- 5/2*h**4 + 0.
-h**2*(h + 1)*(5*h - 1)/2
Suppose -21*d + 70522 = 70459. Let 8/15 + 2/3*c**2 - 2/15*c**d - 16/15*c = 0. What is c?
1, 2
Let l = 8 + -3. Suppose 8*f = 3*f + l. Let -3*u**2 - u**2 - f + 5*u**2 - 2*u**2 - 2*u = 0. What is u?
-1
Let y be (3 - 86/6)/((-2)/(-18)). Let j = y - -104. Factor -1/2*f + 5/2*f**3 - 2*f**j + 0.
f*(f - 1)*(5*f + 1)/2
Let 9/2*a - 1/2*a**3 + 0 + 4*a**2 = 0. What is a?
-1, 0, 9
Let s(h) = 2 + 0 - 2 + 4*h**2 + h. Let k be s(-1). Factor -3*o**k - 9*o**3 + 12*o**2 + 4*o**4 - 15*o + 11*o.
4*o*(o - 1)**3
Let d(h) be the second derivative of -h**6/360 + h**5/60 + h**4/18 + 17*h**2/2 + 12*h. Let s(j) be the first derivative of d(j). Factor s(x).
-x*(x - 4)*(x + 1)/3
Let p(b) be the third derivative of 3*b**6/280 + 29*b**5/140 + 17*b**4/56 - 9*b**3/14 - 272*b**2. Factor p(l).
3*(l + 1)*(l + 9)*(3*l - 1)/7
Let j(y) be the first derivative of -16/5*y + 25 + 2/25*y**5 + 1/2*y**4 - 4/5*y**2 + 4/5*y**3. Determine u, given that j(u) = 0.
-2, 1
Let k(b) be the first derivative of 1/4*b**6 + 0*b**3 - 3/8*b**4 + 0*b**2 + 0*b**5 - 30 + 0*b. Factor k(o).
3*o**3*(o - 1)*(o + 1)/2
Factor 3/7*c**2 - 93/7*c + 0.
3*c*(c - 31)/7
Suppose -5*b = -0*b + 10. Let c be (-199)/b + -2 + (-7 - -4). Find u such that -3*u - 15*u**2 + 0 + 9/4*u**3 + c*u**4 + 405/4*u**5 = 0.
-2/3, -1/3, 0, 2/5
Let j(d) be the third derivative of d**8/560 - 3*d**7/56 + 5*d**6/8 - 25*d**5/8 + 3*d**3 + 21*d**2. Let g(c) be the first derivative of j(c). Factor g(i).
3*i*(i - 5)**3
Suppose -15*x - 12 = -17*x - 3*l, 3*l = 4*x - 6. Factor -8/3*u + 2/3 + 8/3*u**x - 2/3*u**2.
2*(u - 1)*(u + 1)*(4*u - 1)/3
Let j(l) be the first derivative of -l**6/1200 - 7*l**5/600 + l**4/48 + 5*l**3 + 27. Let m(h) be the third derivative of j(h). Let m(a) = 0. What is a?
-5, 1/3
Let o(a) be the third derivative of -a**8/168 - 9*a**7/70 - 7*a**6/10 + 49*a**5/60 - 76*a**2. Factor o(x).
-x**2*(x + 7)**2*(2*x - 1)
Let g(i) = i**4 - i**3 - 2*i**2 + 1. Let w(x) = -6*x**5 - 6*x**4 + 14*x**3 + 10*x**2 - 4*x - 4. Let r(p) = 4*g(p) + w(p). Find f such that r(f) = 0.
-1, 0, 2/3, 1
Let f be 4 - 20/5 - 2*(-4)/16. Factor 1/2 + h**3 - 3/4*h - 1/4*h**5 - f*h**2 + 0*h**4.
-(h - 1)**3*(h + 1)*(h + 2)/4
Suppose -73*n - 29*n + 400 = -22*n. Find r such that 9/5*r**4 + 0*r + 0*r**2 - 3/5*r**3 - 6/5*r**n + 0 = 0.
0, 1/2, 1
Let 1/3*p**4 - 2/9*p**3 + 1/9*p + 1/9*p**5 - 2/3*p**2 + 1/3 = 0. What is p?
-3, -1, 1
Let t be 15/3 - (-1)/(-6)*28. Let r(j) be the first derivative of -1/2*j**2 + 0*j - 2 + t*j**3. Determine z, given that r(z) = 0.
0, 1
Let i = -143110/10089 - -889/59. Let p = 21/19 - i. Factor -p - 2*q**2 + 4/3*q.
-2*(3*q - 1)**2/9
Let p(o) = -13*o**2 - 24 - 42*o + 11*o - o. Let d(n) = -30*n + 8*n**2 + n**2 + 46*n + 12 - 2*n**2. Let b(q) = 5*d(q) + 3*p(q). Factor b(x).
