 0.
-q**2*(q - 1)**2/4
Let o(b) be the third derivative of -b**6/540 + b**5/135 - b**4/108 - 2*b**2. Suppose o(r) = 0. Calculate r.
0, 1
Let u be 1 + -4 + (3 - 0). What is y in -y**5 + u*y**4 - 21*y**3 + 18*y**4 - 3*y - 18*y**2 + 25*y**5 = 0?
-1, -1/2, -1/4, 0, 1
Let t = -6026347/29148 + -1/14574. Let f = -202 - t. Factor -1/2*h + 15/4*h**3 - f*h**4 + 7/4*h**5 - 1/4*h**2 + 0.
h*(h - 1)**3*(7*h + 2)/4
Suppose -4*u = -u - 12. Suppose u = -f + 6. Determine c, given that 4*c + f*c**2 - 2*c**2 - 2*c**2 = 0.
0, 2
Let v(k) = -3*k**3 - k**2 - 16*k - 15. Let s be v(-1). Factor 2/7*q**4 + 2/7*q**5 + 0*q + 0 - 2/7*q**s - 2/7*q**2.
2*q**2*(q - 1)*(q + 1)**2/7
Let d(f) = -3*f**2 + 2*f - 3. Let k(c) = 2*c**2 - 2*c + 2. Let o(z) = -3*d(z) - 4*k(z). Factor o(q).
(q + 1)**2
Suppose 0 = 5*w - 0*g + 2*g + 23, 2*g = 3*w + 1. Let r be 7/2 + 1*w. Factor -8*v**3 - r - 12*v**2 - 9/2*v.
-(v + 1)*(4*v + 1)**2/2
Let k(u) be the third derivative of -7/48*u**4 + 2*u**2 - 1/96*u**8 - 1/6*u**3 + 0*u + 0 + 1/30*u**5 - 1/210*u**7 + 7/120*u**6. Let k(c) = 0. What is c?
-1, -2/7, 1
Let m(c) be the second derivative of -4*c + 0*c**2 - 2/21*c**3 - 1/70*c**5 - 1/14*c**4 + 0. Solve m(x) = 0 for x.
-2, -1, 0
Let l(b) be the first derivative of -b**6 - 14*b**5/5 - 5*b**4/2 - 2*b**3/3 + 8. Solve l(q) = 0.
-1, -1/3, 0
Let j(s) be the second derivative of s**6/10 - 27*s**5/40 + 7*s**4/4 - 9*s**3/4 + 3*s**2/2 - 13*s. Let j(o) = 0. What is o?
1/2, 1, 2
Let l(f) = 7*f**3 - 11*f**2 + 9*f + 3. Let w(i) = -20*i**3 + 32*i**2 - 26*i - 10. Let b(n) = 17*l(n) + 6*w(n). Factor b(x).
-(x - 3)**2*(x + 1)
Let l(g) be the third derivative of -g**6/60 + g**5/6 - 7*g**4/12 + g**3 + 10*g**2 - 2*g. Factor l(w).
-2*(w - 3)*(w - 1)**2
Let z(n) = 5*n**2 + 10*n + 2. Let t = 3 + 0. Let q(w) = 10*w**2 + 21*w + 4. Let x(p) = t*q(p) - 7*z(p). Factor x(o).
-(o + 1)*(5*o + 2)
Suppose 9/5*v**4 - 1/5*v**5 + 0*v + 16/5*v**2 - 24/5*v**3 + 0 = 0. Calculate v.
0, 1, 4
Let q be (-4)/(-5)*(-30)/4. Let i be 2/15 + q/(-9). Factor -2/5*u**3 + i*u**2 + 2/5*u - 4/5.
-2*(u - 2)*(u - 1)*(u + 1)/5
Let n(k) = k**2 - 10*k + 2. Suppose 0 = 2*a - 3*z - 13 - 19, -a - z + 6 = 0. Let l be n(a). Determine j, given that -1/4*j**l - 9/4 - 3/2*j = 0.
-3
Let r(b) be the third derivative of b**5/60 - b**3/6 - b**2. Find m such that r(m) = 0.
-1, 1
Let n = 74 + -72. Let y(k) be the second derivative of 0 + k**3 + 7/40*k**6 + 27/40*k**5 - 4*k + 5/4*k**4 + 1/56*k**7 + 0*k**n. What is u in y(u) = 0?
-2, -1, 0
Let b(c) be the third derivative of -5*c**5/12 + 5*c**4/4 - 3*c**3/2 - 5*c**2. Suppose b(v) = 0. Calculate v.
3/5
Let v(n) be the second derivative of -n**6/35 - n**5/7 - 2*n**4/7 - 2*n**3/7 - n**2/7 - 3*n. Factor v(r).
-2*(r + 1)**3*(3*r + 1)/7
Let z(a) be the third derivative of -5*a**8/1512 + 8*a**7/945 - a**6/540 - a**5/135 + 7*a**2. Suppose z(w) = 0. What is w?
