 s(c) be the third derivative of r(c). Factor s(o).
-o**2*(o - 1)*(o + 1)**2
Let w(y) be the third derivative of -y**7/105 + y**6/30 + y**5/30 - y**4/6 - 11*y**2. Factor w(t).
-2*t*(t - 2)*(t - 1)*(t + 1)
Let k(r) = 30*r**4 + 15*r**3 + 60*r**2 - 25. Let o(b) = b**4 - b**3 + b**2 - 1. Let c(s) = -k(s) + 25*o(s). Determine d, given that c(d) = 0.
-7, -1, 0
Let a(n) = 90*n**4 - 165*n**3 + 70*n**2 + 15*n. Let c(j) = -j**4 + j**3 - j**2 - j. Let v(d) = -a(d) - 5*c(d). Solve v(m) = 0 for m.
-2/17, 0, 1
Suppose c - 5*r = -13, 0 = c + 2*r - 3 + 2. Let d be 0/(0 - 3) - c. Factor 0 - 2/9*n**d + 0*n + 2/9*n**2.
-2*n**2*(n - 1)/9
Suppose -370 = -5*d + 225. Let n = 203 - d. Solve 2 + n*p**3 + 24*p + 15*p**3 + 29*p**3 + 96*p**2 = 0.
-1/4
Let x(d) = d**3 - d**2 + 3*d - 2. Let v be x(2). Let u = v - 6. Factor -l + 2*l + u - 5*l + 2*l**2.
2*(l - 1)**2
Let c(o) = 5*o**2 - 1. Let v be c(1). Find t such that -v*t**2 + 2 + t + t + 0*t = 0.
-1/2, 1
Let -63/5*j - 27/5*j**4 + 99/5*j**3 + 51/5*j**2 + 12/5 = 0. Calculate j.
-1, 1/3, 4
Let o be 2*(-3)/(-90)*3. Solve -2/5*f + 1/5 + o*f**2 = 0 for f.
1
Suppose -4*f = -2*l + 14, 4*l = 8*l + 4. Let u be 2/6*0/f. Factor 2/5*o**2 + u + 4/5*o**3 + 2/5*o**4 + 0*o.
2*o**2*(o + 1)**2/5
Let d(r) be the second derivative of r**7/28 - 7*r**6/60 + 3*r**5/40 + r**4/8 - r**3/6 + r. Factor d(x).
x*(x - 1)**3*(3*x + 2)/2
Let k(c) be the second derivative of -c**6/15 - c**5/5 + 2*c**3/3 + c**2 + 19*c. Factor k(o).
-2*(o - 1)*(o + 1)**3
Suppose 4*q = 4*s - 28, q = -5*s - 0*q + 5. Factor -1/2*r**4 + r**s + 0 + 3/4*r**3 - 1/4*r**5 - r.
-r*(r - 1)**2*(r + 2)**2/4
Let w(h) = 2*h**2 - 7*h + 5. Let m(k) = k**2 - 6*k + 4. Let p(s) = 6*m(s) - 5*w(s). Let r(z) = -5*z**2. Let y(o) = 4*p(o) - 3*r(o). Factor y(b).
-(b + 2)**2
Let c(g) be the third derivative of g**5/20 + g**4 + 8*g**3 + 6*g**2. Find a, given that c(a) = 0.
-4
Suppose 8 = -4*h, 2*h - 18 = -2*v + 6*h. Suppose -v*g + 22 = c - 3, g - 5 = c. Solve -4 + 2*l + l**2 + c + l**2 = 0 for l.
-2, 1
Let g = -140 + 422/3. Find k, given that -g*k + 2/3*k**2 + 0 = 0.
0, 1
Solve 20*g**3 - 14*g - 4 - 27*g**2 + 11*g - 21*g = 0.
-2/5, -1/4, 2
Let r be (-18)/12 + 14/4. Suppose -3*w + 26 = -b - 3*b, -w - 23 = 5*b. Factor g**3 + g**3 + 5*g**r + w*g - g**2.
2*g*(g + 1)**2
Suppose 3*z - i = 6*z, i = -5*z. Suppose 0*k - 1/2*k**2 + z*k**3 + 1/2*k**4 + 0 = 0. Calculate k.
-1, 0, 1
Let k(f) be the first derivative of f**6/120 - f**5/20 + f**4/8 + 5*f**3/3 + 2. Let b(n) be the third derivative of k(n). Factor b(c).
3*(c - 1)**2
Let p = -17 - -21. Suppose -4*m = -s - 16 + 4, 12 = p*m + 4*s. Factor 0*z**2 + 0*z - 3/2*z**4 + 0 - 3*z**m.
-3*z**3*(z + 2)/2
Factor -1/4*r - 3/4*r**3 - 1/4*r**4 + 0 - 3/4*r**2.
