ctor d(o).
3*(o + 5)**3
Let t = 851/5 + -4263/25. Let q = t + 124/75. Factor 1/3*g**3 + 4/3*g**2 + 0 + q*g.
g*(g + 2)**2/3
Factor 3/2*c + 1/2 + 1/2*c**3 + 3/2*c**2.
(c + 1)**3/2
Let v(f) be the third derivative of f**9/90720 - f**7/2520 + f**6/540 + f**5/12 - 5*f**2. Let q(h) be the third derivative of v(h). Factor q(o).
2*(o - 1)**2*(o + 2)/3
Let r be 34/(-68) + 2/(1*2). Let -3/2*w**3 + 0 + 3/2*w**4 + 0*w + r*w**2 - 1/2*w**5 = 0. What is w?
0, 1
Let x(b) = -b**3 - b. Let i(m) = 5*m**4 + 9*m**3 - 27*m**2 + 31*m - 6. Let h(w) = i(w) + 6*x(w). Factor h(o).
(o - 1)**2*(o + 3)*(5*o - 2)
Let o be 0 + 6/153 + 0. Let p = o - -43/204. Factor 0 - p*s**4 - 1/4*s**3 + 1/4*s + 1/4*s**2.
-s*(s - 1)*(s + 1)**2/4
Let k(t) be the first derivative of -4*t**3/3 + 8*t**2 - 12*t + 2. Solve k(v) = 0 for v.
1, 3
Let s be (64/(-60) - -1)/((-18)/90). Factor -1/3*w**2 - s*w**4 + 0 + 0*w - 2/3*w**3.
-w**2*(w + 1)**2/3
Solve 4*v**2 - 2 + 3*v + 0*v - 6 + v = 0 for v.
-2, 1
Let g(y) = 3*y + 81. Let p be g(-26). Factor 0 - 3/5*h - 27/5*h**2 - 72/5*h**p - 48/5*h**4.
-3*h*(h + 1)*(4*h + 1)**2/5
Let i(u) = -u**3 - 11*u**2 + 3. Let j be i(-11). Let c = 23 - 21. Factor 2/7*z**c - 2/7*z**5 - 6/7*z**j + 0*z + 6/7*z**4 + 0.
-2*z**2*(z - 1)**3/7
Let y(u) = -u + 14. Let r be y(11). Let m(z) be the second derivative of 3*z + 0 + z**2 - 1/6*z**4 + 0*z**r. Solve m(s) = 0.
-1, 1
Suppose -t - 8 = -9. Let r be (-3 + 6 + -3)/t. Let -1/3*l**2 - 1/3*l**3 + 0 + r*l = 0. What is l?
-1, 0
Let o(r) = r**2 - r - 4. Let l(w) = 5*w**2 - 4*w - 20. Let q(m) = 2*l(m) - 11*o(m). Let i be q(4). Factor 1/3*u - 5/3*u**2 + 7/3*u**3 - u**4 + i.
-u*(u - 1)**2*(3*u - 1)/3
Let g(f) be the third derivative of -f**3 + 0*f + 4/35*f**7 + 1/10*f**6 - 5*f**2 + 3/112*f**8 - 3/10*f**5 + 0 - 7/8*f**4. Factor g(l).
3*(l - 1)*(l + 1)**3*(3*l + 2)
Let o(r) be the third derivative of -r**7/70 + r**6/24 - r**5/30 - 12*r**2. Suppose o(u) = 0. What is u?
0, 2/3, 1
Factor 0*q + 1/3*q**2 - 1/3.
(q - 1)*(q + 1)/3
Let a = 85/178 + 2/89. Solve 0*z + 1/4*z**4 + 1/4*z**2 + 0 + a*z**3 = 0.
-1, 0
Let c be 0/((-10)/(-35)*14). What is k in -1/7*k**3 + c*k + 1/7*k**2 + 0 = 0?
0, 1
Let k(a) be the first derivative of -2/5*a**5 - 3 + 4*a**2 + 5/2*a**4 - 16/3*a**3 + 0*a. Factor k(p).
-2*p*(p - 2)**2*(p - 1)
Let f(c) be the first derivative of 7*c**4/2 + 10*c**3/3 - 2*c**2 - 61. Factor f(l).
2*l*(l + 1)*(7*l - 2)
Let t(o) = 9*o**2 + 2*o + 7. Let h(w) be the third derivative of 2*w**5/15 + w**4/12 + w**3 - 3*w**2. Let z(i) = -7*h(i) + 6*t(i). Factor z(r).
-2*r*(r + 1)
Let t(z) be the first derivative of 2 + z**2 + 0*z**3 + 1/210*z**5 + 0*z**6 + 0*z**4 + 0*z - 1/735*z**7. Let j(m) be the second derivative of t(m). Factor j(x).
