*(y - 1)*(y + 18)**2
Let m(x) be the first derivative of x**7/1120 + x**6/32 - 13*x**3/3 + x**2 - 15. Let l(g) be the third derivative of m(g). Factor l(d).
3*d**2*(d + 15)/4
Let t(j) be the third derivative of -2*j**7/105 + 11*j**6/6 - 781*j**5/15 + 207*j**4/2 + 972*j**3 + 360*j**2 - j. Suppose t(l) = 0. Calculate l.
-1, 2, 27
Let t(h) = -3*h**2 + h + 2. Let m be t(-1). Let b be (10 - 7)/((-3)/m). What is k in -4*k**2 + 8*k**3 - 2*k**b + 14*k**2 - 6*k - 4 - 4*k**2 - 2*k**5 = 0?
-1, 1, 2
Let i be ((-6)/21)/((-2)/11). Let m be (808 + -810)/((3*-1)/6). Determine c so that 1/7*c**3 + 12/7*c - 3/7*c**m + i*c**2 + 4/7 - 1/7*c**5 = 0.
-2, -1, 2
Suppose 2*z + 5*s - 21 = 134, 3*s - 161 = -2*z. Let n = z - 49. Factor w**2 - 2*w + 0*w - 10*w + n.
(w - 6)**2
Suppose -215 + 166 = 231*u - 742. Let h(t) be the first derivative of -t - 1/3*t**2 - 11 + 1/9*t**u. Factor h(i).
(i - 3)*(i + 1)/3
Let v be 6*(28/8 + 4). Let j be v/6*2*4/12. Suppose 2 - 4*n - j + 6*n**2 + 3*n**2 - 10*n**2 = 0. What is n?
-3, -1
Let k(u) = -u**3 + 3*u**2 - 1. Let d(a) = -2*a**4 + 47*a**3 + 101*a**2 - 344*a + 195. Let w(s) = -2*d(s) - 6*k(s). Factor w(x).
4*(x - 24)*(x - 1)**2*(x + 4)
Let l(w) be the third derivative of 0*w + 0 + 90*w**2 - 7/720*w**6 + 1/45*w**5 + 0*w**3 + 1/9*w**4 + 1/1260*w**7. Let l(k) = 0. What is k?
-1, 0, 4
Suppose -6*r - 1872 = -22*r. Suppose -r*b + 116*b = 0. Factor 2*t**3 + 0 + 4/9*t**2 + b*t.
2*t**2*(9*t + 2)/9
Suppose 0 = 5*k - 2*m - 28, -3*m - 19 = 5*k - 52. Let f be 4 + -6 + (-2 + k - -1). Factor -2/9*a**f + 0*a + 0 + 4/3*a**2.
-2*a**2*(a - 6)/9
Factor -501*q**2 + 216 + 16*q + 204*q + 505*q**2.
4*(q + 1)*(q + 54)
Let w = 1449966 + -100045834/69. Let t = -300/23 + w. Factor -34/3*a**2 + 2*a + 0 + t*a**3.
2*a*(4*a - 1)*(5*a - 3)/3
Let f(g) be the first derivative of -33/4*g**2 + 1/4*g**3 + 63/4*g + 173. Factor f(u).
3*(u - 21)*(u - 1)/4
Let w be (5/7 - 1) + (-36)/(-28). Factor w + 8*z**4 - 18*z - 50*z**3 - 277*z**2 + 361*z**2 - 1.
2*z*(z - 3)**2*(4*z - 1)
Let y(h) be the first derivative of -2*h**3/45 - h**2/3 + 44*h/5 - 164. Factor y(o).
-2*(o - 6)*(o + 11)/15
Let m be ((-22)/(-66))/(2/24). Let -34*j**3 + 4*j**m - 70*j**2 + 38*j**3 + 62*j**2 = 0. What is j?
-2, 0, 1
Suppose 81 - 28 = 16*d - 11. Let -52/3*v**2 + 2/3*v**d + 40*v + 150 - 8/3*v**3 = 0. What is v?
-3, 5
Let c be (-3 - (-24)/((-15120)/(-1862)))/((-4)/72). Factor -112/5*z + c*z**3 + 16/5*z**2 + 128/5.
4*(z - 2)**2*(z + 8)/5
Let l(t) = -t - 51. Let f be l(-30). Let q be f/(-14)*((-10)/6 + 3). Solve -2/13*y**3 - 6/13*y - 8/13*y**q + 0 = 0.
-3, -1, 0
Suppose -11 = -5*t - 0*x + 4*x, 0 = 4*t - 5*x - 7. Determine c so that 38 + 129*c - 312*c**2 - 8 + 1416*c**4 - 818*c**t - 103*c**5 - 205*c**3 - 137*c**5 = 0.
