Let c(i) be the second derivative of 123*i**5/50 - 19*i**4/5 - 3*i**3/5 + 21*i + 3. Factor c(s).
6*s*(s - 1)*(41*s + 3)/5
Let t(y) = y**3 + 3*y**2 - 7*y - 10. Let u be t(-4). Let q(d) be the first derivative of -5/3*d**3 + u - 15/2*d**2 - 10*d. Factor q(x).
-5*(x + 1)*(x + 2)
Let u = -7 + 9. Solve -40*h**2 - 32*h**2 - 65*h - 15 + 12*h**u = 0.
-3/4, -1/3
Solve 51*v**3 - 122*v**3 + 2*v**4 + 61*v**3 = 0 for v.
0, 5
Suppose -494*k + 9 = -495*k, -3*k - 24 = t. Factor 6/5*b**3 + t*b**5 + 0 + 0*b + 0*b**2 + 21/5*b**4.
3*b**3*(b + 1)*(5*b + 2)/5
Let h(n) = 19*n**3 - 94*n**2 + 109*n - 78. Let m(v) = -10*v**3 + 48*v**2 - 54*v + 40. Let d(p) = -6*h(p) - 11*m(p). Factor d(i).
-4*(i - 7)*(i - 1)**2
Let t = 176 - 173. Let k(i) be the first derivative of 0*i - 2/7*i**t + 2/7*i**2 - 5. Find m such that k(m) = 0.
0, 2/3
Let h(k) be the first derivative of 3*k**5/2 - 65*k**4/4 + 25*k**3/2 + 10*k**2 + 434. Determine f so that h(f) = 0.
-1/3, 0, 1, 8
Let c(x) be the first derivative of -5*x**3/12 + 905*x**2/8 - 225*x + 646. Factor c(a).
-5*(a - 180)*(a - 1)/4
Suppose -8 = -4*u + 8. Determine k, given that k**u - 3*k**4 - k**2 + 3*k**4 = 0.
-1, 0, 1
Let o(u) = -2*u**4 - 16*u**3 + 10*u**2 + 52*u + 34. Let m(r) = 3*r**4 + 32*r**3 - 19*r**2 - 102*r - 69. Let f(p) = 2*m(p) + 5*o(p). Factor f(z).
-4*(z - 2)*(z + 1)**2*(z + 4)
Let a(x) be the first derivative of 338*x**3/21 - 832*x**2/7 + 2048*x/7 + 401. Let a(g) = 0. Calculate g.
32/13
Suppose -7*v = 93 - 807. Let 12*k**2 + v*k + 2*k**3 - 102*k = 0. What is k?
-6, 0
What is t in -3/2*t + 1/2*t**2 + 1 = 0?
1, 2
Factor -27*f + 10*f**3 + 22*f - 20*f**2 + 16 + 13*f - 4*f**3.
2*(f - 2)**2*(3*f + 2)
Let h(n) = 10*n**2 - 3*n - 13. Let r(m) = m**2 + m - 1. Let u(a) = -5*a**2 + 4*a + 7. Let w(o) = 2*r(o) - u(o). Let c(s) = 5*h(s) - 7*w(s). Factor c(g).
(g - 2)*(g + 1)
Let o(k) = k**2 - k - 5. Let f be 4 - (1 - 3) - 3. Let g(w) = 0 + 7 + 0 - f. Let d(b) = -3*g(b) - 4*o(b). Find v such that d(v) = 0.
-1, 2
Let s(g) be the third derivative of 0 + 0*g**6 + 5/336*g**8 - 1/42*g**7 + 8*g**2 + 0*g + 0*g**4 + 0*g**5 + 0*g**3. Factor s(w).
5*w**4*(w - 1)
Let w(l) be the second derivative of -l**4/6 + 122*l**3/15 - 48*l**2/5 + 46*l. Determine s, given that w(s) = 0.
2/5, 24
Let j(x) = -x - 3. Let b be j(-5). Let k = 43/20 - 89/60. What is s in -k*s**b + 2*s - 4/3 = 0?
1, 2
Let v(l) = l**2 + 3061*l - 193561. Let u(n) = -510*n + 32260. Let m(f) = 26*u(f) + 4*v(f). Factor m(i).
4*(i - 127)**2
Let t(b) = -b**3 + b. Let d(x) = -11*x**3 - 4*x**2 + 11*x + 4. Suppose -4*o - 9 = 11. Let s(z) = o*t(z) + d(z). Factor s(v).
-2*(v - 1)*(v + 1)*(3*v + 2)
Let n(z) be the second derivative of z**5/4 - 5*z**4/12 - 20*z - 2. Factor n(s).
5*s**2*(s - 1)
Suppose w + 3 = 2*n, -5*n + 119*w - 123*w + 27 = 0. Factor 2/5*u**n + 14/15*u - 4/15 - 16/15*u**2.
