 629*r**3 - r**5 + 735 = 0. Calculate r.
-1, 1, 3/2, 7
Let g(r) = r + 2. Let l be g(0). Determine a, given that 0*a**3 + 21*a**3 + 15*a**l + 6 + 10 - 48*a - 4 = 0.
-2, 2/7, 1
Determine h, given that 90*h - 52/5*h**3 + 8/5*h**4 + 0 + 2/5*h**5 - 24*h**2 = 0.
-5, 0, 3
Suppose 167*h - 116*h = -612. Let k be (-66)/(-330) + (h/(-15) - -2). Suppose 12/7*t**k + 0 - 4/7*t**5 + 8/7*t**4 - 16/7*t**2 - 16/7*t = 0. What is t?
-1, 0, 2
Let j be -38 - (1 - 0 - 2). Let x = 39 + j. Factor -4*p**4 - 2*p**2 - 7*p + 3*p**4 - p**2 - 5*p**3 - 6*p**x - 2.
-(p + 1)**3*(p + 2)
Let u = 44/3 + -40/3. Let c(h) be the first derivative of 0*h + 0*h**2 + 0*h**3 + u*h**6 - 2 + 0*h**4 + 4/5*h**5. Determine n so that c(n) = 0.
-1/2, 0
Suppose -3*v + 47 = 4*u - 30, 66 = 6*u - 36. What is p in -24/5 - 32/5*p + 2/5*p**v - 6/5*p**2 = 0?
-2, -1, 6
Let m be 270/27 + -10 + 5 + 9/(-3). Factor 10*h**m - 745/2*h + 185/2.
5*(h - 37)*(4*h - 1)/2
Suppose 4/23*n**4 + 72/23*n + 104/23*n**2 - 78/23*n**3 + 0 = 0. What is n?
-1/2, 0, 2, 18
Let j(t) be the first derivative of t**4 + 1772*t**3/3 + 98566*t**2 + 195364*t + 1595. Determine w, given that j(w) = 0.
-221, -1
Find u such that -37 + 75/2*u - 1/2*u**2 = 0.
1, 74
Let g(t) be the first derivative of 19/21*t**3 - 53 - 4/7*t - 5/28*t**4 - 8/7*t**2. Factor g(d).
-(d - 2)**2*(5*d + 1)/7
Let r(x) be the third derivative of x**5/180 - 37*x**4/12 + 220*x**3/9 + 1510*x**2. Let r(z) = 0. What is z?
2, 220
Let i be 12 + -27 + 3 + 19 + -5. Factor -4/5*z**i - 40 - 108/5*z.
-4*(z + 2)*(z + 25)/5
Let h = -809 - -811. Suppose -12 = -5*o + h*o. Factor 4/7*c - 2/7*c**o + 0 + 2/7*c**2 - 4/7*c**3.
-2*c*(c - 1)*(c + 1)*(c + 2)/7
Factor 10*w**2 - 563*w - 14*w**2 + 3*w**2 - 194 - 368.
-(w + 1)*(w + 562)
Let v(l) = 57*l**2 + 135*l + 63. Let p(a) = a**3 - 115*a**2 - 268*a - 127. Let z(o) = -3*p(o) - 5*v(o). Let z(t) = 0. Calculate t.
-1, 22
Let a be (-4)/(-2) + (3 - 1) + -2. Suppose 0 = a*x - 4*x, -5*y = -5*x - 10. Factor -q**y + 5 + 3 + 4 + 5*q - 16.
-(q - 4)*(q - 1)
Solve 1400*s**3 + 1341*s**3 + 32*s**2 - 915*s - 2869*s**3 + 3233*s + 3610 = 0.
-19/8, 5
Let f(g) be the third derivative of -g**5/20 - 11*g**4/4 - 85*g**3/2 + 29*g**2 - g. Factor f(c).
-3*(c + 5)*(c + 17)
Let w(p) = 552*p + 27053. Let j be w(-49). What is i in i**4 - 4/3*i**2 + 0*i + 0*i**3 - 1/3*i**j + 0 = 0?
-1, 0, 2
Let q(s) be the first derivative of 32*s**5/5 + 62*s**4 + 76*s**3/3 - 334*s**2 - 168*s + 5781. Solve q(x) = 0 for x.
-7, -2, -1/4, 3/2
Let w(z) = 11*z**3 - 1119*z**2 - 430947*z - 54439939. Let u(x) = -9*x**3 + 1122*x**2 + 430943*x + 54439939. Let i(l) = -6*u(l) - 5*w(l). Solve i(t) = 0 for t.