-1/4, 2/5, 1, 5
Factor 321 - 17*o**2 + 298*o - 35*o + 33*o + 21*o**2 - 29.
4*(o + 1)*(o + 73)
Let j(u) be the second derivative of u**4/20 + 308*u**3/5 + 369*u**2/2 + 651*u + 1. Suppose j(q) = 0. What is q?
-615, -1
Let 116/9*w**4 - 19968*w + 3456*w**2 + 46080 - 2/9*w**5 - 896/3*w**3 = 0. What is w?
10, 12
Factor 6310192*p**5 - 9*p**3 - 10*p**4 - 6310213*p**5 - 26*p**4 + 6*p**2.
-3*p**2*(p + 1)**2*(7*p - 2)
Let -2*c**3 + 1567*c**2 + 0*c**3 - 1545*c**2 = 0. Calculate c.
0, 11
Let n(t) = -2*t**3 - 6*t**2 - 9*t - 6. Let m(y) = -y**3. Let i(f) = m(f) - n(f). Let h(z) be the first derivative of i(z). Determine o, given that h(o) = 0.
-3, -1
Let t be 1*-10 - (-5320)/532. Let k(d) be the third derivative of -1/70*d**7 - 3/10*d**6 + 0*d**4 + 0*d**3 - 10*d**2 + t*d + 0 - 9/5*d**5. Factor k(g).
-3*g**2*(g + 6)**2
Suppose 291610*n**2 - 237*n**4 - 73205*n - 2264*n**4 - 234*n**5 - 45*n**4 - 1064*n**4 + 219*n**5 - 214780*n**3 = 0. Calculate n.
-121, 0, 1/3, 1
Let x(y) = -106*y + 743. Let r be x(7). Suppose 3*h - 16 + 1 = 3*a, -r = h + 2*a. What is w in 1/6*w - 1/6*w**h - 1/6*w**4 - 1 + 7/6*w**2 = 0?
-3, -1, 1, 2
Let c(t) be the third derivative of -33/8*t**4 + 0 + 0*t - 1/2*t**5 - 161*t**2 - 18*t**3 - 1/40*t**6. Factor c(z).
-3*(z + 3)**2*(z + 4)
Let w be (5 + -3)/(0 - 2/(-4)). Solve -4*h + 3*h - h**5 + h + 2*h**2 - 2*h**w + h = 0 for h.
-1, 0, 1
Let t(i) be the second derivative of -85/2*i**3 - 130*i**2 + 101*i - 1/2*i**5 + 0 + 175/4*i**4. Determine g so that t(g) = 0.
-1/2, 1, 52
Let w(t) = -t**3 - 9*t**2 - t + 59. Let x be w(-8). Determine u, given that -7*u**2 + 5*u**3 + 6*u**5 - 5*u**2 - 2*u**5 - 22*u**4 - 4*u**x + 33*u**3 = 0.
0, 1/2, 2, 3
Let w be ((-2415)/100)/(-23) + 6/(-72)*-9. Let 0*o - 3*o**2 + 3/5*o**5 - w*o**4 - 27/5*o**3 + 0 = 0. What is o?
-1, 0, 5
Let j = -7192020/437 + 378600/23. Find t such that 28/19*t**2 + 2/19*t**3 + 86/19*t + j = 0.
-10, -3, -1
Let d be (25/(-4 - -9))/(20/8). Solve -11*m - 12 - 2*m + 2*m**3 + d*m**2 - 3*m + 4 + 8*m = 0 for m.
-2, -1, 2
Suppose 4*y + 2*f - 60 = 2*y, 2*y - 2*f = 40. Suppose 23*z - y + 0*z**2 - 3*z**2 + 7 - 44*z = 0. What is z?
-6, -1
Let p(t) be the first derivative of t**5/20 + t**4/6 - 4*t**3/3 + 65*t - 31. Let b(s) be the first derivative of p(s). Find j, given that b(j) = 0.
-4, 0, 2
Let w(b) be the second derivative of b**6/70 - 141*b**5/35 + 4511*b**4/14 - 8742*b**3/7 + 25947*b**2/14 + 569*b. Factor w(g).
3*(g - 93)**2*(g - 1)**2/7
Let n(p) be the third derivative of -2 - 17/48*p**4 + 1/12*p**5 + 0*p + 90*p**2 + 2/3*p**3 - 1/240*p**6. Factor n(y).
-(y - 8)*(y - 1)**2/2
Let m(y) be the third derivative of y**7/168 - 99*y**6/16 + 29403*y**5/16 + y**2 - 236*y. Let m(z) = 0. What is z?
