 third derivative of 1/60*m**6 + 0*m + 3 + 9*m**2 + 1/5*m**5 + 0*m**3 - 7/12*m**4. Factor c(y).
2*y*(y - 1)*(y + 7)
Factor -738/5*c + 2/5*c**2 + 736/5.
2*(c - 368)*(c - 1)/5
Let n(p) be the second derivative of -p**8/2688 + p**7/2520 - p**6/7200 + 3*p**4/2 + p**3/2 - 130*p. Let o(s) be the third derivative of n(s). Solve o(z) = 0.
0, 1/5
Let z(f) be the third derivative of -f**6/1440 + 13*f**5/240 - 169*f**4/96 - 55*f**3/6 - 2*f**2 + 19. Let v(r) be the first derivative of z(r). Factor v(t).
-(t - 13)**2/4
Suppose -3*f = -440 + 176. Factor -6084*r**2 - 520 - 2808*r - 2438*r**3 + f - 1226*r**3 - 730*r**3.
-2*(13*r + 6)**3
Factor -3*w**3 + 903*w**2 + 759*w**2 + 294*w - 1521*w**2.
-3*w*(w - 49)*(w + 2)
Let c(i) = 2*i**2 + 20*i + 3. Let p be c(-10). Suppose -4 = -p*n + 5. Factor -n*k**4 + 0*k**4 + 6*k + 21*k**2 + 3*k**5 - 18*k**2 - 9*k**3.
3*k*(k - 2)*(k - 1)*(k + 1)**2
Solve -7/3 - 1/3*n + 1/3*n**3 + 7/3*n**2 = 0 for n.
-7, -1, 1
Let w be 52 - 37 - (-86)/(-6). Factor -w*z + 2/3*z**2 - 4.
2*(z - 3)*(z + 2)/3
Suppose 5*t + 2*v = 72, -2*v = 64 - 56. Let x(d) be the second derivative of -t*d + 0*d**3 + 0 - d**5 - 1/6*d**6 + 0*d**2 - 5/4*d**4. Solve x(q) = 0.
-3, -1, 0
Let g = -782498 - -782500. Factor -2/5*t**g + 16/5 - 4/5*t.
-2*(t - 2)*(t + 4)/5
Let d(p) be the first derivative of -140*p**3/3 + 1585*p**2 - 24330*p - 56. Let s(i) = i**3 + i**2 + 2*i - 2. Let v(m) = d(m) + 2*s(m). Factor v(o).
2*(o - 23)**3
Suppose -3*p + a + 43 = 0, -3*a = 4*p + a - 52. Solve -3*g - g**3 + 10*g**2 + 16*g**2 - 18 - p*g**2 - 2*g**3 = 0 for g.
-1, 2, 3
Let m(u) be the first derivative of -u**5/4 + 10*u**4/3 - 55*u**3/6 - 50*u**2 - 131*u + 154. Let s(h) be the first derivative of m(h). Solve s(v) = 0.
-1, 4, 5
Let g(f) be the third derivative of -1/2*f**6 + 0*f - 2*f**2 - 1/3*f**5 + 0*f**3 - 73 + 10/3*f**4 - 1/42*f**7 + 5/336*f**8. Factor g(t).
5*t*(t - 4)*(t - 1)*(t + 2)**2
Solve -322698 + 1424*r**2 + 2605*r + 324114 + 231*r + 4*r**3 = 0 for r.
-354, -1
Solve 0 + 17/3*c**3 + 1/3*c**4 + 52/3*c + 56/3*c**2 = 0 for c.
-13, -2, 0
Let p(w) be the first derivative of 15*w**3 - 21/2*w**2 + w**6 - 27/5*w**5 - 18*w + 15/4*w**4 - 71. Determine x, given that p(x) = 0.
-1, -1/2, 1, 2, 3
Let c(i) = -i**2 + 10*i + 14. Suppose 6*p - 27 = 3*p. Let u be c(p). Factor -q - 4*q**2 - 10*q + u*q + 28*q - 100.
-4*(q - 5)**2
Let i(g) = 5*g**4 + 549*g**3 - 1098*g**2 + 556*g - 3. Let f(l) = l**4 + l**3 + 2*l - 1. Let r(u) = -3*f(u) + i(u). Determine m so that r(m) = 0.
-275, 0, 1
Suppose -5*y - 9*f + 4 = -5*f, -f + 1 = 0. Find t, given that -1/2*t**2 + 9/2 + y*t = 0.
-3, 3
Let l(u) be the third derivative of -2/3*u**4 + 74*u**2 + 0 + 0*u + 1/84*u**8 + 16/3*u**3 + 8/105*u**7 + 1/30*u**6 - 2/3*u**5. Factor l(j).
