 1/2*w**3 + 0*w - 1/4*w**4 + 1/4*w**5 = 0.
-1, 0, 2
Suppose 3*d - 9 = -3. Suppose -3*i + d*i - 2 = 0, 2*i = -2*w. Solve -4/3*h**w + h + 1/3 = 0.
-1/4, 1
Let w(q) be the first derivative of -2/9*q**3 - 3 - 1/12*q**4 + 2/15*q**5 + 0*q + 1/18*q**6 + 0*q**2. Factor w(t).
t**2*(t - 1)*(t + 1)*(t + 2)/3
Suppose 3*t - 8 = -t. Let w = -1164/11 - -106. Factor -2/11*r**t - 2/11*r + 2/11*r**3 + 0 + w*r**4.
2*r*(r - 1)*(r + 1)**2/11
Let t = 2 + 4. Let l be 65/15 + (-2)/t. Find p such that -2*p**5 + p**4 - 2*p**5 - 2*p**l = 0.
-1/4, 0
Let o = 16 - 11. Suppose 0 = -6*h + o + 19. Factor 0*q**2 + 1/3*q**5 - 1/3*q**h + 0*q**3 + 0*q + 0.
q**4*(q - 1)/3
Let o(j) be the third derivative of -j**7/7560 - j**6/540 - j**5/90 - j**4/6 + 3*j**2. Let k(n) be the second derivative of o(n). Let k(w) = 0. What is w?
-2
Let p be 2/(-2)*(-10 - -14)*-1. Let 2/9*m**3 - 2/9*m**5 - 4/9*m**2 + 0 + 0*m + 4/9*m**p = 0. Calculate m.
-1, 0, 1, 2
Let k = -50 + 52. Factor -2/3*s**3 + 0 + 0*s + 0*s**k.
-2*s**3/3
Let u(x) be the third derivative of -x**8/504 + x**7/315 + x**6/180 - x**5/90 - 11*x**2. What is t in u(t) = 0?
-1, 0, 1
Let g be 2/7 - 12/(-7). What is m in 2 - 2 + m**2 + 2*m + m**g = 0?
-1, 0
Let g be 1/(2/2)*-3. Let m be g/2 + 38/20. Factor m - 2/5*n**2 - 2/5*n + 2/5*n**3.
2*(n - 1)**2*(n + 1)/5
Suppose 3*r - 16 = -r. Suppose x + r*l = -3*x, 5*x - 3*l = 0. Factor 0*j + x*j**2 + 1/2*j**3 + 0.
j**3/2
Let i(t) = t + 10. Let c(x) = x**3 - 4*x**2 - 5*x - 7. Let s be c(5). Let j be i(s). Factor -3*o**3 + o**2 + 7*o**j + o**3.
o**2*(5*o + 1)
Find p, given that -1/2*p**5 - 8*p + 12*p**2 - 3*p**4 - 1/2*p**3 + 0 = 0.
-4, 0, 1
Suppose 0 = -8*z - 129 + 169. Find v, given that -1/3 + 1/3*v**z + 1/3*v + 2/3*v**2 - 1/3*v**4 - 2/3*v**3 = 0.
-1, 1
Let c be 12/10 + (-8)/10. Factor -2/5*i + c*i**3 + 0 + 0*i**2.
2*i*(i - 1)*(i + 1)/5
Let k(h) be the third derivative of 6*h**2 - 2/105*h**7 + 0*h - 1/28*h**8 + 0 + 0*h**5 + 0*h**3 + 0*h**6 + 0*h**4. Determine g, given that k(g) = 0.
-1/3, 0
Let d be (-2)/(1*(-3)/6). Let q(n) be the third derivative of -1/150*n**5 + 1/15*n**3 + 0*n**d + 0 + 0*n - 2*n**2. What is r in q(r) = 0?
-1, 1
Let y(f) be the second derivative of -f**7/420 + f**6/60 - f**4/3 + f**3/2 - 2*f. Let r(i) be the second derivative of y(i). Factor r(x).
-2*(x - 2)**2*(x + 1)
Let h(i) be the first derivative of -15*i**4/4 - 3*i**3 + 3*i**2 - 48. Suppose h(l) = 0. What is l?
-1, 0, 2/5
Let w(y) = -y**4 - y**3 + 2*y**2 + 3. Let x(g) = -2*g**3 + 2*g**2 + 2. Let m(n) = 2*w(n) - 3*x(n). Suppose m(q) = 0. Calculate q.
0, 1
Let x be (65/70 - 4/(-7)) + -1. Factor 0*q + 0 - q**2 + 1/2*q**4 - x*q**3.
q**2*(q - 2)*(q + 1)/2
Factor -12*s**2 - 2*s - 4*s**3 + 30*s**4 - 26*s**4 + 8 + 6*s.
