Let t(y) = y - 29. Let u be t(29). Let v(p) be the third derivative of 0 + 0*p + 1/30*p**6 - 2/3*p**4 + 0*p**5 + 12*p**2 + u*p**3. Factor v(i).
4*i*(i - 2)*(i + 2)
Suppose -3*f + 2 = -5*f. Let k = 2 - f. Factor 3*n**k - n - 4 - 8*n**2 + 0*n - 5*n**3 - 9*n.
-2*(n + 1)**2*(n + 2)
Let y(f) be the second derivative of f**10/75600 + f**9/37800 - f**8/16800 - f**7/6300 + 3*f**4/2 - 19*f. Let z(k) be the third derivative of y(k). Factor z(n).
2*n**2*(n - 1)*(n + 1)**2/5
Let h = -334 + 334. Let a(j) be the second derivative of 3/8*j**4 - 3/40*j**5 + h - 1/2*j**3 + 0*j**2 + 6*j. Factor a(s).
-3*s*(s - 2)*(s - 1)/2
Let b = -3/13451 - -94175/80706. Suppose 1/6*v**2 + b*v + 1 = 0. Calculate v.
-6, -1
Let j(o) be the first derivative of 7 - 1/2*o + 1/12*o**3 - 1/8*o**2. Find l such that j(l) = 0.
-1, 2
Let g be 4 - (21/(-14) - 7/(-2)). Factor -t**g + 2*t**2 - 6*t**3 + 14 - 11 + 5*t**3 + 5*t.
-(t - 3)*(t + 1)**2
Let w(v) be the first derivative of -16*v**4 + 41 - 32*v - 112/3*v**3 - 18/5*v**5 - 1/3*v**6 - 48*v**2. Determine h, given that w(h) = 0.
-2, -1
Let z(c) = 2*c**5 + 6*c**4 - 4*c**2. Let w(b) = -b**3 - b**2. Let f(y) = y**3 - 10*y**2 - 2*y + 16. Let d be f(10). Let m(x) = d*w(x) + z(x). Factor m(h).
2*h**3*(h + 1)*(h + 2)
Let t(h) = h - 4. Let n be t(7). Suppose n*m = 4*m. Solve m*u**5 - 3*u**5 + 3*u**5 + u**4 + u**5 = 0.
-1, 0
Let o(l) be the first derivative of l**4/36 + 2*l**3/9 + l**2/2 - 15*l + 3. Let h(r) be the first derivative of o(r). Solve h(c) = 0.
-3, -1
Let x(p) be the first derivative of p**6/18 + 2*p**5/15 + p**4/12 + 81. Factor x(m).
m**3*(m + 1)**2/3
Let q = 1 + 42. Suppose -9*r + q = -29. Factor 0*l + r*l - l**3 - 15*l + 8*l.
-l*(l - 1)*(l + 1)
Let b be 6 + 39/(-15) - (-1)/(-1). Solve 9/5*w**3 - 87/5*w**2 + b - 36/5*w + 15*w**4 + 27/5*w**5 = 0 for w.
-2, -1, 2/9, 1
Let k(s) = -110*s**3 + 1115*s**2 + 25*s. Let y(n) = -9*n**3 + 93*n**2 + 2*n. Let c(a) = 2*k(a) - 25*y(a). What is t in c(t) = 0?
0, 19
Let u(x) be the second derivative of -2*x**7/21 - 2*x**6/5 + 24*x**5/5 - 28*x**4/3 - 29*x + 15. Suppose u(d) = 0. What is d?
-7, 0, 2
Let w(v) = 5*v**3 - 735*v**2 - 36015*v - 588235. Let r(j) = 3*j**3 - 735*j**2 - 36015*j - 588237. Let s(p) = 5*r(p) - 4*w(p). Suppose s(k) = 0. Calculate k.
-49
Let t = 279 - 277. Let n(w) be the first derivative of 1/9*w**6 + 1/2*w**4 + 2/9*w**3 + 2 + 0*w**t + 2/5*w**5 + 0*w. Factor n(g).
2*g**2*(g + 1)**3/3
Let y(c) be the second derivative of 8*c + 0 - 1/6*c**2 + 1/120*c**5 + 5/36*c**3 - 1/18*c**4. Solve y(m) = 0.
1, 2
Factor 3834 - 36169 - 330*b**2 + 5*b**3 - 20905 + 7260*b.
5*(b - 22)**3
Solve -47*j**2 + 5*j + 31*j - 3 - 8 + 3 + 4 + 15*j**3 = 0 for j.
2/15, 1, 2
Let r be (0 - -1)/(5*5/150). Let w(x) be the third derivative of 0*x**3 + 0 + 1/90*x**5 + 6*x**2 + 0*x + 1/72*x**4 + 1/360*x**r. Factor w(s).
s*(s + 1)**2/3
Factor 66 + 5*o**2 + 135*o + 3*o**3 + 54*o**2 + 13*o**2.
