q**2*(q + 1)**2/7
Let l be (-8)/(-5)*10/4. Suppose 0 = 2*a + 4*o + 7 - 31, l*a + o = 13. Let c**a + 0*c + c + 0*c = 0. Calculate c.
-1, 0
Let d = 2 - 0. Let y be -2 + d/2 + 3. Determine z so that z**2 - y*z + 2*z**3 - 5*z**2 + 4*z = 0.
0, 1
Let o(v) be the second derivative of -v**6/80 - 3*v**5/160 + v**4/32 + v**3/16 - 10*v. Suppose o(k) = 0. What is k?
-1, 0, 1
Suppose 4*r + 38 = 3*j, -3*r + 4*r = -5*j + 25. Suppose v = -1 + j. Factor 1/2*g**3 - 1/4*g**v + 0*g**2 + 0 + 0*g**4 - 1/4*g.
-g*(g - 1)**2*(g + 1)**2/4
Let r(p) = -2*p**4 + p**3 + 6*p**2 + 7*p + 4. Let b(m) = m**4 + m**3 - m - 1. Let t(u) = 6*b(u) + 2*r(u). Factor t(g).
2*(g + 1)**4
Suppose -10 = 6*k - k. Let d(w) = -4*w**2 - 3*w + 2. Let p(s) = s**2 + 1. Let a(x) = k*p(x) + d(x). Solve a(m) = 0 for m.
-1/2, 0
Let g(c) be the first derivative of 2*c**3/27 - 2*c**2/9 + 2*c/9 + 5. Solve g(t) = 0.
1
Suppose -p - 5 = -10. Suppose 13 - p = 4*f. Solve -2/11*c**f + 0 + 0*c**3 + 2/11*c**4 + 0*c = 0.
-1, 0, 1
Factor 0 + 7/5*p**3 - 3/5*p - 2/5*p**2 - 2/5*p**4.
-p*(p - 3)*(p - 1)*(2*p + 1)/5
Let r(h) be the second derivative of 3*h**5/40 - h**3/4 - 6*h. Factor r(y).
3*y*(y - 1)*(y + 1)/2
Let q(o) be the first derivative of 2 + 2/15*o**5 + 5/12*o**4 - 1/3*o + 1/3*o**3 - 1/6*o**2. Let q(w) = 0. Calculate w.
-1, 1/2
Let j(v) be the first derivative of 1/30*v**4 - 2 + 2/15*v**3 - v + 0*v**2. Let p(k) be the first derivative of j(k). Factor p(z).
2*z*(z + 2)/5
Let b(u) be the first derivative of u**6/720 - u**4/144 + u**2/2 + 4. Let t(x) be the second derivative of b(x). Factor t(p).
p*(p - 1)*(p + 1)/6
Suppose -y - 2*y - 1455 = 0. Let g = y + 3403/7. Factor -8/7*i**4 + 20/7*i**2 - 2/7*i**5 - 2/7*i**3 - 16/7 + g*i.
-2*(i - 1)**2*(i + 2)**3/7
Let j = -31/21 + 15/7. Let m(i) be the second derivative of -1/6*i**4 + 0 + 2*i - i**2 - j*i**3. Suppose m(v) = 0. What is v?
-1
Let h be (-1 + 9/(-12))*(-4)/14. Let b(y) be the first derivative of 0*y**5 - 2*y**3 + 4 + 9/4*y**4 - h*y**6 + 0*y**2 + 0*y. Factor b(q).
-3*q**2*(q - 1)**2*(q + 2)
Let f(w) be the first derivative of -w**4/16 + w**3/12 + w**2/4 + 6. Factor f(k).
-k*(k - 2)*(k + 1)/4
Let b(m) be the second derivative of 0 + 1/54*m**4 + 1/9*m**2 + m + 2/27*m**3. Suppose b(o) = 0. What is o?
-1
Factor -2/15*x**2 - 8/15 - 8/15*x.
-2*(x + 2)**2/15
Let l(p) be the second derivative of -p**7/168 - p**6/30 - p**5/40 + p**4/12 + p**3/8 - 38*p. Let l(n) = 0. Calculate n.
-3, -1, 0, 1
Let d(c) = 8*c - 45. Let y be d(6). Factor 0*r + 0 - 2/9*r**2 + 2/9*r**y.
2*r**2*(r - 1)/9
Factor 0 - 1/4*b**4 + 0*b - 1/2*b**3 - 1/4*b**2.
-b**2*(b + 1)**2/4
Let j = 5 - 3. Suppose -26*q = -24*q. Factor 1/2*x**j + x + q.
x*(x + 2)/2
Let h(i) = i**3 - 12*i**2 - 44*i - 13. Let f be h(15). Solve k**3 + 2/3*k**f + 0*k + 1/3*k**4 + 0 = 0 for k.
