k**3 + 0*k + 0 + 24/11*k**2.
-2*k**2*(k - 3)*(k - 2)**2/11
Suppose 0 = -2*u + 4*j + 44, 2*u + 49 = 3*j + 82. Factor u*b**2 + 0*b - 3/5*b**5 + 0 - 18/5*b**4 - 27/5*b**3.
-3*b**3*(b + 3)**2/5
Suppose -7*q + 329 = -2*q + 3*r, -4*r = -5*q + 343. Let f = q - 64. Factor 15*t**3 + 0*t**4 - t**4 - 18*t**f.
-t**3*(t + 3)
Let o(t) be the third derivative of t**6/2520 - 13*t**5/84 + 4225*t**4/168 - 22*t**3 - 8*t**2 - t. Let w(u) be the first derivative of o(u). Factor w(a).
(a - 65)**2/7
Let t(h) be the third derivative of -h**8/336 - h**7/8 + h**6/72 + 7*h**5/8 - 17*h**3/2 + 38*h**2. Let a(x) be the first derivative of t(x). Factor a(r).
-5*r*(r - 1)*(r + 1)*(r + 21)
Let q(t) be the second derivative of -t**4/18 + 47*t**3/9 - 44*t**2 - 299*t. Factor q(f).
-2*(f - 44)*(f - 3)/3
Let r = 61/16817 + 32597/285889. Factor r*v**3 - 14/17*v + 4/17*v**2 + 8/17.
2*(v - 1)**2*(v + 4)/17
Let i(q) = 2*q**3 - 2*q**2 + 1. Let r(m) = 3*m**4 - 28*m**3 - 34*m**2 - 114*m + 30. Let s(b) = 30*i(b) + 2*r(b). What is w in s(w) = 0?
-3, 1/3, 5
Let u = -2/101379 + 1317931/202758. Find q, given that u*q - 5/2*q**2 + 3 = 0.
-2/5, 3
Let g be ((-1072)/(-402))/(3049/3048 - 1). Let d be (-18)/4*g/(-2921). What is s in -48/23*s - 2/23*s**2 - d = 0?
-12
Let a(s) be the second derivative of s**6/900 + s**5/150 + s**4/60 - s**3/6 + 13*s**2 + 2*s - 3. Let o(h) be the second derivative of a(h). Factor o(k).
2*(k + 1)**2/5
Let n(c) be the third derivative of -c**6/840 + 11*c**5/30 - 107*c**4/24 + 298*c**3/21 - c**2 + 823. Find o such that n(o) = 0.
1, 4, 149
Let c = 2868462/16471 - 16962/181. Let i = c + -562/7. Factor 10/13*u**2 - i*u**3 - 10/13 + 2/13*u.
-2*(u - 5)*(u - 1)*(u + 1)/13
Let f(q) be the first derivative of -5*q**4 - 2072*q**3/3 - 2614*q**2 + 2424*q + 3510. Factor f(c).
-4*(c + 3)*(c + 101)*(5*c - 2)
Let i be (-1 + -5)*(-28)/42. Suppose -29 = i*l - 37. Determine s so that 9 + 6*s**2 + 4*s**2 - 13*s**l + 6*s = 0.
-1, 3
Let t be (-80)/(-700)*(-203)/(-58). Factor t*i**4 + 198/5*i**2 + 0 + 162/5*i + 38/5*i**3.
2*i*(i + 1)*(i + 9)**2/5
Let m(a) be the second derivative of -a**4/6 - 151*a**3/3 - 870*a**2 - 12*a + 42. Suppose m(i) = 0. What is i?
-145, -6
Find m, given that 306/5 - 42*m**4 + 9/5*m**5 + 766/5*m**3 + 1937/5*m + 3336/5*m**2 = 0.
-2, -1/3, 9, 17
Let q(p) be the second derivative of -13/15*p**3 + 0 + 36/5*p**2 + 183*p + 1/30*p**4. Find n such that q(n) = 0.
4, 9
Let z(s) = 11*s**3 + 69*s**2 + 76*s + 6. Let m(q) = -20*q**3 - 138*q**2 - 151*q - 11. Let h(b) = 6*m(b) + 11*z(b). Solve h(u) = 0.
-1, 0, 70
Suppose 0 = 4*l - w - 16, 3739*l - 24 = 3743*l + 4*w. Factor -12/17*m + 16/17 + 2/17*m**l.
2*(m - 4)*(m - 2)/17
Let f be (-91*(-50)/(-325))/(-7). Solve -f - 3/5*d + 1/5*d**2 = 0 for d.
-2, 5
Let j = -1493 - -1509. Let h be (-2)/j*16/(-4). Find d such that 3/2*d**2 - d + 0 - 3/2*d**4 + h*d**3 + 1/2*d**5 = 0.
