, -2, -1, 0, 4
Let 1300/3*h**2 + 16/9*h**4 - 1108/9*h - 2252/9*h**3 - 556/9 = 0. Calculate h.
-1/4, 1, 139
Let m = 77 - 77. Suppose m*g = 3*g + q - 14, 2*q + 2 = 0. Factor -192*s**2 + 195*s**2 - 23*s + g*s - 21.
3*(s - 7)*(s + 1)
Let 8405 + 11413*r - 36218*r - 1061036*r**4 + 23990*r**2 - 5*r**5 - 7190*r**3 + 1060641*r**4 = 0. Calculate r.
-41, 1
Let d = -5608/1491 - -862/213. Factor 0 + 78/7*w**2 - d*w**4 + 40/7*w + 36/7*w**3.
-2*w*(w - 20)*(w + 1)**2/7
Let a = 25535/3 - 8493. Let w(s) be the first derivative of -98/9*s**3 - 32/3*s - a*s**2 + 21. Solve w(i) = 0.
-4/7
What is k in 295200*k - 190076 - 335221 - 338703 + 4*k**3 - 3*k**3 + 4*k**3 - 2415*k**2 = 0?
3, 240
Suppose 5*f + 8 = 3*m, -4*f = -4*m + 19 + 5. Let y be 177/30 - m/(-110) - 3. Find x, given that -6/7 + 10/7*x**4 - 4/7*x**2 + 2/7*x**5 - 2*x + 12/7*x**y = 0.
-3, -1, 1
Determine a, given that 40/3*a**3 + 38/3 - 40/3*a - 12*a**2 - 2/3*a**4 = 0.
-1, 1, 19
Factor 434281/3 + 1/12*b**2 + 659/3*b.
(b + 1318)**2/12
Let c(f) be the third 