r**2 + u*r**4 - 2*r**5 + 5*r**2 = 0.
0, 1
Let i(z) be the second derivative of 1/30*z**3 - 6*z + 0*z**2 - 1/150*z**6 + 1/60*z**4 - 1/100*z**5 + 0. Solve i(q) = 0 for q.
-1, 0, 1
Let y(c) be the third derivative of 6/7*c**7 - 14/15*c**5 + 0 - 9/28*c**8 - 1/5*c**6 + 5*c**2 + 2/3*c**3 + 1/6*c**4 + 0*c. Solve y(h) = 0 for h.
-1/3, 1/3, 1
Let l(n) be the first derivative of -n**2 + 2*n - 9. Let v be l(-1). Suppose 0*u**3 + 3/2*u**2 - 3/2*u**v + 0 + 3/4*u - 3/4*u**5 = 0. Calculate u.
-1, 0, 1
Let s(j) be the third derivative of -j**7/14 + 3*j**6/5 - 7*j**5/4 + 3*j**4/2 + 2*j**3 + 2*j**2. Suppose s(f) = 0. What is f?
-1/5, 1, 2
Let q(n) be the first derivative of -2/3*n**3 + 0*n - 1/2*n**4 + 0*n**2 + 1. Factor q(j).
-2*j**2*(j + 1)
Let j = 230 + -227. Find y, given that 2/5*y**j + 4/5*y**2 + 0 + 0*y - 6/5*y**4 = 0.
-2/3, 0, 1
Let u be ((-1)/4)/((-4)/(3168/55)). Solve -6*b**2 - 4/5 + 22/5*b**3 - 6/5*b**4 + u*b = 0 for b.
2/3, 1
Let x = 21 - 13. Suppose 2*f**3 - 22*f**2 + 4*f**3 + 17*f + 4*f + 3*f - x = 0. What is f?
2/3, 1, 2
Suppose -25 = -2*q - q + 5*t, 4*q - 20 = 4*t. Let o(i) be the first derivative of 1 + q*i + 1/2*i**4 + 2/5*i**5 - i**2 - 2/3*i**3. Factor o(n).
2*n*(n - 1)*(n + 1)**2
Factor -2/5*j**3 - 2/5*j**2 + 0 + 2/5*j**4 + 2/5*j.
2*j*(j - 1)**2*(j + 1)/5
Let k = -103 + 1135/11. Determine p so that -2/11 + k*p**2 + 0*p = 0.
-1, 1
Let b(m) = -m**4 + m**3 + m**2. Let g(j) = 2*j**3 + 5*j**2 + 2*j**3 + j**3 + 3*j**5 - 2*j**4. Let u(o) = -5*b(o) + g(o). Factor u(r).
3*r**4*(r + 1)
Let c = -5599 - -173589/31. Let a = 421/124 - c. What is d in 1/2*d**3 - a*d**4 + 0*d**2 + 0 + 0*d + 15/4*d**5 = 0?
0, 1/3, 2/5
Let v(z) be the second derivative of -z**5/40 + z**4/6 + z**3/12 - z**2 + 5*z - 3. Let v(i) = 0. What is i?
-1, 1, 4
Let h(m) be the first derivative of 2/3*m**3 + 1/6*m**4 + m**2 + m + 2. Let d(u) be the first derivative of h(u). Factor d(x).
2*(x + 1)**2
Let r be 29/6 + (-1)/(-6). Solve -3*n**r + 4*n**3 - 2*n + 2*n**5 - 3*n**5 + 2*n**5 = 0.
-1, 0, 1
Let b(i) = -i**3 + i**2 + 7*i - 7. Let q be b(2). What is x in 3/2*x**2 + 3/2 - q*x = 0?
1
Let k be 8/(-28) - 64/(-126). Let z be (6 - (-150)/(-24))*-8. Factor -k*g**z - 4/3*g - 2.
-2*(g + 3)**2/9
Let g(c) be the third derivative of c**5/90 - 5*c**4/36 + 4*c**3/9 + 5*c**2. Determine d, given that g(d) = 0.
1, 4
Let t(u) be the first derivative of -u**6/360 + u**5/30 - u**4/6 - 5*u**3/3 - 5. Let x(p) be the third derivative of t(p). Find c, given that x(c) = 0.
2
What is o in 1/4*o**4 + o + 0 - 3/4*o**3 + 0*o**2 = 0?
-1, 0, 2
Let i be (-6)/(-2) - 495/190. Let t = i - -2/19. Solve t*y - 1/2*y**2 + 1 = 0.
-1, 2
Factor 0*a**2 + 0*a + 0 - 3/5*a**5 + 0*a**3 + 3/5*a**4.
-3*a**4*(a - 1)/5
Let u = 54 + -484/9. Factor 4/9 - 2/3*b + u*b**2.