-2, -1, 0
Let d(r) = -r**3 - 8*r**2 + 6. Let s be d(-8). Let 4*u - s*u - 2*u**4 + 2*u**2 + 3*u**3 + 0*u**3 - u**3 = 0. Calculate u.
-1, 0, 1
Suppose 4*s - 3*s = 0. Let o(t) be the third derivative of -2*t**2 + 0*t**4 + 0 - 1/120*t**5 + 0*t + s*t**3 - 1/240*t**6. Factor o(n).
-n**2*(n + 1)/2
Suppose -u = -0 - 2. Factor 12*i**u + 3*i - 3*i**4 - 17*i**2 - 7*i**3 - 3*i - i.
-i*(i + 1)**2*(3*i + 1)
Suppose -5*r = 5*a - 8 - 7, 4*a = -2*r - 2. Let f(g) be the second derivative of 3*g + 1/3*g**6 + g**2 + 1/7*g**r - 1/5*g**5 + 0 - g**4 - 1/3*g**3. Factor f(q).
2*(q - 1)*(q + 1)**3*(3*q - 1)
Let i(m) = -5*m**3 + 16*m**2 + m - 6. Let f(c) = 5*c**3 - 15*c**2 + 5. Let b(q) = -6*f(q) - 5*i(q). Factor b(a).
-5*a*(a - 1)**2
Let q(c) = c**2 - 5 + 2*c**2 - c**2 - 2. Let g(o) = -3*o**2 + 11. Let h(k) = -9*k + 1. Let m be h(1). Let i(s) = m*q(s) - 5*g(s). Factor i(r).
-(r - 1)*(r + 1)
Let k be (-1 - (-3 + 2))/(-2). Suppose 2*n + 3*m + 1 = -k*n, -4*m = 4*n. Let 7/2*w - n + 9/2*w**2 = 0. Calculate w.
-1, 2/9
Let s(d) = d**2 + 2*d + 1. Let z be s(-2). Let 0*m**4 - 2*m**2 + 5*m**4 - 1 + z - 3*m**3 = 0. What is m?
-2/5, 0, 1
Let -45*i**2 - 7*i**3 - 120*i - 36 - 44 - 5*i**3 + 7*i**3 = 0. What is i?
-4, -1
Let c = 251/3 - 83. Factor 0*f**4 + 0 + 2/3*f**5 + 0*f + 0*f**2 - c*f**3.
2*f**3*(f - 1)*(f + 1)/3
Let a(z) = -12*z**3 - 12*z**2 - 2*z + 2. Suppose 4 = 4*x - 4. Let y(d) = -25*d**3 - 23*d**2 - 3*d + 5. Let r(v) = x*y(v) - 5*a(v). Let r(c) = 0. Calculate c.
-1, -2/5, 0
Suppose -q + 5*q - 8 = 0. Let s be (4 - q)*6/4. Factor -5*j - 2*j**2 + j + 1 - s.
-2*(j + 1)**2
Let l(m) be the second derivative of -m**6/240 + m**5/40 - m**3/3 + 3*m**2/2 - m. Let a(c) be the first derivative of l(c). Factor a(h).
-(h - 2)**2*(h + 1)/2
Let r(q) be the second derivative of -q**6/135 - q**5/15 - 13*q**4/54 - 4*q**3/9 - 4*q**2/9 + 7*q. Let r(n) = 0. What is n?
-2, -1
Let h be 75/126 + (-3 - 5/(-2)). Let w(s) be the second derivative of -1/7*s**2 - 1/42*s**4 + h*s**3 - 2*s + 0. Determine m, given that w(m) = 0.
1
Let n(a) = -a - 1. Let j be n(-7). Let d = 12 - j. Find w, given that -2*w**3 + 6*w**3 - 4*w**2 + 2*w**5 + 6*w**4 - d*w + 0*w**4 - 2 = 0.
-1, 1
Suppose 0 = t - 6*t + 15. Suppose 0 = -w + 2*w - 2, -q - t*w = -8. What is b in -6*b**2 + 10*b - 2*b**2 + 4 + 2*b**q = 0?
-1/3, 2
Suppose -2*s - 84 = 2*s. Let v be (-4)/6 + (-20)/s. Factor 2/7*t**3 - v*t**2 - 4/7*t + 0.
2*t*(t - 2)*(t + 1)/7
Let s = -39/5 + 161/20. Determine x, given that 0 - 1/2*x - s*x**2 = 0.
-2, 0
Let z be 7/(-21) + 2/6. Let r(q) be the first derivative of 0*q + 1/16*q**4 + z*q**2 - 1/24*q**6 + 1/12*q**3 - 1 - 1/20*q**5. What is k in r(k) = 0?