-379
Let d(n) be the third derivative of -n**8/1344 - 7*n**7/120 - 707*n**6/480 - 2543*n**5/240 - 11*n**4 + 363*n**3/2 + 43*n**2 + 5*n + 1. Let d(c) = 0. What is c?
-22, -3, 1
Factor 659 - 415 - 469*m + 99*m - 2*m**2 + 884.
-2*(m - 3)*(m + 188)
Let i(c) = -875*c**3 - 2190*c**2 - 585*c + 190. Let p(a) = -219*a**3 - 547*a**2 - 146*a + 48. Let q(n) = 6*i(n) - 25*p(n). Determine t, given that q(t) = 0.
-2, -3/5, 2/9
Let s = -618 - -624. Let t be (-435)/(-58)*1/s. Solve h + t*h**2 - 1/4*h**5 + 0 - 3/4*h**3 - 5/4*h**4 = 0 for h.
-4, -1, 0, 1
Let i(h) = -h**3 - 10*h**2 - 4*h - 17. Let t be i(-10). Let f = t + -20. Factor 4*q - 2 - 2*q + f*q**2 - 5*q - 4.
3*(q - 2)*(q + 1)
Factor -7/6*k**3 + 1/6*k**4 + 0 + 8/3*k - 5/3*k**2.
k*(k - 8)*(k - 1)*(k + 2)/6
Let v(g) = -g**2 + 5*g + 1. Let j(d) = -6*d**3 + 15*d**2 - d - 19. Let w(q) = j(q) + 7*v(q). Factor w(x).
-2*(x - 3)*(x + 2)*(3*x - 1)
Let i be 0 + 3 - (-487 - -464). Let o(w) be the second derivative of 0 + i*w - w**2 + 2/3*w**3 - 1/6*w**4. Factor o(v).
-2*(v - 1)**2
Let f(x) be the first derivative of x**4/24 + 256*x**3/9 + 16384*x**2/3 - 696. Suppose f(u) = 0. What is u?
-256, 0
Suppose 11/4 + 21/4*t - 1/2*t**2 - 9/4*t**4 + 1/4*t**5 - 11/2*t**3 = 0. Calculate t.
-1, 1, 11
Find l, given that 458461 - 127789 + 4434154*l - 4436146*l + 3*l**2 = 0.
332
Let h = -138607/24 + 11551/2. Let i(g) be the second derivative of 5/4*g**3 + h*g**4 - 5*g**2 + 0 - g. Factor i(s).
5*(s - 1)*(s + 4)/2
Let q(i) = 2*i**3 + 1. Let s(y) = -28*y**3 + 632*y**2 - 636*y - 16. Let x(a) = 16*q(a) + s(a). Factor x(w).
4*w*(w - 1)*(w + 159)
Let g(x) be the first derivative of -625*x**4/4 + 1625*x**3 - 12675*x**2/2 + 10985*x - 1037. Factor g(j).
-5*(5*j - 13)**3
Let d(t) be the second derivative of 28*t**4 + 0*t**2 + 6 + 9*t + 88/3*t**3 - 2/5*t**6 + 5*t**5. What is l in d(l) = 0?
-2, -2/3, 0, 11
Let n be (1 + 1)*9/6. Suppose -w = 3*q - 13, -7*q = -2*q + 2*w - 23. Factor -12*r**2 + n*r**4 + 0*r + q*r**2 - 5*r - r.
3*r*(r - 2)*(r + 1)**2
Factor 0 - 2/15*c**2 - 284/15*c.
-2*c*(c + 142)/15
Suppose -260*p = -232*p - 364. Let t(f) be the third derivative of -1/30*f**5 + 0*f - 3/4*f**4 - p*f**2 - 8/3*f**3 + 0. Factor t(d).
-2*(d + 1)*(d + 8)
Let t(v) be the second derivative of -v**6/10 - 33*v**5/20 - 9*v**4/4 + 11*v**3/2 + 15*v**2 - 3*v + 141. Let t(x) = 0. What is x?
-10, -1, 1
Let i(t) = -2*t**3 - 154*t**2 + 2512*t + 21164. Let v(w) = 4*w**3 + 153*w**2 - 2508*w - 21162. Let h(d) = -6*i(d) - 4*v(d). Let h(b) = 0. Calculate b.
-6, 42
Suppose 35 = -3*z + 3*i - 19, -3*i + 34 = -2*z. Let y be (-15)/z*2*(-60)/(-70). Determine l so that y + 6/7*l + 1/7*l**2 = 0.
-3
Let q(y) be the second derivative of -y**4/4 - 944*y**3 - 1336704*y**2 - 2303*y. Factor q(f).
-3*(f + 944)**2
Suppose 0 = -8*z + 6 + 10. Factor -99*i - 30*i**3 + 2*i**z - 21*i**2 - 26*i**3 + 55*i**3 - 81.