-r*(r + 1)**3/4
Let p = -1/178 - -45/89. Factor -q + 0 - p*q**2.
-q*(q + 2)/2
Let l = 474 + -472. Factor 0 + 0*w**3 + 0*w**l - 3/7*w**4 + 0*w.
-3*w**4/7
Let i(t) be the second derivative of -1/3*t**3 - 2/3*t**2 + 0 - 3*t - 1/18*t**4. Factor i(h).
-2*(h + 1)*(h + 2)/3
Let r = -13 + 15. Suppose r*b - 3*j = j, 0 = -b + 5*j. Determine q so that -1/2*q**4 + b + q**3 + 0*q - 1/2*q**2 = 0.
0, 1
Factor 3*q**2 + 3 + 3*q + 3*q + 0*q.
3*(q + 1)**2
Let s = 712/5415 + 2/1083. Let x(v) be the first derivative of -s*v**5 - 1 + 0*v + 1/3*v**2 - 2/3*v**3 + 1/2*v**4. Factor x(n).
-2*n*(n - 1)**3/3
Suppose x + 44*x**2 - 4*x - 68*x**2 + 3*x**3 + 24 = 0. Calculate x.
-1, 1, 8
Let y(x) be the third derivative of -3*x**7/70 + 7*x**6/120 + x**5/30 - 18*x**2. Suppose y(o) = 0. What is o?
-2/9, 0, 1
Suppose -p = -5*k + 14, 5*k + 3*p + 6 = 2*k. Let u(a) be the first derivative of a**k + 0*a + 1/4*a**4 + a**3 - 1. Suppose u(l) = 0. Calculate l.
-2, -1, 0
Let s be (20/8 - 2)*0. Let z(t) be the second derivative of 3*t - 1/15*t**3 - 2/75*t**6 + 0*t**5 + 1/105*t**7 + s*t**2 + 0 + 1/15*t**4. Factor z(a).
2*a*(a - 1)**3*(a + 1)/5
Let t(m) = m**2 - 1. Let x(s) = s**3 - s**2 - 3*s - 1. Let a(y) = -5*t(y) - 5*x(y). What is o in a(o) = 0?
-1, 2
Let d(f) be the second derivative of 0 - 1/8*f**4 - 3/4*f**2 + 7*f + 1/2*f**3. Determine w so that d(w) = 0.
1
Suppose c = -2*c - 12. Let w = -4 - c. Factor u + 0*u**3 - 2*u**2 + w*u**3 + 0*u**3 + u**3.
u*(u - 1)**2
Let l = 43/2 - 21. Let u(m) be the second derivative of -l*m**4 + 0*m**2 - 3/10*m**5 - 1/3*m**3 + 0 - m - 1/15*m**6. Factor u(k).
-2*k*(k + 1)**3
Let u = -94/5 - -19. Determine q, given that 0 + u*q**2 - 1/5*q**3 + 0*q = 0.
0, 1
Let n(c) be the third derivative of c**6/120 - 3*c**5/50 + c**4/10 + 4*c**3/15 + 6*c**2. Factor n(f).
(f - 2)**2*(5*f + 2)/5
Let x(o) = o**3 - o. Let c be (-3 + 1)*1 + 1. Let n be x(c). Factor n*v**2 + 2/3*v + 0 - 2/3*v**3.
-2*v*(v - 1)*(v + 1)/3
Let g = -270 - -1368/5. Determine x, given that 6/5*x + 12/5*x**2 - 2/5 - 42/5*x**4 - g*x**5 - 4*x**3 = 0.
-1, 1/3
Let i(p) = -p**4 + 4*p**3 + 3*p**2 - 3. Let v = -11 - -8. Let h(k) = 2*k**4 - 9*k**3 - 7*k**2 + 7. Let l(r) = v*h(r) - 7*i(r). Solve l(s) = 0 for s.
0, 1
Suppose -2*z - 39 = 13. Let y = z + 28. Let 2/5*j**y - 2/5*j**3 + 0*j + 0 = 0. Calculate j.
0, 1
Suppose u**3 - 6 - u**4 + 8*u**2 + 8*u**2 + 4*u - 9*u**2 - 5*u = 0. What is u?
-2, -1, 1, 3
Let c be (1 + 2/(-4))*(22 + -22). Solve 1/2*b**5 + 0*b + 0*b**4 + c*b**2 + 0 - 1/2*b**3 = 0.
-1, 0, 1
Suppose 3*d = 7*d. Suppose 8*q - 9 = 5*q, d = p + 5*q - 17. Determine k so that -2*k**2 - 2*k**p - k**3 - k**2 - k + 3*k**2 = 0.
-1, 0
Let r(f) be the second derivative of 1/4*f**4 + 3/20*f**5 + 0*f**3 + 6*f + 0*f**2 + 0. Let r(y) = 0. Calculate y.