4*(s - 2)*(s - 1)*(s + 1)**2
Factor -2*x + 0*x**4 + 4*x**4 + 2*x.
4*x**4
Let x(y) = -5*y**3 - 5*y**2 + 25*y - 15. Let p(t) = -85*t**3 - 85*t**2 + 425*t - 255. Let s(i) = 2*p(i) - 35*x(i). Factor s(w).
5*(w - 1)**2*(w + 3)
Determine b, given that 43 + 2*b**2 - 48 - 10*b - 7*b**2 = 0.
-1
Let w be 0 - -1*(-97)/(-5). Let q = w - 863/45. Factor 0*r + 0*r**3 - q*r**4 + 0 + 2/9*r**2.
-2*r**2*(r - 1)*(r + 1)/9
Let s(t) be the second derivative of 1/2*t**4 - 10*t - 1/5*t**6 - 1/2*t**3 - 3/14*t**7 + 3/5*t**5 + 0 + 0*t**2. Suppose s(a) = 0. What is a?
-1, 0, 1/3, 1
Let m(o) be the third derivative of -o**7/490 + o**6/28 - 33*o**5/140 + 5*o**4/7 - 8*o**3/7 + 18*o**2. Factor m(x).
-3*(x - 4)**2*(x - 1)**2/7
Suppose 10*c = 4 - 4. Factor -4/11*w**2 + 24/11*w**4 + 10/11*w**3 + 0*w + c.
2*w**2*(3*w + 2)*(4*w - 1)/11
Let k be 2/3 + 12/9. Let p(d) = 4*d**3 + 4*d**2 + 2*d + 2. Let q(r) = -5*r**3 - 5*r**2 - 3*r - 3. Let l(v) = k*q(v) + 3*p(v). What is z in l(z) = 0?
-1, 0
Let s(z) = z**3 + 4*z**2 - 4*z + 7. Let c be s(-5). Factor -2*x**2 - 3 + c - x - 3*x + 4*x**3 + 3.
2*(x - 1)*(x + 1)*(2*x - 1)
Let -6/5 - 6*t**3 + 38/5*t**2 - 2/5*t = 0. Calculate t.
-1/3, 3/5, 1
Suppose -4*z + 3 = 5*p - 3, 3*z + 3*p = 6. Let r = 4 - z. Factor o**2 + 3*o + r*o**2 - 4*o.
o*(o - 1)
Determine n, given that 4*n**3 - 4*n**4 + 0*n**4 + 0*n**4 = 0.
0, 1
Factor -7*r**4 + 2*r**3 + 11*r**4 - 6*r**4.
-2*r**3*(r - 1)
Let h = -8 - -74/9. Find b such that 8/9*b + 8/9 + h*b**2 = 0.
-2
Let q be 1/1 + (-4)/(280/42). Factor 2*h - 6/5 - q*h**2 - 2/5*h**3.
-2*(h - 1)**2*(h + 3)/5
Let f(r) be the third derivative of r**9/84672 + r**8/70560 - r**7/7056 - r**6/2520 - r**5/20 + 3*r**2. Let t(k) be the third derivative of f(k). Factor t(x).
(x - 1)*(x + 1)*(5*x + 2)/7
Suppose 0 = -0*r - 5*r. Let y(m) be the second derivative of 1/48*m**4 + m + r + 1/8*m**3 + 1/4*m**2. Suppose y(h) = 0. What is h?
-2, -1
Let j(v) be the first derivative of 5 - 9*v + 3*v**2 - 1/3*v**3. Solve j(t) = 0 for t.
3
Factor 0*d**4 + 4*d**4 - 5*d**2 + d**2.
4*d**2*(d - 1)*(d + 1)
Let h(i) = 0*i + i - 2*i + 2. Let b be h(1). Let p(u) = 8*u**4 - 6*u**3 - 14*u**2 - 10*u. Let a(y) = y**4 - y**2 - y. Let q(f) = b*p(f) - 10*a(f). Factor q(m).
-2*m**2*(m + 1)*(m + 2)
Let c = -25 + 28. Factor 0*l - 10/3*l**2 + 8/9 + 10/3*l**4 - 10/9*l**c + 2*l**5.
2*(l + 1)**3*(3*l - 2)**2/9
Let a(b) be the second derivative of b**4/12 - b**3/3 - 5*b**2/2 - b. Let r be a(4). Solve -j**r + j - 4*j**2 + 3*j**2 - 2*j**2 + j**4 + 2 = 0 for j.
-1, 1, 2
Let g(v) = -v**3 + 2*v**2 - 6*v + 5. Let z = 9 - 14. Let d(j) = -j**3 + 2*j**2 - 7*j + 6. Let m(s) = z*d(s) + 6*g(s). Factor m(b).
-b*(b - 1)**2
Let p be ((-66)/(-88))/((-9)/(-24)). Factor 2/15 - 4/15*m**p + 0*m + 0*m**3 + 2/15*m**4.