2*(b - 2)*(b - 1)/9
Factor 0*l - 81/2*l**2 + 0 + 17/2*l**4 - 1/2*l**5 - 63/2*l**3.
-l**2*(l - 9)**2*(l + 1)/2
Determine l, given that -3*l**2 + l**2 + 3*l**3 - l**3 - 4*l = 0.
-1, 0, 2
Let m(b) be the first derivative of -b**7/735 + b**6/420 + b**5/210 - b**4/84 + 3*b**2/2 + 8. Let x(j) be the second derivative of m(j). Factor x(h).
-2*h*(h - 1)**2*(h + 1)/7
Let x(f) be the first derivative of f**5/20 - f**4/12 - f**3/6 + f**2/2 + 5*f + 2. Let o(g) be the first derivative of x(g). Factor o(a).
(a - 1)**2*(a + 1)
Let i = 22/93 - -3/31. Determine a, given that -i*a**2 + 0*a + 1/3 = 0.
-1, 1
Suppose -8*y - 35 = -3*y. Let j = y + 9. Let -2 - 6*a**j - 2*a - 6*a + 2*a - 2*a**3 + 0 = 0. What is a?
-1
Let s(z) be the first derivative of z**6/30 + z**5/25 - z**4/10 - 4. Determine j, given that s(j) = 0.
-2, 0, 1
Let n(y) = -11*y**2 + 23*y - 17. Let i(g) = -4*g**2 + 8*g - 6. Suppose 4*u + 82 = 14. Let t(h) = u*i(h) + 6*n(h). Find j such that t(j) = 0.
-1, 0
Solve 1/4*c**2 + 2*c + 4 = 0.
-4
Let h(o) be the first derivative of -3*o**4/4 + 3*o**3 + 1. Factor h(t).
-3*t**2*(t - 3)
Let x(a) = 20*a**2 - 278*a - 20. Let s be x(14). Factor -16/5 - s*w + 18/5*w**3 - 12/5*w**2.
2*(w - 2)*(3*w + 2)**2/5
Let t be (-1)/(-2)*(1 + 43). Suppose 5*w - w + 52 = 4*d, 2*d - w - t = 0. Factor -d*y**2 + 9*y**4 + 6*y**3 - 6*y + 4*y**5 - 3*y**3 - y**5.
3*y*(y - 1)*(y + 1)**2*(y + 2)
Let k(t) be the first derivative of 0*t**2 - 2/3*t**3 + 0*t - 2. Solve k(l) = 0.
0
Let a(w) be the third derivative of -w**9/21600 + w**8/10080 + w**7/6300 + w**5/60 - 2*w**2. Let c(s) be the third derivative of a(s). Solve c(p) = 0.
-2/7, 0, 1
Let r(k) be the first derivative of 0*k - k**2 + 7/3*k**3 + 1. Find q, given that r(q) = 0.
0, 2/7
Let 0*y + 2/3*y**4 + 0*y**2 + 0 + 2/3*y**3 = 0. Calculate y.
-1, 0
Let g(j) be the third derivative of 4*j**7/1365 - 3*j**6/260 + j**5/65 - j**4/156 + 9*j**2. Suppose g(v) = 0. Calculate v.
0, 1/4, 1
Let v = 497/8 - 62. Let h = v - -3/8. Factor 1/4*t**5 - 1/4 - 1/4*t**4 + 1/2*t**2 + 1/4*t - h*t**3.
(t - 1)**3*(t + 1)**2/4
Factor -12*o**4 + 85*o**3 + 54*o + 5*o**5 - 85*o**2 - 23*o**4 - 24*o.
5*o*(o - 3)*(o - 2)*(o - 1)**2
Solve -3*c - 15*c**4 + 2*c - 21*c**2 + 4*c - 4*c**3 + 37*c**3 = 0 for c.
0, 1/5, 1
Suppose -5*v = 5*g - 4*v - 7, -3*g + 15 = -3*v. What is z in -4/9*z + 2/9*z**4 - 2/9*z**g + 0 + 10/9*z**3 - 2/3*z**5 = 0?
-1, -2/3, 0, 1
Factor -5/4*g**4 + 0*g + 3/4*g**3 + 0 + 1/2*g**2.
-g**2*(g - 1)*(5*g + 2)/4
Let n = 62 + -59. Solve -2/3 - 38/3*x**2 - 14/3*x**4 + 13*x**n + 5*x = 0.
2/7, 1/2, 1
Factor 3*f**3 + 5*f**2 - f - 11*f**2 + 4*f.
3*f*(f - 1)**2
Let u(i) be the first derivative of i**4 + 4*i**3 - 16*i + 8. Solve u(d) = 0 for d.
-2, 1
Let i = -264 - -2906/11. Factor 0*t**2 - i*t**4 + 0 - 2/11*t**3 + 0*t.