-1, 0, 1
Let s(q) be the first derivative of 3*q**4/16 - 3*q**3/4 + 9*q**2/8 - 3*q/4 - 19. Solve s(j) = 0 for j.
1
Let n(o) be the third derivative of o**5/15 - 7*o**4/6 - 16*o**3/3 + 18*o**2. Factor n(k).
4*(k - 8)*(k + 1)
Let q(p) be the first derivative of -4*p**3/3 - 6*p**2 - 8*p + 6. Let q(j) = 0. What is j?
-2, -1
Let a be 351/(-416)*4/(-3) - 1. Factor 0 + a*l**2 + 1/8*l.
l*(l + 1)/8
Factor 2/5*w + 0 + 0*w**4 + 0*w**2 + 2/5*w**5 - 4/5*w**3.
2*w*(w - 1)**2*(w + 1)**2/5
Let i(k) be the third derivative of -k**5/40 - k**4/8 - 26*k**2. Suppose i(g) = 0. What is g?
-2, 0
Suppose -c - 4 = -2*c. Let n(v) be the first derivative of 2 + 2/5*v - 2/15*v**3 - 1/5*v**2 + 1/10*v**c. Determine f, given that n(f) = 0.
-1, 1
Let p(r) be the third derivative of 0*r + 3*r**2 + 0 + 0*r**4 - 1/3*r**3 + 1/30*r**5. Determine y so that p(y) = 0.
-1, 1
Factor 0 + 9/5*b**2 + 3/5*b**4 - 12/5*b**3 + 0*b.
3*b**2*(b - 3)*(b - 1)/5
Let a(f) be the second derivative of f**9/10080 + f**8/1920 + f**7/2520 + f**4/12 + 2*f. Let c(p) be the third derivative of a(p). Factor c(v).
v**2*(v + 2)*(3*v + 1)/2
Let n(w) = -8*w**3 + w**3 - 5*w**2 + 3 - 2*w - 4*w + 3. Let s(p) = 20*p**3 + 14*p**2 + 17*p - 17. Let i(g) = 17*n(g) + 6*s(g). Factor i(d).
d**2*(d - 1)
Factor -4*a**2 + 2*a**2 + a - a**3 - 2*a + 0*a.
-a*(a + 1)**2
Let u = -104/3 - -347/10. Let q(j) be the third derivative of -13/150*j**5 + 1/15*j**6 + u*j**4 + 3*j**2 + 0*j + 0*j**3 + 0 - 3/175*j**7. Factor q(w).
-2*w*(w - 1)**2*(9*w - 2)/5
Let h be 1905/2520 + (-6)/8. Let v(n) be the third derivative of 0*n**5 + 0 + 0*n**6 - 1/105*n**7 + n**2 + 0*n**4 + 0*n**3 + 0*n + h*n**8. Factor v(t).
2*t**4*(t - 1)
Let r(z) be the third derivative of 13*z**6/24 + 49*z**5/60 - 5*z**4/6 - 2*z**3/3 + 8*z**2. Suppose r(m) = 0. Calculate m.
-1, -2/13, 2/5
Let a be (-13)/(-7) - 2/(-14). Factor -b**2 - 3*b**2 - 2*b + 1 - 2 + 3*b**a.
-(b + 1)**2
Let f(t) be the second derivative of -t**6/375 + t**4/150 + 6*t - 3. Determine j so that f(j) = 0.
-1, 0, 1
Suppose -25 = -6*d + d. Factor u - 2*u**2 + 0*u - d*u.
-2*u*(u + 2)
Let 1/3*j**3 + 3 + j - 5/3*j**2 = 0. Calculate j.
-1, 3
Suppose 0 = -0*k + 6*k - 12. Let d(g) be the first derivative of -g**3 + 3/2*g**2 + k + 0*g. Factor d(l).
-3*l*(l - 1)
Let h be 22/(-24) - (6 - 7). Let g(w) be the first derivative of -h*w**3 - 1/4*w - 1 - 1/4*w**2. Factor g(i).
-(i + 1)**2/4
Let q(b) = -5*b**3 - 4*b**2 - b + 7. Let p(c) = 14*c**3 + 12*c**2 + 2*c - 20. Let h(n) = 3*p(n) + 8*q(n). Find l, given that h(l) = 0.
-2, -1, 1
Let n(p) = -p**2 - 10*p - 7. Let u be n(-9). Let d be (0 + u + -2)/1. Factor 0 + d*m - 1/2*m**3 + 1/4*m**4 + 1/4*m**2.
m**2*(m - 1)**2/4
Determine d so that 0*d**2 - 1/5*d + 0 + 1/5*d**3 = 0.
-1, 0, 1
Let t be (0/2)/(-3 + 4). Let a(m) be the third derivative of -1/60*m**6 + 0*m + 1/24*m**4 + t*m**5 + 0*m**7 + 0*m**3 + 1/336*m**