4*(j - 1)**2*(j + 2)**3
Let w(v) = v**3 - 7*v + 9. Let z be w(3). Suppose 10*j + 20 = z*j. Factor -2*l**3 + 2*l + 0 + 1 - 5 + 0 + j*l**2.
-2*(l - 2)*(l - 1)*(l + 1)
Let i = -24665/9 - -2741. Let u(c) be the first derivative of -i*c**3 + 1/3*c**5 + 0*c**2 - 4 - 2/3*c**4 + 0*c. Factor u(l).
l**2*(l - 2)*(5*l + 2)/3
Let p(o) be the third derivative of -o**5/150 - 272*o**4/15 - 295936*o**3/15 - 1521*o**2. Factor p(a).
-2*(a + 544)**2/5
Solve 2*y**4 - 9/2*y**5 + 2 + 9*y**3 - 4*y**2 - 9/2*y = 0.
-1, 4/9, 1
Let b(x) be the second derivative of 0*x**2 + 6*x + 25*x**4 - 9/4*x**5 - 10 - 250/3*x**3. Suppose b(t) = 0. What is t?
0, 10/3
Let c(d) be the first derivative of d**3/3 - 253*d**2/2 - 187. Find s, given that c(s) = 0.
0, 253
Suppose -50*w + 55*w = -4*m + 30, 0 = 5*w + 2*m - 20. Let v(f) be the first derivative of f**w + 4*f - 1/8*f**4 + 12 - 1/3*f**3. Factor v(g).
-(g - 2)*(g + 2)**2/2
Let m be (-4 + (-9)/2*-1)*(330 - 329). Factor -v**3 + m*v**2 - 3/2*v**4 + 0*v + 0.
-v**2*(v + 1)*(3*v - 1)/2
Suppose 0 = 2*g - s + 53 - 107, 18*g - 552 = -2*s. Factor -5/3*u**5 - g*u**3 + 100/3*u**2 - 40/3*u + 35/3*u**4 + 0.
-5*u*(u - 2)**3*(u - 1)/3
Factor -34*n**2 + 18/7*n**3 - 24 + 808/7*n.
2*(n - 7)*(n - 6)*(9*n - 2)/7
Let r(w) = 6*w**4 + 11*w**3 - 2*w**2 + 14*w + 21. Let v(j) = 5*j**4 + 9*j**3 - 2*j**2 + 12*j + 18. Let y(n) = 6*r(n) - 7*v(n). Find i such that y(i) = 0.
-2, -1, 0
Suppose 3*o + m = 18, 5*o + 16 = 3*m - 10. Factor -20*i + 25/3*i**o + 12.
(5*i - 6)**2/3
Let d(o) be the second derivative of -o**6/24 + o**5/2 + 5*o**4/24 - 5*o**3 - 11*o**2 - 22*o. Let c(w) be the first derivative of d(w). Factor c(n).
-5*(n - 6)*(n - 1)*(n + 1)
Let p(z) = -7*z**4 + 12*z**3 - 39*z**2 + 82*z - 48. Let b(f) = -f**4 + 2*f**2 - f. Let q = 83 + -82. Let j(g) = q*p(g) - 6*b(g). What is o in j(o) = 0?
1, 3, 4
Let x = 4189 - 29272/7. Factor -6/7*p**2 - x + 15*p.
-3*(p - 17)*(2*p - 1)/7
Suppose -9*c**5 + 17*c**2 + 26*c**3 - 17*c**2 + 22*c**4 - 24*c**2 - c**4 = 0. What is c?
-4/3, 0, 2/3, 3
Let g = 91/303 - -10/303. Let q = 7/36 + 293/36. Suppose -q - g*f**2 + 10/3*f = 0. Calculate f.
5
Let 13810 - 6*q**2 + 1425*q + 210*q**2 + 133*q**2 - 1125*q**3 - 14171 + 324*q**4 = 0. What is q?
-1, 1/4, 19/9
Suppose 4*f**4 - 36*f**2 - 220*f**2 - 252*f - 20*f**3 - 68*f**2 - 32*f**3 - 16*f**3 = 0. Calculate f.
-3, -1, 0, 21
Let l(p) be the first derivative of -p**6/960 + p**5/96 - 241*p**2/2 + 223. Let u(q) be the second derivative of l(q). Determine i so that u(i) = 0.
0, 5
Suppose 387 - 4512 = -11*f. Let j = f + -2623/7. What is r in -j - r**2 + 9/7*r = 0?
2/7, 1
Let p(i) be the second derivative of 45/4*i**2 + 11/8*i**3 - 17/48*i**4 + 71*i - 9/80*i**5 - 1/120*i**6 + 0. Determine l, given that p(l) = 0.