-2*t**3*(t + 1)/11
Let n(f) be the third derivative of f**8/1008 - f**7/315 - f**6/360 + f**5/90 + 7*f**2. What is v in n(v) = 0?
-1, 0, 1, 2
Let f = 15 - 15. Let a(k) be the second derivative of 0 + f*k**3 + 1/20*k**5 + 0*k**2 + k + 1/12*k**4. Factor a(p).
p**2*(p + 1)
Let i = -392/5 + 80. Determine f so that -8/5*f - i - 2/5*f**2 = 0.
-2
Let d(n) be the second derivative of n**7/14 + n**6/10 - 3*n**5/10 - n**4/2 + n**3/2 + 3*n**2/2 - 44*n. Let d(u) = 0. What is u?
-1, 1
Let u(d) be the second derivative of d**4/24 - 3*d**3/4 + 20*d. Solve u(k) = 0.
0, 9
Let l(i) be the first derivative of i**2 - 1 + 7/120*i**5 + 1/4*i**4 - 1/3*i**3 + 0*i. Let j(w) be the second derivative of l(w). Find y, given that j(y) = 0.
-2, 2/7
Let m(o) be the second derivative of 5*o**4/12 + 5*o**3/3 + 13*o. Suppose m(x) = 0. What is x?
-2, 0
Factor -51*s**3 - 260*s**2 - 112*s**3 - 61*s - 187*s**3 + 21*s + 245*s**4.
5*s*(s - 2)*(7*s + 2)**2
Let h(y) be the first derivative of 1/24*y**4 + 0*y**3 + 0*y**2 + 2 - 1/40*y**5 + 2*y - 1/30*y**6. Let t(a) be the first derivative of h(a). Factor t(z).
-z**2*(z + 1)*(2*z - 1)/2
Let l(s) = -2*s**3 - 10*s**2 + 2*s + 10. Let c(j) = 3*j**3 + 11*j**2 - 3*j - 11. Let w(i) = -4*c(i) - 5*l(i). What is n in w(n) = 0?
-1, 1, 3
Let k(h) be the first derivative of -12*h**5/5 - 8*h**4 - 8*h**3 + 4*h + 7. Factor k(b).
-4*(b + 1)**3*(3*b - 1)
Let l = -3 - -9. Let s be (-7)/7 + 8/l. Solve -z - 1/3*z**3 - s - z**2 = 0 for z.
-1
Let o(s) = 10*s + 5. Let k(u) = u**2 - 10*u - 5. Let l(m) = 5*k(m) + 6*o(m). Let l(i) = 0. Calculate i.
-1
Factor -2 + 3*c**3 - 13/2*c**2 + 6*c - 1/2*c**4.
-(c - 2)**2*(c - 1)**2/2
Let v be (-99)/3*5/(-3). Suppose 3*l = 2 - 17, 5*h + 3*l - v = 0. Suppose 4*q - h*q**4 - 6*q**2 + 24*q**3 - 5*q - 3*q = 0. What is q?
-2/7, 0, 1
Let y(v) = 3*v**5 - 3*v**4 - 3*v**3 - 3*v**2 + 3*v + 3. Let j(k) = k**4 - k**3 + 7 - 3 + k**2 - 5. Let f(u) = 3*j(u) + y(u). Factor f(r).
3*r*(r - 1)**2*(r + 1)**2
Let z = 169/15 - 29/3. Determine p, given that -4/5*p**2 + z + 4/5*p = 0.
-1, 2
Suppose 0 = 2*n + 5*o - 12, 0 = -3*n + 7*n + 2*o - 24. Let d be 2/(-3)*n/(-9). Factor 0*a**2 + 2/9*a**5 + 0 + 0*a + d*a**4 + 2/9*a**3.
2*a**3*(a + 1)**2/9
Determine j so that -16/5*j - 7/5*j**2 - 12/5 - 1/5*j**3 = 0.
-3, -2
Let p(n) be the second derivative of -1/15*n**6 + 4*n + 0*n**3 - 2/5*n**5 + 0*n**2 + 0 - 2/3*n**4. Factor p(v).
-2*v**2*(v + 2)**2
Let t(f) = f**2 - 3*f - 5. Let x be t(-2). Solve 0*a + 0 + a**4 - 1/2*a**x + 0*a**2 + 0*a**3 = 0 for a.
0, 2
Let i(t) = t**3 - 6. Let v be i(0). Let r be (-4)/v + (-44)/165. Let 0 - 2/5*o - r*o**2 = 0. What is o?
-1, 0
Let 0 - 8/3*i - 4/3*i**3 + 4*i**2 = 0. What is i?
0, 1, 2
Let u(c) be the first derivative of -6*c**5/5 - 7*c**4/2 - 10*c**3/3 - c**