2*(m - 1)**2*(m + 1)**2/15
Let p(r) be the third derivative of 0*r + 1/8*r**4 + 1/20*r**5 - r**3 + 0 + 3*r**2. Factor p(d).
3*(d - 1)*(d + 2)
Determine p so that -2 - 1/2*p**2 - 2*p = 0.
-2
Let a(x) = -5*x**2 + 82*x - 318. Let i(g) = -85*g**2 + 1395*g - 5405. Let j(l) = -35*a(l) + 2*i(l). Find t, given that j(t) = 0.
8
Let w(o) be the second derivative of -9*o**5/20 + o**4/4 + 4*o**3/3 - 2*o**2 - 2*o. Factor w(b).
-(b + 1)*(3*b - 2)**2
Let x(j) be the first derivative of 2*j**5/5 - 3*j**4 + 26*j**3/3 - 12*j**2 + 8*j - 9. Factor x(h).
2*(h - 2)**2*(h - 1)**2
Let m(d) be the third derivative of -d**8/13440 - d**7/1680 + d**5/60 - d**4/4 + 4*d**2. Let b(w) be the second derivative of m(w). Find q, given that b(q) = 0.
-2, 1
Let n(c) be the second derivative of 0 + 1/18*c**3 + 6*c + 1/36*c**4 + 0*c**2. Factor n(v).
v*(v + 1)/3
Solve 0*a - 4/3*a**2 + 0 + 2/3*a**4 - 2/3*a**3 = 0.
-1, 0, 2
Let c(l) = -2*l**2 + 20*l + 18. Let r(t) = t**2 - 19*t - 18. Let s(n) = 4*c(n) + 5*r(n). Factor s(q).
-3*(q + 2)*(q + 3)
Find f such that -65/4*f**3 + 5 + 95/4*f**2 - 35/4*f**5 + 25*f - 115/4*f**4 = 0.
-2, -1, -2/7, 1
Let i = 14 + -41/3. Let q = -58/3 + 20. Find c, given that 1/3 - q*c**2 + i*c**4 + 0*c + 0*c**3 = 0.
-1, 1
Let n = 6 - 4. Suppose -5*y + 9 = -2*y. Factor -2*r**5 + 5*r**2 + 4*r**4 - 5*r**n - 2*r**y.
-2*r**3*(r - 1)**2
Let l be (-2)/12*-9 - 3/2. Factor 4/11*m**2 + 0*m + l - 2/11*m**3.
-2*m**2*(m - 2)/11
Suppose 2 = -2*l - 0, 5*x - l = 21. Factor -x*q - 7*q + 6*q - q + 2*q**2.
2*q*(q - 3)
Let z = 41/90 - 1/18. Let x(w) be the first derivative of -z*w**5 - 1/4*w**4 + 1/2*w**2 + 2/3*w**3 + 0*w - 2. Determine o so that x(o) = 0.
-1, -1/2, 0, 1
Let k(p) be the second derivative of 1/72*p**4 + p + 0 + 0*p**2 + 1/36*p**3. Factor k(y).
y*(y + 1)/6
Let g(q) be the second derivative of q**6/1140 - q**5/285 + q**4/228 - 3*q**2/2 + 3*q. Let r(u) be the first derivative of g(u). Factor r(y).
2*y*(y - 1)**2/19
Factor 0 + 0*h**2 + 1/5*h**3 - 1/5*h.
h*(h - 1)*(h + 1)/5
Let i(j) be the third derivative of -j**7/840 + j**6/120 + j**5/80 - 7*j**4/48 + j**3/3 - 3*j**2. Factor i(m).
-(m - 4)*(m - 1)**2*(m + 2)/4
Let h(k) be the second derivative of k**7/126 + k**6/30 + k**5/60 - k**4/12 - k**3/9 - 27*k. Factor h(w).
w*(w - 1)*(w + 1)**2*(w + 2)/3
Let m be (-4)/3*4/(-8). Suppose 0 = k + 3, -4*k - 12 - 16 = -4*b. Factor 0 - 8/3*l**4 - 8/3*l**2 - m*l - 2/3*l**5 - b*l**3.
-2*l*(l + 1)**4/3
Let o(f) be the second derivative of -1/24*f**3 - 1/48*f**4 - 3*f + 0 + 0*f**2. Factor o(u).
-u*(u + 1)/4
Factor 125 - c**4 - 66 - 60 + 2*c**2.
-(c - 1)**2*(c + 1)**2
Let b(p) be the first derivative of -p**6/420 - p**5/210 + p**4/42 + p**2/2 + 2. Let w(q) be the second derivative of b(q). Solve w(g) = 0 for g.
-2, 0, 1
Let m(s) = -s + 21. Let i be m(19). Let g(n) be the first derivative of 4/3*n**