3*(o + 1)**2*(o + 22)
Let g be -10 + 3 - (3 - 1). Let b = g - -13. Suppose -c**5 - 16*c**2 + 2*c**b + c + 0*c**5 + 14*c**2 = 0. Calculate c.
-1, 0, 1
Let s(t) = 20*t**2 - 360*t + 2. Let c be s(18). Factor -8/7*x + 5/7*x**c - 4/7.
(x - 2)*(5*x + 2)/7
Let r be 3/(12/56)*3/7. Let m(w) be the second derivative of 0 - 3/20*w**5 + 0*w**3 + 7/12*w**4 - 2*w**2 - r*w. Suppose m(i) = 0. Calculate i.
-2/3, 1, 2
Let w = 37 + -100/3. Let z(c) be the first derivative of c**2 - 5 - 4/5*c**5 + 13/4*c**4 - w*c**3 + 0*c. Factor z(v).
-v*(v - 2)*(v - 1)*(4*v - 1)
Let h = 5567/6684 + 1/2228. Let s(w) be the second derivative of -3/2*w**2 - 1/12*w**4 + 0 - 1/20*w**5 + w + h*w**3. Let s(r) = 0. What is r?
-3, 1
Let a be 5 + 9/(-3) + (81 - -2). Let y = a - 85. Factor 0 + y*u**2 - 2/11*u**3 + 0*u - 2/11*u**4.
-2*u**3*(u + 1)/11
Suppose -1/9*i**2 - 20/9*i - 19/9 = 0. Calculate i.
-19, -1
Let h be 2 - (597/36)/(-1). Let p = h + -69/4. Factor -2/3 + 4/3*r**3 + 0*r**2 - p*r + 2/3*r**4.
2*(r - 1)*(r + 1)**3/3
Let m(x) be the third derivative of -x**8/6720 - x**7/840 + x**4/4 - 9*x**2. Let n(f) be the second derivative of m(f). Factor n(y).
-y**2*(y + 3)
Let b(v) = -7*v**2 - 33*v - 52. Let p(i) = -8*i**2 - 32*i - 53. Let o(m) = -3*b(m) + 2*p(m). Suppose o(k) = 0. Calculate k.
-5, -2
Let t(k) = k**2 + 22*k + 21. Let m(s) = s**3 + s**2 + s. Let q be m(-3). Let w be t(q). Suppose -1/2*u**2 + w + 1/4*u + 1/4*u**3 = 0. Calculate u.
0, 1
Find i, given that -9*i + 1/4*i**4 + 33/4*i**2 - 5/2*i**3 + 0 = 0.
0, 3, 4
Let h(g) = g**3 + 7*g**2 - 7*g + 10. Let j be h(-8). Factor 3*w**j + 0*w - 11*w - 3*w**3 + 11*w.
-3*w**2*(w - 1)
Suppose -68*t + 16 + 43 = -77. Factor -1/3 + 1/3*h + 10/3*h**t + 8/3*h**3.
(h + 1)*(2*h + 1)*(4*h - 1)/3
Let o(f) be the first derivative of f**6/9 - 142*f**5/15 + 323*f**4 - 49708*f**3/9 + 142477*f**2/3 - 167042*f + 300. Factor o(c).
2*(c - 17)**4*(c - 3)/3
Let c(x) be the second derivative of -x**4/48 - x**3 - 10*x**2 - 714*x. Determine g so that c(g) = 0.
-20, -4
Let c(h) be the first derivative of 2*h**3/3 - 16*h**2 + 96*h - 246. Factor c(b).
2*(b - 12)*(b - 4)
Let h(c) be the third derivative of -c**7/70 - 3*c**6/20 - 13*c**5/20 - 3*c**4/2 - 2*c**3 + 7*c**2 - 2. Find g such that h(g) = 0.
-2, -1
Let l(d) = -1. Let p(w) = w - 1. Let i(j) = 2*l(j) - p(j). Let m be i(-1). Factor 3/2*f**2 + m*f + 3/2*f**3 + 0.
3*f**2*(f + 1)/2
Let u be 2*(-6 - -7)/30. Let o(v) be the third derivative of 0*v + 0 + u*v**5 - 4/3*v**4 - 3*v**2 + 32/3*v**3. Factor o(j).
4*(j - 4)**2
Let b = 7 - -75. Suppose 22*q + 5*q**5 - 18*q**4 - 40 - b*q + 55*q**3 + 10*q**2 + 48*q**4 = 0. What is q?