-1, 0, 1, 2
Suppose -5*q - 127 + 53 = -2*h, -5*h + 2*q = -227. Suppose -10 = 42*a - h*a. Let 0 - 4/15*c**a - 2/15*c = 0. Calculate c.
-1/2, 0
Let c(n) = -n**2 - 31*n + 1742. Let g be c(-60). Let r(b) be the first derivative of 8/21*b**3 - 5 + 5/7*b**g + 4/7*b + 1/14*b**4. Factor r(m).
2*(m + 1)**2*(m + 2)/7
Let b(h) be the first derivative of h**3/5 + 366*h**2/5 + 44652*h/5 + 4345. Suppose b(m) = 0. Calculate m.
-122
Let s(q) be the third derivative of -2/15*q**6 + 0*q**7 + 109*q**2 + 1/2*q**4 - 4/3*q**3 + 0*q + 1/84*q**8 + 2/15*q**5 + 0. Solve s(b) = 0 for b.
-2, -1, 1
Let t(i) be the third derivative of i**5/90 + 23*i**4/18 + 956*i**2. Factor t(f).
2*f*(f + 46)/3
Let z(y) = -3 + 92*y - 4 + 35*y. Let n be z(3). Factor 10 + 13 - n*v**2 + 7 - 9*v + 371*v**2.
-3*(v - 2)*(v + 5)
Let x(o) = 11*o**4 + 98*o**3 - 61*o**2 - 24*o - 8. Let z(n) = -9*n**4 - 97*n**3 + 62*n**2 + 26*n + 6. Let u(v) = -3*x(v) - 4*z(v). Factor u(j).
j*(j - 1)*(j + 32)*(3*j + 1)
Let q(d) be the first derivative of -1/24*d**3 - 3/4*d**2 + 19 + 0*d. Let q(s) = 0. Calculate s.
-12, 0
Factor 0*y**2 + 0*y**2 + 2*y**2 + y**2 - 7*y - 2*y**2.
y*(y - 7)
Let l = 55 + -55. Let p be (0 + 2 + 2)*(l + 1). Find q, given that 0*q**4 + q**5 + 7*q + 5*q**2 + 3*q - 5*q**p - 15*q**3 + 4*q**5 = 0.
-1, 0, 1, 2
Let g(n) = 6*n**3 + 35*n**2 + 38*n + 65. Let l be g(-5). Factor l*i**2 + 0*i + 10/21*i**3 - 2/21*i**4 + 0.
-2*i**3*(i - 5)/21
Let a(c) = -17*c**2 + 67*c - 265. Let r(o) = 54*o**2 - 202*o + 796. Let u(y) = 16*a(y) + 5*r(y). Suppose u(t) = 0. Calculate t.
5, 26
Let w be (-4)/18 + (120/(-27))/(-2). Let h(a) = 2*a**2 - 2*a - 1. Let d be h(w). Factor 12*n - n**2 - 22*n**2 - 339*n**d + 359*n**3 - 4*n**4 - 5*n**2.
-4*n*(n - 3)*(n - 1)**2
Suppose 7*d = -52 + 87. Suppose -3*a = -4*h - 6*a + d, -a = 1. Factor 0 + 3*r**3 + 3/2*r**h + 0*r.
3*r**2*(2*r + 1)/2
Let l = 32875/462 + -498/7. Let c(w) be the second derivative of 18*w + l*w**4 + 1/110*w**5 + 0 - 1/33*w**3 - 1/11*w**2. Determine n so that c(n) = 0.
-1, 1
Suppose 11*c - 185 = -845. Let s be 5 - c/(-45)*(-6)/(-4). Determine d, given that 0*d - 16/9*d**s - 2/9*d**5 + 10/9*d**4 + 8/9*d**2 + 0 = 0.
0, 1, 2
Factor -11232/5*q + 2/5*q**5 - 32/5*q**4 + 20736/5 + 1728/5*q**2 + 48/5*q**3.
2*(q - 6)**4*(q + 8)/5
Suppose 2*q - 20 = l - 5*l, -3*q + 18 = 3*l. Let g(j) be the first derivative of -1/46*j**4 - 75/23*j**q + 250/23*j + 10/23*j**3 - 10. Factor g(n).
-2*(n - 5)**3/23
Let l(j) be the second derivative of 169*j**5/100 - 13*j**4/5 + 6*j**3/5 - 2*j - 31. Suppose l(p) = 0. What is p?
0, 6/13
Factor 383 - 5 + 10 + 20*t**2 - 100 + 174*t - 2*t**3.
-2*(t - 16)*(t + 3)**2
Let z(b) be the third derivative of 2/105*b**7 + 2/3*b**4 + 0*b - 1/30*b**6 - 52*b**2 + 0 - 2/3*b**5 + 16*b**3. Factor z(l).
