 - 2/3*a**2 + 2/3*a**3 + m*a.
2*a**2*(a - 1)/3
Let s(w) be the third derivative of -1/33*w**4 + 1/11*w**5 + 3*w**2 - 8/33*w**3 - 23/660*w**6 + 0*w + 1/231*w**7 + 0. Suppose s(t) = 0. Calculate t.
-2/5, 1, 2
Let g(l) be the first derivative of 8*l**3/15 + 526*l**2/5 + 524*l/5 + 14. Suppose g(t) = 0. Calculate t.
-131, -1/2
Let o(s) = -s**2 + 2*s + 9. Let v(w) = -2*w**2 + 4*w + 19. Let c(k) = -6*k - 73. Let j be c(-10). Let i(m) = j*o(m) + 6*v(m). Find f, given that i(f) = 0.
-1, 3
Suppose 0 = 72*g + 3*g - 15*g. Let k(v) be the first derivative of 4 + g*v**2 + 1/5*v**6 + 2/25*v**5 + 0*v**3 + 0*v - 1/5*v**4. What is x in k(x) = 0?
-1, 0, 2/3
Factor 1115*b**2 + 1188*b**2 + 115*b - 15*b**3 - 2253*b**2 + 50.
-5*(b - 5)*(b + 1)*(3*b + 2)
Let w(h) = -2*h**3 + 2*h**2 - h - 2. Let b be w(-1). Let z(v) be the first derivative of 0*v**2 + 4 - 1/12*v**4 + 2/9*v**b + 0*v. Factor z(x).
-x**2*(x - 2)/3
Let b(w) = -w**3 - w**2 + w + 1. Let t(z) = -66 - 2*z**3 - 8*z**2 + 41 - z**4 + 30 + 6*z. Let a(v) = -10*b(v) + 2*t(v). Determine r, given that a(r) = 0.
0, 1
Let v(s) be the first derivative of s**4/8 + 3*s**3/2 + 27*s**2/4 + 27*s/2 + 225. Factor v(o).
(o + 3)**3/2
Let v = -267 + 271. Let i(s) be the first derivative of 1/2*s**v + 0*s**2 + 0*s - 2/3*s**3 + 2. Factor i(l).
2*l**2*(l - 1)
Suppose -1728*s + 1727*s = -3. Let k(f) be the first derivative of -1/3*f + 1/9*f**s + 4 + 0*f**2. Determine v so that k(v) = 0.
-1, 1
Let x(v) = v**3 + v**2 + 3*v - 2. Let g be x(2). Suppose 0 = -2*m + 6*m - g. Solve 2*f**2 + 2*f**m + 2*f**2 - 6*f**3 + 0*f**2 = 0 for f.
0, 1, 2
Suppose 5*z + 35 = 10, 3*i - z - 5 = 0. Let b(v) be the first derivative of i*v**3 + 1/8*v**2 + 4 - 1/16*v**4 + 0*v. Factor b(r).
-r*(r - 1)*(r + 1)/4
Factor 57/4*w - 45 - 3/4*w**2.
-3*(w - 15)*(w - 4)/4
Let g be (-6)/(-2) - (47 - 44). Let b(h) be the third derivative of 0 + 0*h**4 + 4*h**2 + 1/1155*h**7 - 1/330*h**5 + 0*h + 0*h**6 + g*h**3. Factor b(x).
2*x**2*(x - 1)*(x + 1)/11
Let -40/3*k**3 + 44/3*k + 0*k**2 - 4/3*k**5 + 8 - 8*k**4 = 0. What is k?
-3, -2, -1, 1
Let y be (-3)/30*3/3*-16. Let w be 2 + -5 + 14/2. Factor -2*x**2 + 4/5*x + 0 - 2/5*x**w + y*x**3.
-2*x*(x - 2)*(x - 1)**2/5
Let h(b) = 1899*b**4 + 57*b**3 + 33*b**2 + 33*b + 33. Let m(o) = 237*o**4 + 7*o**3 + 4*o**2 + 4*o + 4. Let w(r) = -4*h(r) + 33*m(r). Find x such that w(x) = 0.
-1/75, 0
Suppose 3*b - 108 = 3*q, 6*q = -3*b + 3*q + 114. Suppose 0 = t + 33 - b. Factor 0*h**2 - 2/5*h**t + 0*h + 0 + 2/5*h**3.
-2*h**3*(h - 1)/5
Let m = 10277/5 - 2055. Determine i, given that m*i**2 + 0*i + 0 = 0.
0
Let m(i) be the third derivative of i**8/2352 + i**7/490 - 13*i**6/840 - 11*i**5/420 + i**4/7 + 10*i**3/21 - 48*i**2. Solve m(t) = 0.
-5, -1, 2
Let b = 16 - 0. Suppose -13 = h - b. What is c in 0 - 32/5*c**4 + 6/5*c**h + 8/5*c + 32/5*c**2 - 14/5*c**5 = 0?
-2, -1, -2/7, 0, 1
Let b be 2*2/(-4) + (-72)/(-42). Let p = -2/7 + b. Let 0 - p*w - 6/7*w**2 - 3/7*w**3 = 0. Calculate w.
-1, 0
Let k be 5*(-1)/10 + (-5)/(-2). Let r(j) be the first derivative of 0*j**k + 2 - 6/5*j**5 + 1/3*j**6 + 8/3*j**3 + 0*j**4 + 0*j. Factor r(h).