-2/5, 0, 1
Suppose -3*o - 6*o + 2*o**2 - 11*o**2 + 3*o = 0. What is o?
-2/3, 0
Solve 3/4 - 3/4*k**4 + 3/2*k + 0*k**2 - 3/2*k**3 = 0.
-1, 1
Let k = 80 + -78. Let f(p) be the first derivative of k + 2/5*p + 0*p**3 - 1/5*p**4 + 2/5*p**2 - 2/25*p**5. Suppose f(t) = 0. Calculate t.
-1, 1
Let i(j) be the first derivative of 0*j + 0*j**3 + 1/150*j**5 - 1/2*j**2 + 0*j**4 - 1. Let b(k) be the second derivative of i(k). Solve b(v) = 0.
0
Let h(u) be the second derivative of 5*u**4/8 + u**3/6 + 23*u. Suppose h(g) = 0. Calculate g.
-2/15, 0
Factor k - 1/5*k**2 - 3/5 - 1/5*k**3.
-(k - 1)**2*(k + 3)/5
Let v(t) = -4*t**2 + 5*t. Let u(d) be the third derivative of -d**5/20 + d**4/6 - 2*d**2. Let p(s) = 5*u(s) - 4*v(s). Factor p(r).
r**2
Suppose 27*d - 33*d = 0. Factor d - 6/5*q**3 + 2/5*q**4 + 4/5*q**2 + 0*q.
2*q**2*(q - 2)*(q - 1)/5
Factor 0*w - 2/9*w**2 + 0.
-2*w**2/9
Let c(p) be the first derivative of -4/15*p**3 - 2 + 1/15*p**4 + 0*p + p**2 - 1/150*p**5. Let u(w) be the second derivative of c(w). Let u(f) = 0. What is f?
2
Let h(l) be the third derivative of -l**5/300 - l**4/12 - 5*l**3/6 - 9*l**2. What is z in h(z) = 0?
-5
Let a(h) be the second derivative of h**6/180 - h**5/90 - h**4/36 + h**3/3 - 5*h. Let g(j) be the second derivative of a(j). Factor g(x).
2*(x - 1)*(3*x + 1)/3
Let u(j) be the first derivative of -686*j**5/5 - 49*j**4/2 + 140*j**3 - 76*j**2 + 16*j + 6. Find s such that u(s) = 0.
-1, 2/7
Let r(h) be the first derivative of -h**5/20 + h**4/8 + h**3/12 - h**2/4 + 2. Suppose r(n) = 0. Calculate n.
-1, 0, 1, 2
Let i(p) = -47*p**3 + 57*p**2 + 72*p + 16. Let y(z) = -93*z**3 + 113*z**2 + 144*z + 32. Let l(k) = -14*i(k) + 6*y(k). Factor l(s).
4*(s - 2)*(5*s + 2)**2
Let s(t) = 2*t**5 - 2*t**3 - 3*t. Let l(x) = 2*x**2 - 2*x - 2. Let m be l(2). Let y(p) = p**5 + p**4 - p. Let q(v) = m*s(v) - 6*y(v). Factor q(o).
-2*o**3*(o + 1)*(o + 2)
Let j(w) be the second derivative of 4*w + 1/60*w**6 + 1/20*w**5 + 1/4*w**2 + 0 - 1/12*w**4 - 1/84*w**7 - 1/12*w**3. Factor j(v).
-(v - 1)**3*(v + 1)**2/2
Let p(x) be the second derivative of 0*x**2 + 1/60*x**6 + 1/24*x**3 + 1/12*x**4 + 0 + x + 1/16*x**5. What is c in p(c) = 0?
-1, -1/2, 0
Let d(z) be the third derivative of -z**8/336 + z**7/42 - z**6/20 - z**5/30 + 7*z**4/24 - z**3/2 - 4*z**2. Let d(w) = 0. Calculate w.
-1, 1, 3
Suppose 2*j = 13 + 1. Suppose -2*g + j = -3, -2 = z - g. Let 26*i + 16*i**5 - 6*i**5 - 3 - 1 - 64*i**2 + 76*i**z - 44*i**4 = 0. What is i?
2/5, 1
Determine v, given that 2*v - 3/2*v**3 - 2*v**2 + 0 - 1/2*v**5 + 2*v**4 = 0.
-1, 0, 1, 2
Let m = 36 - 69/2. Let a be (35/(-2))/5 - -4. Factor -a*q**4 + q + 0 + 0*q**3 + m*q**2.
-q*(q - 2)*(q + 1)**2/2
Let r(x) be the second derivative of 10*x**6/9 - 14*x**5/3 + 23*x**4/3 - 56*x**3/9 + 8*x**2/3 + 28*x. Factor r(d).