-2*x**2*(x - 1)*(x + 1)/7
Let x(y) be the third derivative of 9*y**7/70 - 7*y**6/40 - y**5/10 + 5*y**2. Determine d, given that x(d) = 0.
-2/9, 0, 1
Suppose 5*s + 4*i + 5 = 0, 0 = -i - 3*i - 20. Solve 6/7*y**2 + 2/7*y + 0 + 4/7*y**s = 0.
-1, -1/2, 0
Let z(m) be the third derivative of m**5/30 - 5*m**4/6 + 25*m**3/3 + 3*m**2. Factor z(i).
2*(i - 5)**2
Let t(u) be the second derivative of u**5/30 - u**4/18 - 2*u**3/9 - 11*u. Factor t(c).
2*c*(c - 2)*(c + 1)/3
Let f be ((8/9)/4)/((-10)/(-15)). Factor 0 + 2/3*i**2 + f*i.
i*(2*i + 1)/3
Determine f, given that 20*f**4 + 28*f**3 - 6*f**2 + 2*f**2 - 16 + 8*f - 15*f + 4*f**5 - 25*f = 0.
-2, -1, 1
Factor -1 + i**2 + 8/3*i.
(i + 3)*(3*i - 1)/3
Factor 15/8*k + 9/8*k**2 - 3/4.
3*(k + 2)*(3*k - 1)/8
Suppose 4*i = 75 - 71. Let c(f) be the first derivative of -i + 1/6*f**4 + 0*f**2 + 0*f**3 + 0*f. Determine z, given that c(z) = 0.
0
Let l(t) = 2*t**3 - 2*t**2 - 4*t - 1. Let y(u) = 1. Let g(f) = -l(f) - y(f). Factor g(q).
-2*q*(q - 2)*(q + 1)
Let v(j) be the first derivative of 64*j**3/3 + 40*j**2 + 25*j + 51. Factor v(p).
(8*p + 5)**2
Let a(j) be the first derivative of -3*j + 3 - 1/4*j**3 - 3/2*j**2. Factor a(b).
-3*(b + 2)**2/4
Let r(n) be the third derivative of -7*n**5/270 + n**4/12 - 2*n**3/27 + 6*n**2. Factor r(b).
-2*(b - 1)*(7*b - 2)/9
Suppose 2*w = -4*w. Let s(v) be the second derivative of w*v**3 - 1/7*v**2 + v + 1/42*v**4 + 0. Factor s(z).
2*(z - 1)*(z + 1)/7
Let n(g) = -g**3 - 7*g**2. Let u(t) = -t**2 + t - 1. Let f be u(3). Let m be n(f). Factor 1/4 - 1/2*h**2 + m*h**3 + 1/4*h**4 + 0*h.
(h - 1)**2*(h + 1)**2/4
Let c(f) = -f**3 - 13*f**2 + 10*f - 53. Let p be c(-14). Factor 0*a**p + 1/3*a**2 - 1/3*a**4 + 0 + 0*a.
-a**2*(a - 1)*(a + 1)/3
Factor -2/3*b**4 + 2/3*b**2 + 0 + 2/3*b - 2/3*b**3.
-2*b*(b - 1)*(b + 1)**2/3
Let h = 27/119 - -1/17. What is r in 0 - h*r**2 + 2/7*r**3 + 0*r = 0?
0, 1
Let c be -2 + 6 - (-3 - -3). Let u = 6 - c. Find k such that 2*k**2 + u*k + 2/3 + 2/3*k**3 = 0.
-1
Determine q, given that -32*q - 14 + 4*q**2 - 60 + 102 = 0.
1, 7
Determine j so that 1/2*j + 1/4*j**4 - 1/2*j**3 + 0*j**2 - 1/4 = 0.
-1, 1
Let b(p) = -p + 7. Let f be b(5). Let s(l) be the third derivative of 2/3*l**3 + 0 - l**f + 1/10*l**5 + 5/12*l**4 + 0*l. Determine x, given that s(x) = 0.
-1, -2/3
Let j(o) = -o**3 + o. Let l(i) = 12*i**3 + 6*i**2 - 6*i. Let m(n) = -3*j(n) - l(n). Determine c so that m(c) = 0.
-1, 0, 1/3
Suppose 0 = -3*y + 4*y + m, 2*y + 4*m - 10 = 0. Let l(q) = -q**2 - 5*q + 2. Let b be l(y). Suppose p**2 + 3*p**b - 2*p**2 + p - p**2 = 0. What is p?
-1, 0
Factor -2/5*h**3 + 0 + 8/15*h + 0*h**2 + 2/15*h**4.
2*h*(h - 2)**2*(h + 1)/15
Let w be 90/25 + 12/30. Suppose 3/4*k**w - 3/2*k + 0*k**3 - 9/4*k**2 + 0 = 0. What is k?