2*(u - 1)**2*(3*u - 2)/15
Suppose 0 = -r - 5*q + 10, 0 = 2*r - 2*q - 1 - 7. Let o(m) be the second derivative of 0*m**5 + 0*m**4 + 0 - 1/45*m**6 + 0*m**3 + 0*m**2 - r*m. Factor o(c).
-2*c**4/3
Find j such that 311*j**3 + 64 - 315*j**3 - j - j - 64*j**2 - j + 7*j = 0.
-16, -1, 1
Let h(k) be the first derivative of -k**6/6 + 3*k**5/5 + k**4 - 482. What is i in h(i) = 0?
-1, 0, 4
Let h be 186*((-2346)/(-12540) - 4/22). Let a = 30/19 - h. Factor -3/5*r + a - 6/5*r**2 + 6/5*r**3 - 3/5*r**5 + 3/5*r**4.
-3*(r - 1)**3*(r + 1)**2/5
Let r be 2 + (-3)/3 - -17. Suppose -45 = -o - r. Suppose o*g**4 - 20*g + 3 + 66*g**2 + 7*g**3 - 79*g**3 - 4*g = 0. Calculate g.
1/3, 1
Let l be (-1 + 1)/((-29)/(580/40)). Solve -1/3*v**3 + 2/3 + l*v**2 + v = 0 for v.
-1, 2
Let q be (220/(-28) - -8)*14/24. Let m(i) be the first derivative of -1/8*i**4 + 6 + 0*i**2 + 0*i - q*i**3 - 1/20*i**5. Suppose m(s) = 0. What is s?
-1, 0
Suppose 0 = 4*w, -3*m - 6*w - w = -0*w - 2*w. Solve m + 2/25*d + 4/25*d**2 + 2/25*d**3 = 0 for d.
-1, 0
Let u(n) be the second derivative of -n**5/5 - 11*n**4/3 - 56*n**3/3 + 569*n. Factor u(p).
-4*p*(p + 4)*(p + 7)
Let z = -8656 - -43336/5. Factor 68/5*u**2 + z*u - 4*u**3 - 32/5.
-4*(u - 4)*(u + 1)*(5*u - 2)/5
Let o(q) be the third derivative of -11*q**5/72 - 85*q**4/36 - 5*q**3/3 - 99*q**2. Factor o(r).
-5*(r + 6)*(11*r + 2)/6
Let n(w) = w**2 - 3*w - 2. Let p be n(4). Factor -10 + 3*c**p - c + 10 - 8*c.
3*c*(c - 3)
Let -3/2*a**3 + 51/2*a**2 + 297/2 - 225/2*a = 0. What is a?
3, 11
Let s(n) = 6*n**2 + 3*n - 12. Let q be (-8)/(-12)*5/((-20)/18). Let f(y) = y**2 + y. Let c(b) = q*f(b) + s(b). Factor c(t).
3*(t - 2)*(t + 2)
Let i(k) = -k**3 + k**2 - k - 2. Let t be i(0). Let a = t + 5. Solve 1 - 1 - a*x**4 + 4*x**3 - x**3 = 0 for x.
0, 1
Let a(q) = -4*q - 8. Let w be a(-3). Let o be -4 - ((-6)/10 - w). Determine j so that 3/5*j - o*j**2 + 0 = 0.
0, 1
Let y(d) = d + 13. Let s be y(-11). Factor 12 - 8*u**s + 2*u + 2*u**2 + 11*u**2 - 7*u**2.
-2*(u - 3)*(u + 2)
Let g(y) be the first derivative of 3*y**5/35 + 3*y**4/2 + 12*y**3/7 - 405*y**2/7 + 729*y/7 + 147. Suppose g(l) = 0. Calculate l.
-9, 1, 3
Determine b, given that -9*b**4 + 3*b**2 - 3*b**5 - 24*b**3 - 19*b**2 + 2*b**5 = 0.
-4, -1, 0
Let z be ((-1)/((-2)/1))/(4/94). Let n = z - 41/4. Determine o, given that 0 - n*o**4 - 1/2*o**3 + 1/2*o + 3/2*o**2 = 0.
-1, -1/3, 0, 1
Let t(p) be the third derivative of -p**5/20 + 9*p**4/8 + 74*p**2. Suppose t(c) = 0. What is c?
0, 9
Let b(l) be the second derivative of -l**8/2520 - l**7/420 - l**6/180 - l**5/180 - 7*l**3/6 + 10*l. Let o(c) be the second derivative of b(c). Factor o(q).
-2*q*(q + 1)**3/3
Suppose -5*o + 9 = a, -2*a = -2*o + 4*o - 10. Suppose a*f - 16 = -z, -2*z + 3*z - f = 1. Factor 3*d**3 + 11*d**2 + 2*d**z + d - 8*d**2 - d**4.
d*(d + 1)**3
Factor 3*j**3 + 2*j**2 + 17*j - j**4 - 14*j**3 + 7*j**3 - 5*j - 9.