4*(d - 1)**2*(5*d - 2)**2/3
Factor -18*y**2 - 18*y**4 + 6*y**4 + 3*y**5 - 6*y**5 + 33*y**3.
-3*y**2*(y - 1)**2*(y + 6)
Suppose -4 = -3*l + l. Solve s**l + 0 - 3*s - 4*s**2 + 6 = 0.
-2, 1
Let q(i) be the third derivative of i**6/540 + i**5/270 - 5*i**4/108 + i**3/9 + 21*i**2. Factor q(p).
2*(p - 1)**2*(p + 3)/9
Let 6*o**3 + 3*o**4 - 5*o**5 - 6*o**5 - 8*o**2 - 9*o**5 + 19*o**5 = 0. Calculate o.
-2, 0, 1, 4
Let p(k) be the second derivative of 1/4*k**4 - 3*k**3 + 27/2*k**2 + 2*k + 0. Let p(r) = 0. What is r?
3
Let t be (8/(-12) + (-10)/(-15))/3. Let r = -19/2 + 10. Find b such that 0 + t*b - r*b**2 = 0.
0
Let d(z) be the third derivative of -10*z**2 + 1/84*z**8 + 4/3*z**4 + 8/3*z**3 + 0*z - 2/105*z**7 + 1/15*z**5 - 1/6*z**6 + 0. Factor d(u).
4*(u - 2)**2*(u + 1)**3
Suppose 0 + 1/9*h**4 + 1/9*h**2 + 0*h - 2/9*h**3 = 0. Calculate h.
0, 1
Let o(v) = 12*v - 3*v - v**4 - 14*v**4 - 3*v**3. Let i(l) = 7*l**4 + l**3 - 4*l. Let b(m) = 9*i(m) + 4*o(m). Factor b(a).
3*a**3*(a - 1)
Let n(m) be the first derivative of -2 - 1/20*m**4 + 2/5*m**2 + 0*m**3 + 0*m. Factor n(a).
-a*(a - 2)*(a + 2)/5
Suppose 0 = -2*u - u. Let b be u/(-1) + 0 - -3. Let t - 4*t**2 - t + t**b + 3*t**2 = 0. Calculate t.
0, 1
Suppose 5*x = -5*o + 3*x + 185, 3*x = -15. What is m in -m**2 + 39 - o - m = 0?
-1, 0
Let t = -67 + 269/4. Factor -t*g**2 - 1/2*g + 0.
-g*(g + 2)/4
Factor -9/4*z + 0 + 3/4*z**2.
3*z*(z - 3)/4
Suppose 2 = 2*r + 12. Let x(k) = -5*k**4 - 3*k**3 + 3*k**2 + 3*k - 2. Let y(l) = -5*l**4 - 3*l**3 + 2*l**2 + 3*l - 2. Let a(q) = r*x(q) + 4*y(q). Factor a(i).
(i - 1)*(i + 1)**2*(5*i - 2)
Suppose -3*m**3 + 4*m - 3*m + 3*m**4 - 1443*m**2 + 1434*m**2 + 6 + 2*m = 0. What is m?
-1, 1, 2
Let y = 2 + 0. Find i such that -6*i**3 + 6*i**4 + 4*i**4 - 3*i**5 - i**4 + 11*i - 3 - y*i - 6*i**2 = 0.
-1, 1
Let b(w) be the first derivative of -1/6*w**3 + 1/16*w**4 - 2 + 0*w**2 + 0*w. Solve b(p) = 0 for p.
0, 2
Solve 2/5*v**3 + 0 + 1/5*v**5 + 0*v**2 - 3/5*v**4 + 0*v = 0 for v.
0, 1, 2
Let u be 20/6 + 6/(-3 - -1). Factor 0 + u*a + 1/3*a**2.
a*(a + 1)/3
Let i(n) = 13*n**2 - 13*n - 21. Let s(m) = 7*m**2 - 7*m - 11. Let z(g) = 3*i(g) - 5*s(g). Solve z(c) = 0.
-1, 2
Let d be 4664/154 - 2/7. Let p = d + -51/2. Solve 0 + 0*r**2 + 6*r**3 + p*r**5 - 12*r**4 + 0*r = 0.
0, 2/3, 2
Let z(w) = -20*w**2 - 7*w. Let h(j) = 20*j**2 + 8*j. Let u(y) = -3*h(y) - 4*z(y). Factor u(f).
4*f*(5*f + 1)
Let z be (-2)/(-9) + (-76)/18. Let m(w) = w**2 + 2*w - 5. Let p be m(z). Factor -5*u**p + 1/2 - 5/2*u + 5*u**2 - 1/2*u**5 + 5/2*u**4.
-(u - 1)**5/2
Let r = -5 + 5. Solve -3*f - f**2 + r*f + 2*f = 0 for f.
-1, 0
Let b(a) = -2*a**2 + 3*a - 1. Let z(o) 