-1, 0
Let q(x) be the third derivative of -1/9*x**3 + 0 + 1/360*x**6 + 5/72*x**4 - 3*x**2 + 0*x - 1/45*x**5. Factor q(h).
(h - 2)*(h - 1)**2/3
Let o(n) be the first derivative of n**3 - 9*n**2 + 25. What is m in o(m) = 0?
0, 6
Suppose 0 = 3*l + 4*c + 2, 5*c = 3*l - 6*l - 4. Let d(q) be the first derivative of -2/21*q**3 + 0*q - 3 + 0*q**l. What is y in d(y) = 0?
0
Let l(g) be the second derivative of g**7/840 - g**6/180 - g**5/30 + g**4/3 + g**3 - 4*g. Let c(z) be the second derivative of l(z). What is r in c(r) = 0?
-2, 2
Solve -7/3*v**2 - 3 - 1/3*v**3 + 17/3*v = 0 for v.
-9, 1
Let u(i) be the third derivative of i**7/210 - i**5/30 + i**3/6 - 8*i**2. Determine x, given that u(x) = 0.
-1, 1
Let i(f) = -f**3 - 4*f**2 + 5*f. Let w be i(-5). Let h(p) be the second derivative of w + 1/54*p**4 - 2/27*p**3 - p + 1/9*p**2. Factor h(o).
2*(o - 1)**2/9
Let z(a) = 57*a**3 - 48*a**2 - 33*a + 33. Let s(c) = -7*c**3 + 6*c**2 + 4*c - 4. Let u(t) = -33*s(t) - 4*z(t). Determine g, given that u(g) = 0.
0, 2
Determine k so that 0 + 1/4*k**2 + 1/4*k = 0.
-1, 0
Let c = 683 - 40979/60. Let x(w) be the second derivative of -1/24*w**4 + c*w**6 - 1/12*w**3 + 0*w**2 + 1/40*w**5 + 0 - w. Let x(i) = 0. What is i?
-1, 0, 1
Let l(y) be the third derivative of -y**8/6720 + y**7/1260 - y**6/720 + y**5/60 + 3*y**2. Let m(g) be the third derivative of l(g). Factor m(p).
-(p - 1)*(3*p - 1)
Factor 2/23*f**5 + 10/23*f**4 + 8/23*f**2 + 16/23*f**3 + 0*f + 0.
2*f**2*(f + 1)*(f + 2)**2/23
Let z(h) be the third derivative of h**8/1008 + 2*h**7/315 + h**6/120 - 23*h**2. Determine b so that z(b) = 0.
-3, -1, 0
Let v be (-35)/(-21)*(-1)/(-10). Let z(x) be the second derivative of -2*x**2 - x**3 + 0 - v*x**4 - 3*x. Factor z(b).
-2*(b + 1)*(b + 2)
Let r be (-11 + 2)*(-1)/3. Determine d, given that -12*d + 5*d - d**4 + 3*d**2 - 4*d**4 - r + 5 + 7*d**3 = 0.
-1, 2/5, 1
Let n = 590 + -4126/7. Factor -1/7*t**3 + t + n + 2/7*t**2.
-(t - 4)*(t + 1)**2/7
Let w(c) = -c - 1. Let z(o) = -2*o - 11. Let i(q) = -3*w(q) + z(q). Let r be i(8). Factor 0 + r*d**2 - 2 + 2*d**2.
2*(d - 1)*(d + 1)
Let d(s) = 2*s**4 - 4*s**3 - 6*s**2 - s - 4. Let c(u) = 5*u**4 - 12*u**3 - 18*u**2 - 4*u - 11. Let v(o) = 3*c(o) - 8*d(o). Factor v(y).
-(y + 1)**4
Let y be 62/51 - (-6)/51. Factor 0*g**3 + 0 + 4/3*g**4 - y*g**2 - 2/3*g**5 + 2/3*g.
-2*g*(g - 1)**3*(g + 1)/3
Let v(n) be the second derivative of -3*n + 0 + 3/10*n**5 - 1/3*n**4 - 1/21*n**7 + 0*n**3 + 0*n**2 + 0*n**6. Solve v(g) = 0.
-2, 0, 1
Let l(i) = -i**2 + 6*i - 5. Let z be l(5). Let h(a) = a - 2. Let r be h(4). Factor -6/5*k**r - 2/5*k - 6/5*k**3 + z - 2/5*k**4.
-2*k*(k + 1)**3/5
Let j(y) = y + 2 + y**3 - 2 - y**2. Suppose 7*m + 2*m = 45. Let k(v) = -4*v**3 + 4*v**2 - 7*v. Let w(o) = m*j(o) + k(o). Find i, given that w(i) = 0.
-1, 0, 2
Let n(q) be the secon