-5, -3, 2
Suppose 5/2*i**2 + 3300 + 355*i = 0. What is i?
-132, -10
Let o(d) be the first derivative of 128*d**3/21 - 240*d**2 + 3150*d - 3141. Factor o(s).
2*(8*s - 105)**2/7
Let g(f) be the second derivative of -5*f**4/12 + 5*f**3 + 40*f**2 + 3*f - 453. What is y in g(y) = 0?
-2, 8
Let c = -44561/28 + 7199/4. Let c + 108/7*s + 2/7*s**2 = 0. What is s?
-27
Let i(o) be the second derivative of -o**5/70 - 79*o**4/42 - 26*o**3/7 + 1793*o. Let i(k) = 0. What is k?
-78, -1, 0
Suppose -75*i - 24 = -69*i. Let n(w) = 5*w**2 + 24*w + 18. Let t be n(i). Factor -9/4*k**4 - 3/4*k**t + 3/4*k**5 + 9/4*k**3 + 0*k + 0.
3*k**2*(k - 1)**3/4
Let w(q) be the first derivative of 4*q**5 + 342*q**4 + 22244*q**3/3 - 20160*q**2 - 19600*q - 1181. Determine c, given that w(c) = 0.
-35, -2/5, 2
Solve 316/5*c**3 + 32/5*c**5 + 0 + 186/5*c**4 + 126/5*c**2 - 36/5*c = 0 for c.
-3, -2, -1, 0, 3/16
Let w(p) = 3*p**2 + 8346*p - 8361. Let j(t) = -3*t**2 - 8352*t + 8369. Let l(x) = 6*j(x) + 7*w(x). Factor l(y).
3*(y - 1)*(y + 2771)
Suppose 4*s - 3 = 13. Let c be (-30)/22*36168/(-8220)*(-21)/(-54). Factor 1/3*w**2 + 0*w + 3*w**5 + 5*w**s + 0 + c*w**3.
w**2*(w + 1)*(3*w + 1)**2/3
Suppose 3/2*h**2 - 6 + 2*h - 1/2*h**3 = 0. Calculate h.
-2, 2, 3
Let r(t) be the third derivative of -t**6/24 - 137*t**5/12 - 2800*t**4/3 + 12250*t**3 - 871*t**2. Factor r(h).
-5*(h - 3)*(h + 70)**2
Let k(f) = f - 20. Let h be k(17). Let n be (9 - -70) + (-2 - h). Factor -20 - n*g**2 - 5*g**3 + 23*g + 62*g + 20*g**3.
5*(g - 4)*(g - 1)*(3*g - 1)
Let c be ((-15)/27*3)/((-2)/6). Let u(x) be the third derivative of 1/150*x**c + 1/300*x**6 - 10*x**2 + 0 - 1/30*x**4 + 0*x + 0*x**3. Factor u(b).
2*b*(b - 1)*(b + 2)/5
Factor 0 - 1/10*s**4 - 1353/5*s**3 + 0*s + 0*s**2.
-s**3*(s + 2706)/10
Let z(h) = -8*h**2 + 127*h + 1081. Let r be z(22). Let 32/15 + 16/15*q - 14/15*q**2 + 2/15*q**r = 0. What is q?
-1, 4
Let r(q) be the second derivative of q**5/20 + q**4/12 - 25*q**3/6 - 25*q**2/2 - 690*q. Factor r(b).
(b - 5)*(b + 1)*(b + 5)
Let i be ((-70)/(-28) - 8)*((-320)/385 - (-22)/77). Determine q, given that 9/4*q - 2*q**4 + 0 + 2*q**2 + 1/4*q**5 - 5/2*q**i = 0.
-1, 0, 1, 9
Find h such that 576 - 4339*h**2 + 2167*h**2 + 2174*h**2 + 152*h = 0.
-72, -4
Let d = 18 + -16. Factor 490*o**d - 70*o**3 - 518*o - 165*o**2 + 18*o + 73*o**4 - 68*o**4.
5*o*(o - 5)**2*(o - 4)
Let w(u) be the first derivative of -u**6/24 + 127*u**5/24 - 35*u**4/4 + u**3/3 + 7*u**2 - 22. Let d(n) be the third derivative of w(n). Factor d(y).
-5*(y - 42)*(3*y - 1)
Let r(v) be the third derivative of -v**6/30 + 226*v**5/15 - 446*v**4/3 + 592*v**3 + 9418*v**2. Let r(q) = 0. Calculate q.
2, 222
Let r be 747 - 742 - ((-817)/(-165) - (-24)/(-180)). Let 0*l + 0 - r*l**5 - 14/11*l**3 - 10/11*l**4 - 6/11*l**2 = 0. What is l?
-3, -1, 0
Suppose 0 = 3*x