4*(l - 3)*(l - 2)*(l + 2)**2
Let w(o) be the first derivative of 1/24*o**5 + 19 - 1/18*o**4 - 35*o + 0*o**3 - 1/180*o**6 + 0*o**2. Let y(x) be the first derivative of w(x). Factor y(p).
-p**2*(p - 4)*(p - 1)/6
Let m be -67 + (-780)/(-5040)*434. Let -7/6*v**2 + 11/6*v - 5/6 + m*v**3 = 0. What is v?
1, 5
Factor -q**3 + 40*q - 117*q**2 + 24*q + 128 + 115*q**2.
-(q - 8)*(q + 2)*(q + 8)
Suppose -21*q + 124 - 40 = 0. Suppose -2*l - 4*i + 0 = -16, 20 = -q*l + 5*i. Solve -1/3*f + 2/3*f**3 - 7/6*f**2 + l = 0.
-1/4, 0, 2
Let w = -144 + 147. Factor -w - 4*b**2 + 4*b - 10*b + b**2.
-3*(b + 1)**2
Suppose -o = 2*h - 7, -2*h - 7*o + 4*o + 9 = 0. Suppose 27*q**5 - 8*q + 7*q**4 + 0*q - 12*q**2 - 57*q**5 + 27*q**5 + 6*q**h = 0. What is q?
-1, -2/3, 0, 2
Let z(s) be the third derivative of 37*s**7/1365 + 161*s**6/260 + 827*s**5/195 + 106*s**4/13 + 64*s**3/39 - 6385*s**2. Suppose z(p) = 0. What is p?
-8, -4, -1, -2/37
Suppose 1010*q = 1026*q. What is a in 0 - 36/5*a**4 - 4*a**5 + 4/5*a**2 - 12/5*a**3 + q*a = 0?
-1, 0, 1/5
Let t = -3 + 6. Let i(c) = -9*c**3 - 3*c**2. Let o(w) = -237*w - 18 + 238*w + 18 + 10*w**3 + 3*w**2. Let r(a) = t*o(a) + 4*i(a). Factor r(k).
-3*k*(k + 1)*(2*k - 1)
Let x be (11 + -7)*(-33)/(-4488)*51. Factor x*g**3 + 3*g**2 + 1/4*g**4 + 3/4 + 5/2*g.
(g + 1)**3*(g + 3)/4
Let x(h) be the first derivative of h**5/30 + 47*h**4/24 - h**3/6 - 143*h**2/12 - 47*h/3 - 706. Factor x(a).
(a - 2)*(a + 1)**2*(a + 47)/6
Let r(y) be the second derivative of y**5/4 - 125*y**4/12 + 345*y**3/2 - 2835*y**2/2 - 8*y - 92. Solve r(c) = 0.
7, 9
Let f(l) be the first derivative of 4*l**5/35 + 30*l**4/7 - 272*l**3/7 + 848*l**2/7 - 1152*l/7 + 1018. Factor f(w).
4*(w - 2)**3*(w + 36)/7
Let t(d) be the first derivative of -27/4*d**4 + 3*d**2 - 45 + 7*d**3 + 0*d. Find a such that t(a) = 0.
-2/9, 0, 1
Factor -16*h**2 + 0*h + 38*h - 692 - 2*h**3 - 698 + 1370.
-2*(h - 1)**2*(h + 10)
Let a(j) be the first derivative of -32*j**4/5 - 1028*j**3/5 - 1872*j**2 - 1728*j/5 + 10480. Factor a(u).
-4*(u + 12)**2*(32*u + 3)/5
Suppose 0 = 37*o - 42*o, 5*o + 1 + 5 = 2*a. Determine t so that 0*t + 6/13*t**a + 0 + 6/13*t**4 + 2/13*t**5 + 2/13*t**2 = 0.
-1, 0
Let y = 188 + -186. Find l such that -145*l**3 - 145*l**3 + l**y + 291*l**3 + 20 - 16*l = 0.
-5, 2
Let g(a) be the first derivative of 2*a**3/5 + 9*a**2 + 84*a/5 - 1138. Factor g(u).
6*(u + 1)*(u + 14)/5
Let c = 24371/29844 + 2/37305. Let f(n) be the third derivative of 0*n + 0 - 7/75*n**5 - c*n**4 - 11*n**2 - 1/300*n**6 + 0*n**3. Factor f(v).
-2*v*(v + 7)**2/5
Suppose 10*s + 0*s - 30 = 0. Suppose -s*h - 12 = -18. Suppose -9*t - 8 + 4 + 1 + 11 + t**h = 0. Calculate t.
1, 8
Let u(l) be the 