-(j - 1)**2*(j + 3)**2
Suppose 1080*k - 1120*k + 80 = 0. Suppose -10/11*x**4 - 4/11*x - 14/11*x**k - 2/11*x**5 + 0 - 18/11*x**3 = 0. What is x?
-2, -1, 0
Suppose 5*d - 2*c - 15 = 0, 400*c - 10 = 3*d + 395*c. Suppose 2/3*k**d - 14/3*k**2 + 6*k**3 - 10/3*k**4 + 0 + 4/3*k = 0. Calculate k.
0, 1, 2
Suppose 2*s + 20 = -r, -2*r + 2*s - 25 = 3*s. Let g be 6/(-15) - 20/r. Suppose 4/5*x**2 + 4/5 + g*x = 0. Calculate x.
-1
Let 0*t + 0*t**3 + 5/3*t**2 - 5/3*t**4 + 0 = 0. Calculate t.
-1, 0, 1
Let r = -1373 + 1375. Let q(c) be the first derivative of r*c**5 + 0*c**3 - 3 + 5/2*c**2 - 2*c - 1/2*c**6 - 5/2*c**4. Solve q(l) = 0 for l.
-2/3, 1
Let f(z) be the first derivative of 2*z**3/5 - 58*z**2 - 194*z/5 - 57. Factor f(n).
2*(n - 97)*(3*n + 1)/5
Suppose -2 = u - 4. Factor -6*p**u + p**3 - 2*p**2 + 0*p**2 + 3*p**3.
4*p**2*(p - 2)
Let a(g) = -6*g - 10. Let b(r) = r + 1. Let k(n) = a(n) + 5*b(n). Let m be k(-8). Solve -l**4 + 2*l**4 + 27*l**2 + l**m + 2*l**3 - 25*l**2 = 0.
-2, -1, 0
Let s(p) be the first derivative of 0*p + 2/11*p**2 - 2/33*p**3 - 11. Factor s(z).
-2*z*(z - 2)/11
Let a(d) = d**3 - 9*d**2 + 8*d + 7. Let g be a(8). Suppose g*q - q = 2*q. Factor 0 + 1/2*c**3 + q*c**2 - 1/2*c.
c*(c - 1)*(c + 1)/2
Let f(c) = 2*c**4 - 90*c**2 - 6*c + 402. Let i(k) = -15*k**4 + 720*k**2 + 50*k - 3215. Let d(u) = 25*f(u) + 3*i(u). Factor d(v).
5*(v - 3)**2*(v + 3)**2
Suppose 0 = 4*b - 4*x - 24, -12 = -2*b + 7*x - 3*x. Factor 0*a**2 + b + 4*a**2 - a**2 + 0*a**2 + 9*a.
3*(a + 1)*(a + 2)
Solve 25/8*o + 0 - 9/8*o**3 + 15/8*o**2 + 1/8*o**4 = 0.
-1, 0, 5
Let w be 4936/(-364) - 10/65. Let j = w - -494/35. Let -j*a + 1/5*a**2 - 3/5 = 0. What is a?
-1, 3
Let d = -5168 + 5171. Find u such that 0*u + 3/5*u**4 - 3*u**2 + 0*u**d + 12/5 = 0.
-2, -1, 1, 2
Solve 247*g**2 - 112*g**2 + 125*g**4 - 270*g**3 - 45*g**3 - 15*g**5 + 270*g = 0 for g.
-2/3, 0, 3
Let 160*c**2 - 2*c - 5*c**4 - 5*c**5 - 30*c**4 - 30*c**3 + 174*c - 12*c = 0. Calculate c.
-4, -1, 0, 2
Let n = -401 - -403. Let q(x) be the first derivative of -4*x - n*x**3 + 2/5*x**5 - 1/2*x**4 + 6 + 5*x**2. Factor q(f).
2*(f - 1)**3*(f + 2)
Suppose -2*p + 6*p = -232. Let n = 178/3 + p. Factor 1/3*z**2 - n + 0*z.
(z - 2)*(z + 2)/3
What is k in -15*k + 75*k**2 + 100*k**3 + 19*k + 6*k - 35*k**3 = 0?
-1, -2/13, 0
Let w be -52*((-39)/54 + 6/27). Suppose 7*m - w = -12. Find p, given that 2/13*p + 0 - 12/13*p**m = 0.
0, 1/6
Let v(p) be the second derivative of -p**4/3 + 10*p**3/3 + 12*p**2 + 15*p + 3. Factor v(u).
-4*(u - 6)*(u + 1)
Let y(z) be the first derivative of -z**7/7560 - z**6/3240 + z**5/540 + 5*z**3 + 