-4*(x + 1)*(x + 3)
Let w(b) be the first derivative of -b**8/420 + b**7/84 - b**6/45 + b**5/60 + 4*b**3 - 14. Let l(v) be the third derivative of w(v). Let l(o) = 0. Calculate o.
0, 1/2, 1
Suppose 2*g - 2 = 3*g + l, 16 = -4*l. Factor -6*m**g + 1606 + 4*m**3 - 1590 - 6*m**2.
4*(m - 2)**2*(m + 1)
Let d(v) = -v**3 + 5*v**2 - 5*v + 4. Let s be d(4). Factor 5 + s - 12*a - 12*a**3 + 18*a**2 + 5*a**4 - 2*a**4 - 2.
3*(a - 1)**4
Let i = -113/85 + 679/255. Let -i*t**2 - 56/3*t - 196/3 = 0. Calculate t.
-7
Let v be (0 + 6)*20/24. Let m(c) be the first derivative of 0*c - 6 + 2/55*c**v + 3/22*c**4 + 0*c**2 + 4/33*c**3. Factor m(r).
2*r**2*(r + 1)*(r + 2)/11
Let n = 67 - 52. Let a be 2*((-1)/n)/(2/(-6)). Let -a + 0*f + 2/5*f**2 = 0. Calculate f.
-1, 1
Suppose j - 16 = -2*k - 8, k - 1 = j. Let o(z) be the third derivative of 1/8*z**4 + 1/480*z**6 + 0*z - 1/3*z**3 - 4*z**j + 0 - 1/40*z**5. Factor o(d).
(d - 2)**3/4
Let 3*y - 28 - 23*y - 4*y + 4*y**2 = 0. What is y?
-1, 7
Let p(b) be the third derivative of -b**5/60 + 18*b**2. Let q(t) = -4*t**3 + 6*t**2. Let v(j) = 2*p(j) + q(j). Factor v(f).
-4*f**2*(f - 1)
Let f(r) = r**2 + 7*r. Let y be f(-8). Suppose 3*m - y = -2*m + 4*s, m - 4*s = -8. Factor 0 - 4/9*t - 8/9*t**3 + 14/9*t**2 - 8/9*t**m.
-2*t*(t + 2)*(2*t - 1)**2/9
Let h(o) be the first derivative of o**7/840 + o**6/90 - o**5/40 - 3*o**4/4 + 4*o**3 + 4. Let t(c) be the third derivative of h(c). Find l, given that t(l) = 0.
-3, 2
Let v = -18685/21 - -890. Let g = 29/63 - v. Factor 4/9*p + 2/9 + g*p**2.
2*(p + 1)**2/9
Let p(q) be the first derivative of -2*q**3/3 - 5*q**2 + 208*q - 545. Factor p(b).
-2*(b - 8)*(b + 13)
Let i = -7 - -11. Suppose -p + 12 = -5*p, 0 = -i*t - 3*p + 7. Determine z, given that -1/4*z**t + 1/2*z**3 - 1/4*z**5 - 1/4*z + 1/2*z**2 - 1/4 = 0.
-1, 1
Let -10*x**4 - 408/13*x - 662/13*x**2 - 14/13*x**5 - 34*x**3 - 72/13 = 0. What is x?
-3, -2, -1, -2/7
Let q = 7 + -52. Let n = 45 + q. Suppose -1/2*g**2 + n - 1/2*g = 0. What is g?
-1, 0
Suppose 0 = 6*i - 16*i - 20. Let m be (-9)/(-15) + (68/90)/i. Factor 4/9*p**3 + 2/9*p**5 + m - 2/3*p**4 - 2/3*p + 4/9*p**2.
2*(p - 1)**4*(p + 1)/9
Let x = 2140 - 10697/5. Factor -12/5 + x*w**3 - 3/5*w + 12/5*w**2.
3*(w - 1)*(w + 1)*(w + 4)/5
Suppose 190*z - 191*z = -14. Suppose 2*q = -2*l + z, -5*l = -4*q + 2 - 1. Let -1/6*k**5 - 8/3*k - 2/3 - 19/6*k**3 - 7/6*k**q - 25/6*k**2 = 0. Calculate k.
-2, -1
Let j(l) = -4*l**3 + 108*l**2 - l + 31. Let t be j(27). Let f(p) be the third derivative of 0*p - t*p**2 + 5/3*p**4 + 4/3*p**3 + 5/6*p**5 + 0. Factor f(n).
2*(5*n + 2)**2
Let k = -3316 - -3319. Let f be (3 + 4)*(-3)/(-4). Suppose 0*r**2 + 15/4*r**4 + f*r**5 + 0*r + 0 - 3/2*r**k = 0. What is r?
-1, 0, 2/7
Let f(w) be the first derivative of 48*w**3 + 39*w**2 + 3*w + 351. Determine q, given that f(q) = 0.