-2, -1, 1
Let c(d) = d**2 + 12*d + 3. Let l(t) = -t**2 + 8*t - 4. Let f be l(9). Let b be c(f). Factor -32*n**3 - 9 + 21 - 10 + b*n**2 + 14*n.
-2*(n - 1)*(4*n + 1)**2
Suppose -127 - 3 = -26*k. Let w(b) be the second derivative of 0*b**3 + 0 - 1/70*b**7 - 3/100*b**5 + 0*b**2 + 1/25*b**6 - k*b + 0*b**4. Solve w(d) = 0 for d.
0, 1
Let i(p) be the first derivative of 0*p + 5/3*p**3 - 10 + 5*p**2. Determine z, given that i(z) = 0.
-2, 0
Let b be 429/431 - (7 - 140/21). Let x = b + 2/431. Factor 2/3*o**2 + x + 4/3*o.
2*(o + 1)**2/3
Suppose 2*c - y = 9, 74*c = 73*c + y + 6. What is n in 2/5*n + 1/5*n**c - 3/5*n**2 + 0 = 0?
0, 1, 2
Suppose 20 = 7*k - 8. Suppose 2*x + k = -z, 3*z = -6*x + 3*x - 3. Let -9/4*a**3 - 1/4*a + 3/2*a**z + 0 + a**4 = 0. What is a?
0, 1/4, 1
Let g(f) be the second derivative of -f**5/70 - 4*f**4/21 - 13*f**3/21 - 6*f**2/7 - 138*f. What is a in g(a) = 0?
-6, -1
Let i(c) = c**4 + 5*c**3 + 26*c**2 - 14*c + 12. Let d(x) = 10*x**4 + 45*x**3 + 235*x**2 - 125*x + 110. Let v(n) = 6*d(n) - 55*i(n). Factor v(s).
5*s*(s - 2)*(s - 1)*(s + 2)
Let h(k) be the second derivative of k**4/4 - 5*k**3/2 - 36*k**2 - 2*k + 5. Factor h(u).
3*(u - 8)*(u + 3)
Let w be (-6)/(-9) - 13/3. Let b = w - -4. Factor -2/3*f + b*f**4 + 0 + 0*f**3 - f**2.
f*(f - 2)*(f + 1)**2/3
Let t(y) = y**2 - 13*y + 31. Let u be t(18). Let a = u + -1087/9. Determine f, given that -a*f**2 + 0 + 0*f = 0.
0
Factor -1/3*z**3 - 1/6*z**4 + 0*z + 0 - 1/6*z**2.
-z**2*(z + 1)**2/6
Let g be (8 + -5 + -3)*(-10)/30. Let y(q) be the second derivative of 9*q - 1/3*q**4 + g - 3*q**2 + 7/3*q**3. Factor y(j).
-2*(j - 3)*(2*j - 1)
Let w(t) = -13*t + 1097. Let z be w(84). Suppose 19/5*g**3 - 4/5*g**z + 1/5*g**2 - 12/5*g + 0*g**4 - 4/5 = 0. Calculate g.
-2, -1/2, 1, 2
Let f(b) = -15*b**4 - 8*b**3 + 7*b**2 + 11. Let i(x) = -30 + 36 + x**2 - 8*x**4 - x**3 - 3*x**3 + 3*x**2. Let y(l) = -6*f(l) + 11*i(l). Factor y(v).
2*v**2*(v + 1)**2
Let z(u) be the first derivative of 1 + 0*u - 9/2*u**3 + 9/4*u**4 - 3/10*u**5 + 0*u**2. Factor z(n).
-3*n**2*(n - 3)**2/2
Let v = -1053 - -1053. Suppose 2/7*m + v + 0*m**2 - 2/7*m**3 = 0. Calculate m.
-1, 0, 1
Let i be (-1)/((-404)/134 - -3). Factor -66*a**5 + 4*a**3 - a**4 + 5*a**4 + i*a**5 - 2 + a**2 - 3*a**2 - 5*a.
(a - 1)*(a + 1)**3*(a + 2)
Let i(q) be the second derivative of 2*q**4 + 70*q**3/3 - q - 14. Factor i(w).
4*w*(6*w + 35)
Factor 29/3*p - 43/3*p**2 + 4/3*p**3 + 10/3.
(p - 10)*(p - 1)*(4*p + 1)/3
Factor -25/3*u - 9*u**2 + 2/3.
-(u + 1)*(27*u - 2)/3
Let o = 5 + 20. Suppose 9*q = 4*q + o. Factor 12*w**3 - 16*w + w - 6 + 2*w**5 + 4*w**2 - 10*w**2 + w**q + 12*w**4.
3*(w - 1)*(w + 1)**3*(w + 2)
Let p(s) be the second derivative of 49*s**6/165 + 126*s**5/55 + 218*s**4/33 + 96*s**3/11 + 64*s**2/11 - 72*s. 