-1, 0, 2
Let x(d) = -21*d**2 + 17*d - 1. Let f = 30 - 21. Suppose 2*c - 5 = f. Let r(l) = -31*l**2 + 25*l - 1. Let h(k) = c*x(k) - 5*r(k). Suppose h(g) = 0. What is g?
-1/4, 1
Let a(n) = 31*n**3 - 16*n**2 + 85*n**2 + 6 + 5 + 80*n. Let r(y) = 6*y**3 + 14*y**2 + 16*y + 2. Let z(x) = 2*a(x) - 11*r(x). Factor z(w).
-4*w*(w + 2)**2
Let m(a) be the second derivative of -a**5/270 + a**3/27 - a**2 + 2*a. Let k(v) be the first derivative of m(v). Suppose k(s) = 0. What is s?
-1, 1
Find r, given that -16/3 - 1/3*r**2 + 8/3*r = 0.
4
Let w(h) = -13*h**2 - 5*h - 9. Let c(o) = 3*o**2 + o + 2. Let n(j) = -18*c(j) - 4*w(j). Suppose n(s) = 0. What is s?
0, 1
Let w(u) be the third derivative of u**7/1155 - u**6/110 + 13*u**5/330 - u**4/11 + 4*u**3/33 + 4*u**2. Solve w(j) = 0.
1, 2
Let q(t) be the third derivative of 1/210*t**7 + 0 + 0*t**3 - 5*t**2 + 0*t - 1/72*t**6 + 1/112*t**8 + 1/180*t**5 + 0*t**4. Let q(h) = 0. Calculate h.
-1, 0, 1/3
Let w(p) be the first derivative of 2*p**5/5 - 3*p**4 + 26*p**3/3 - 12*p**2 + 8*p + 12. Let w(m) = 0. What is m?
1, 2
Factor -2/9*o**2 + 0*o + 2/9*o**4 + 0 + 0*o**3.
2*o**2*(o - 1)*(o + 1)/9
Let v(f) = -f - 9. Let d(c) = -3*c**2 + 2*c - 3. Let a be d(2). Let y be v(a). Factor 2*q - 2*q**3 - 19*q**2 + 19*q**y.
-2*q*(q - 1)*(q + 1)
Let o(p) be the third derivative of 9/35*p**7 + 9/112*p**8 + 0*p + 0*p**3 + 3/10*p**6 + 0 + 1/24*p**4 - 5*p**2 + 1/6*p**5. Suppose o(v) = 0. What is v?
-1, -1/3, 0
Let w = 59 + -59. Suppose 0 + 0*u**3 + 1/2*u**4 + w*u**2 + 0*u + 1/2*u**5 = 0. Calculate u.
-1, 0
Let z(h) be the third derivative of h**6/200 - h**5/100 - h**4/20 - 14*h**2. Factor z(o).
3*o*(o - 2)*(o + 1)/5
Let a(l) be the first derivative of l**6/9 - l**4/2 - 4*l**3/9 - 9. Factor a(d).
2*d**2*(d - 2)*(d + 1)**2/3
Let x(k) = 9*k**2. Let l be x(-1). Let -2*f**3 - 6 + 0*f**3 - 2*f**3 + f**3 + l*f = 0. Calculate f.
-2, 1
Factor -1/6*z**5 + 7/6 + 1/2*z**4 + 19/3*z**2 + 9/2*z + 11/3*z**3.
-(z - 7)*(z + 1)**4/6
Let w(x) be the third derivative of 3*x**6/80 - x**5/4 + x**4/4 + 2*x**3 + 13*x**2. Factor w(m).
3*(m - 2)**2*(3*m + 2)/2
Factor 0*p + 2/3*p**4 - 2/3*p**3 + 0 + 0*p**2.
2*p**3*(p - 1)/3
Let c(l) be the first derivative of 2*l**6/3 + 2*l**5/5 - 23*l**4/16 - 7*l**3/12 + 7*l**2/8 - l/4 - 11. Let c(y) = 0. What is y?
-1, 1/4, 1
Let f(o) = 5*o**3 + 47*o**2 - 88*o + 50. Let l(q) = -5*q**3 - 46*q**2 + 89*q - 50. Let w(t) = 6*f(t) + 7*l(t). Factor w(j).
-5*(j - 1)**2*(j + 10)
Let s(a) be the first derivative of a**5/330 - a**4/132 + 3*a**2/2 - 3. Let z(x) be the second derivative of s(x). Find h, given that z(h) = 0.
0, 1
Let z(s) be the second derivative of s**7/42 - 2*s**6/15 + 3*s**5/10 - s**4/3 + s**3/6 + 6*s. Factor z(x).
x*(x - 1)**4
Suppose -a = -2*c - 0*c - 11, c = -a - 1. Let y = c + 6. Factor -1/4*u**y - u - 1.
-(u + 2)**2/4
Let o(q) be the secon