-1/2, -1/24
Let d(o) be the first derivative of -3*o**4/4 - o**3 + 3*o**2 - 39. Solve d(t) = 0 for t.
-2, 0, 1
Let q be (-264)/(-110)*10/3. Let w be (-69)/92*q/(-3). Factor -3/2 - 3*l**w - 15/4*l - 3/4*l**3.
-3*(l + 1)**2*(l + 2)/4
Suppose 0 = -42*b + 51*b - 27. Suppose -b*k = -13 + 4. Determine v so that 4/3*v + 2/3*v**k + 0 + 2*v**2 = 0.
-2, -1, 0
Let p(t) be the third derivative of t**6/24 + 29*t**5/12 + 175*t**4/3 + 750*t**3 + 4*t**2 + 45*t. Factor p(i).
5*(i + 9)*(i + 10)**2
Let k(c) = -5*c**5 - 435*c**4 - 355*c**3 + 25*c + 25. Let m(w) = w**5 + 108*w**4 + 89*w**3 - 6*w - 6. Let v(t) = 6*k(t) + 25*m(t). Solve v(r) = 0 for r.
-1, 0, 19
Let l(o) be the first derivative of -4/15*o**5 - 40000/3*o - 8000/3*o**2 - 800/3*o**3 - 40/3*o**4 + 25. Let l(u) = 0. Calculate u.
-10
Suppose 3*n + 2*f + 7 = -3*f, 0 = 4*n - 4*f - 12. Let z be n/7 + (2 + -3)/7. Suppose z + 1/4*v**3 - 1/2*v + 1/4*v**2 = 0. Calculate v.
-2, 0, 1
Let h be (45/(-60) - (-78)/72)*6. Factor -1/2*m**3 - 1/2 - 3/2*m**h - 3/2*m.
-(m + 1)**3/2
Let b(f) be the second derivative of f**6/75 - 13*f**5/50 + 9*f**4/5 - 92*f**3/15 + 56*f**2/5 - 196*f + 1. Find k, given that b(k) = 0.
2, 7
Suppose 0 = r + 3*x - 9, 4 = -3*r + 5*x - 11. Let n be 8/(-6)*(-6 + r). Factor -p**2 - n*p + 8*p.
-p**2
Let z(t) = -5*t**4 - 6*t**3 + 9*t**2 + 2*t + 4. Let y(b) = 14*b**4 + 17*b**3 - 25*b**2 - 6*b - 11. Let o(i) = -4*y(i) - 11*z(i). Solve o(j) = 0 for j.
-2, -1, 0, 1
Let u(o) = -5*o**2 - 151*o - 134. Let p(j) = -9*j**2 - 301*j - 272. Let x(l) = -3*p(l) + 5*u(l). Factor x(d).
2*(d + 1)*(d + 73)
Factor 80/3 + 124/9*w + 2/9*w**2.
2*(w + 2)*(w + 60)/9
Let s = -83 + 78. Let v(a) = 12*a**2 + 2*a + 5. Let c(l) = -12*l**2 - l - 4. Let p(n) = s*c(n) - 4*v(n). Solve p(f) = 0.
0, 1/4
Let j(n) be the second derivative of n**5/30 - 20*n**4/9 + 400*n**3/9 - 4*n + 40. Factor j(o).
2*o*(o - 20)**2/3
Let q be ((-3)/1)/((-9)/(-78)). Let g be (-9)/(-26) + (-1)/q*4. Solve 1/2*n**3 + 0*n - g*n**2 + 0 = 0 for n.
0, 1
Let c = 1607/610 + 4/61. What is w in 27/10*w**4 - 13/5*w**2 + c*w**5 - 9/10*w - 9/5*w**3 - 1/10 = 0?
-1, -1/3, 1
Let p(a) be the third derivative of a**7/105 - 13*a**6/15 + a**2 - 56*a. Factor p(s).
2*s**3*(s - 52)
Factor 884/3*b + 97682/3 + 2/3*b**2.
2*(b + 221)**2/3
Factor 22*j + 6*j + 3*j**3 + 25 - j**3 - 22*j**2 + 36*j - 81.
2*(j - 7)*(j - 2)**2
Let b(q) = 7*q**2 + 323*q - 13796. Let z(l) = -3*l**2 - 162*l + 6897. Let o(w) = 4*b(w) + 9*z(w). Factor o(p).
(p - 83)**2
Suppose -3*w = -5*k + 25, -3*k + 2*w + 6 + 9 = 0. Factor -10*l - 4*l**2 - 2*l**k + 2*l**4 + 12*l**3 - 6 + 0*l**2 + 4*l**2 + 4*l**2.
-2*(l - 3)*(l - 1)*(l + 1)**3
Let t(y) be the second derivative of -y**6/50 + 24*y*