-(i + 1)*(i + 9)**2
Let l = -424613/180 + 2359. Let d(s) be the third derivative of 0*s + 1/120*s**6 + 1/36*s**4 - s**2 + 0*s**3 + 0 - l*s**5. Suppose d(a) = 0. What is a?
0, 1/3, 2
Let f be 1990/(-796) + 81/10. Factor -44/5*u - 4/5*u**3 - 4 - f*u**2.
-4*(u + 1)**2*(u + 5)/5
Suppose 48*s - 4 = 47*s. Factor -15 - w**4 + 48*w**2 + 5*w**s - 24*w**3 + 15 + 0*w**4 - 32*w.
4*w*(w - 2)**3
Let r(t) be the second derivative of -1/7*t**4 - 9/140*t**5 + 1/98*t**7 - 11 + 1/35*t**6 + 0*t**2 + 2/7*t**3 + t. Suppose r(u) = 0. Calculate u.
-2, 0, 1
Suppose 0 = b + 4, -24 = 2*g + 2*b - 20. Let x(j) be the first derivative of 7 + 1/4*j**4 - 2/3*j**3 + 0*j**g + 0*j. Factor x(z).
z**2*(z - 2)
Let u(v) be the first derivative of v**4/26 - 18*v**3/13 + 51*v**2/13 - 50*v/13 + 1038. Determine j, given that u(j) = 0.
1, 25
Suppose -19*l + 14 + 62 = 0. Let q be ((-616)/(-144) + -4)*l/5. Factor -q*s**2 - 8/9 + 8/9*s.
-2*(s - 2)**2/9
Let j be ((-112)/252)/(119/510*2/(-70)). Factor -j + 20/3*f - 1/6*f**2.
-(f - 20)**2/6
Let f(x) be the third derivative of x**6/120 + 8*x**5/45 - 317*x**4/72 + 17*x**3/3 + 51*x**2 + 5*x. Factor f(o).
(o - 6)*(o + 17)*(3*o - 1)/3
Let b(d) be the first derivative of 5*d**3/3 - 1275*d**2/2 + 6250*d + 9247. What is c in b(c) = 0?
5, 250
Suppose -6273*z + 3062 = -2690 - 1714 - 5080. Factor -2/9*h**z - 4/3 + 14/9*h.
-2*(h - 6)*(h - 1)/9
Factor -30276 - 174*u - 1/4*u**2.
-(u + 348)**2/4
Let w(v) be the third derivative of 9 + 0*v**6 + 81/14*v**3 - 9/70*v**5 + 0*v**4 + 0*v + 1/490*v**7 - 2*v**2. Suppose w(a) = 0. What is a?
-3, 3
Let b(r) be the first derivative of 0*r + 0*r**3 - 1/160*r**5 + 1/64*r**4 - 3*r**2 - 2. Let v(x) be the second derivative of b(x). Factor v(n).
-3*n*(n - 1)/8
Let o(d) be the first derivative of -17 + 8*d**3 + 1/4*d**4 + d + 96*d**2. Let w(r) be the first derivative of o(r). Determine t, given that w(t) = 0.
-8
Let f(l) be the third derivative of l**5/15 + 1900*l**4/3 + 7220000*l**3/3 + 3*l**2 + 2*l - 586. Find d, given that f(d) = 0.
-1900
Suppose 13*i + 9 = 10*i. Let n(q) = 13*q**2 + 166*q. Let v(a) = -5*a**2 - 55*a. Let k(c) = i*n(c) - 8*v(c). Determine m, given that k(m) = 0.
0, 58
Let x(l) be the second derivative of -7*l**6/60 + 1809*l**5/80 - 63*l**4/8 - 1159*l**3/24 - 129*l**2/4 - 553*l - 8. Find d, given that x(d) = 0.
-1/2, -2/7, 1, 129
Let i = 2898 + -2894. Let x(z) be the third derivative of -1/135*z**5 + 0 - 1/540*z**6 + 1/108*z**i - 8*z**2 + 0*z + 2/27*z**3. Factor x(v).
-2*(v - 1)*(v + 1)*(v + 2)/9
Suppose -5*n - 121 - 325 = 4*u, 0 = 2*n + u + 179. Let y be (n/(-525))/(3*(-2)/(-120)). Factor y*w - 8/7 - 22/7*w**2 + 6/7*w**3.
2*(w - 2)*(w - 1)*(3*w - 2)/7
Let b(n) be the first derivative of 0*n**2 - 3/28*n**4 + 0*n - 1/7*n**3 + 74. Find g, given that b(g) = 0.
-1, 0
Factor 120 + 1/2*k**2 - 61*k.
(k 