0, 297
Let k(r) be the second derivative of r**6/540 + 7*r**5/90 + 49*r**4/36 + 2*r**3 - 2*r**2 - 101*r. Let a(m) be the second derivative of k(m). Factor a(n).
2*(n + 7)**2/3
Factor 37301*d - 37109*d + 3315*d**2 + 172*d**3 + 821*d**2.
4*d*(d + 24)*(43*d + 2)
Solve -1/3*i**2 - 43/6*i - 1/6*i**5 - 10/3*i**4 + 22/3*i**3 + 11/3 = 0 for i.
-22, -1, 1
Let w(j) be the third derivative of -j**5/75 + 349*j**4/5 - 730806*j**3/5 + 7*j**2 - 35*j - 2. Factor w(b).
-4*(b - 1047)**2/5
Let a be 5/3*38/(-475)*(1 + -16). Let g(o) be the first derivative of -4/3*o + 20 - 1/3*o**a + 2/9*o**3. Factor g(p).
2*(p - 2)*(p + 1)/3
Let l(f) be the second derivative of 59/4*f**2 - 5*f**3 + 268*f + 0 + 1/24*f**4. What is c in l(c) = 0?
1, 59
Let p(t) = -t**2 - 36*t - 45. Let m = 247 - 242. Let c(f) = 2*f**2 + 54*f + 68. Let q(g) = m*c(g) + 8*p(g). Find y such that q(y) = 0.
-1, 10
Suppose -58*w + 61*w + 32 = -4*b, -22*b = 308. Factor 20/3*n**2 + 0 - w*n**3 + 16*n + 4/3*n**4.
4*n*(n - 4)*(n - 3)*(n + 1)/3
Let o(a) = -28*a**3 - 828*a**2 - 6008*a + 2736. Let z(j) = -j**3 + 8*j + 1. Let u(q) = -o(q) + 48*z(q). Solve u(n) = 0 for n.
-7, 2/5, 48
Let g(l) be the second derivative of 3*l**7/14 + 97*l**6/30 + 151*l**5/20 + 21*l**4/4 + 22*l - 13. Find k, given that g(k) = 0.
-9, -1, -7/9, 0
Let x(n) be the second derivative of n**5/80 - 3*n**4/4 - 67*n**3/8 - 41*n**2/2 - 3*n + 158. Suppose x(b) = 0. What is b?
-4, -1, 41
Let c(p) be the second derivative of p**6/10 + 261*p**5/20 + 1485*p**4/4 + 6413*p**3/2 - 11979*p**2 - 916*p - 3. Determine d so that c(d) = 0.
-66, -11, 1
Let x(g) be the third derivative of -68*g**2 - 1/13*g**4 - 1/390*g**5 - 11/39*g**3 + 0*g + 0. Factor x(i).
-2*(i + 1)*(i + 11)/13
Let d(j) be the third derivative of 0 + 0*j**3 + 2*j**2 + 1/21*j**4 + 1/35*j**5 - 32*j - 2/35*j**6 + 2/105*j**7. Let d(s) = 0. Calculate s.
-2/7, 0, 1
What is w in -159*w - 13*w**3 - 659*w**4 - 8*w**3 + 656*w**4 + 66 + 117*w**2 = 0?
-11, 1, 2
Let s(a) = -6*a**2 + 757*a - 123. Let k be s(126). Let n = -54/13 - -214/39. Solve -2*t**4 + 2/3*t**k + 2/3*t**5 + 0 + 2*t**2 - n*t = 0 for t.
-1, 0, 1, 2
Let g = -920 - -1018. Suppose -4*u = 86 - g. Let -12/7*f**2 + 0*f + 64/7 - 2/7*f**u = 0. What is f?
-4, 2
Suppose -113 = -6*f + 1189. Factor 123*y**2 - 6*y**3 + 983 + f - 1320*y + 3*y**3.
-3*(y - 20)**2*(y - 1)
Suppose 129*k - 260*k = -134*k + 6. Factor 0 + 1/2*p**5 + 7*p**k + 23/2*p**3 + 0*p + 5*p**4.
p**2*(p + 1)*(p + 2)*(p + 7)/2
Let u(v) be the first derivative of -2*v**3/15 - 200*v**2 - 100000*v - 1215. Factor u(p).
-2*(p + 500)**2/5
Let z(u) be the first derivative of -7/5*u**4 + 0*u**2 + 24/5*u**3 - 4/25*u**5 + 118 + 0*u. Factor z(q).
-4*q**2*(q - 2)*(q + 9)/5
Suppose 2*m = 3*w + 8, 11 = 2*m + 3. Let a(o) be the second derivative of 1/2*o**3 + 3*o**2 - 1/2*o**4 - 14*o - 3/20*o**5 + w. Factor a(y).
-3*(y - 1)*(y +