2*h**2*(h - 2)**2*(h + 1)
Factor -6*r - 35/2*r**2 + 6*r**3 - 1/2*r**4 + 18.
-(r - 6)**2*(r - 1)*(r + 1)/2
Suppose 18*y - 93 = -21. Let t(j) be the third derivative of 0 + j**2 - 7/30*j**6 - 26/15*j**5 + 4*j**3 - 13/6*j**y + 0*j. Factor t(k).
-4*(k + 1)*(k + 3)*(7*k - 2)
Let p(c) be the second derivative of -1/3*c**2 + 0 + 1/63*c**7 - 16*c - 1/45*c**6 - 1/15*c**5 + 1/9*c**4 + 1/9*c**3. Determine j so that p(j) = 0.
-1, 1
Solve -289*t**2 + 0 + 0 + 288*t**2 + 17*t = 0 for t.
0, 17
Factor -10*n**2 - 9*n**2 + 7*n**2 + 50*n + 143 + 25 + 10*n**2.
-2*(n - 28)*(n + 3)
Let m(v) be the first derivative of -v**7/84 + 3*v**5/160 - v**4/96 - 15*v + 19. Let u(l) be the first derivative of m(l). Find p such that u(p) = 0.
-1, 0, 1/2
Factor 312*f + 42*f**3 + 158 + 3*f**4 + 220*f**2 + 34 - 40*f**2.
3*(f + 2)**3*(f + 8)
Let w = 6 - 2. Let i(g) = -g**2 + 2*g - 1. Let n be i(1). Suppose -3*b**3 + n*b**2 + 0*b**2 + w*b**5 - b**5 = 0. Calculate b.
-1, 0, 1
Let o(n) be the second derivative of 0*n**5 + 1/14*n**4 - 4*n - 3/14*n**2 + 0*n**3 + 0 - 1/70*n**6. Find i, given that o(i) = 0.
-1, 1
Factor 24 - 114 - 25*u**2 + 54093*u - 54328*u.
-5*(u + 9)*(5*u + 2)
Suppose 0 = -11*m + 22539 - 22495. Suppose 0 - 2/3*c**5 + 0*c + 10/3*c**m + 8/3*c**2 - 16/3*c**3 = 0. Calculate c.
0, 1, 2
Let l be ((-16)/26)/(294/(-273)). Factor -4/7*z**2 + 0 - 1/7*z**5 + 3/7*z**3 - l*z + 2/7*z**4.
-z*(z - 2)**2*(z + 1)**2/7
Let b(m) = -m**4 + m**2 - m + 1. Let p(q) = -30*q**4 + 205*q**3 - 110*q**2 - 80*q + 15. Let v(s) = 15*b(s) - p(s). Factor v(w).
5*w*(w - 13)*(w - 1)*(3*w + 1)
Let q(r) be the third derivative of -r**5/60 - r**4/24 + r**3/6 + 6*r**2. Let i(y) = -y**2 + 4*y + 7. Let l(n) = 3*i(n) - 6*q(n). Factor l(j).
3*(j + 1)*(j + 5)
Let q be 3/9*0 + 2. Find m, given that 27*m + 24 - 16*m - 12*m**3 + 9*m**q - 3*m**4 + 14*m + 17*m = 0.
-4, -1, 2
Let o = -35 - -49. Let l be (8 - o)/((-3)/2). Factor 4*k - 9*k**3 + 7*k**l + 0*k**2 - 11*k**2 - k**2.
k*(k - 2)*(k + 1)*(7*k - 2)
Let l = 3248/5 + -646. Let i be 0*((1 - 4) + 2). Solve -4/5*f - l*f**2 + i = 0 for f.
-2/9, 0
Let g = 19512 + -58526/3. Factor -10/3 - 5/6*x**2 - g*x.
-5*(x + 2)**2/6
Let q(s) = 3*s**2 - 5*s - 23. Let u be q(4). Let c(o) be the first derivative of -1/6*o**4 + 0*o**2 + 0*o + 2/15*o**u + 1 + 0*o**3. Solve c(w) = 0.
0, 1
Let l = 27064 - 27061. Factor -2*u**4 + 0*u**2 - 3/2*u**l + 1/4*u + 0 - 3/4*u**5.
-u*(u + 1)**3*(3*u - 1)/4
Let g = 3/3886 + 11637/27202. Factor 0 + 0*y**2 + 0*y**3 + g*y**4 + 0*y.
3*y**4/7
Let j(q) be the second derivative of -q**8/6720 - q**7/1260 + q**4/2 - 14*q. Let k(u) be the third derivative of j(u). Suppose k(a) = 0. What is a?
-2, 0
Let h(t) be the second derivative of -1/18*t**3 + 1/36*t**4 - t + 0 - 1/90*t**6 + 1/60*t**5 + 0*t**2. Find s, given that h(s) = 0.
-1, 0, 1
Let b be ((-5)/(10/(-6)))/((-143)/(-22) - 5). Suppose -4*d + 3*r - 3 = -0*r, 4*d + 4*r - 4 = 0. Factor -9/5*s + d - 3/5*s**b.
-3*s*(s + 3)/5
Let f(b) be the third derivative of b**7/42 - b**5/6 + 5*b**3/6 - 22*b**2. Determine g, given that f(g) = 0.
-1, 1
Let p be (-82)/78 - (-10)/15. Let u = 61/91 + p. Factor 2/7*y**4 + 0 + 4/7*y**3 - u*y**2 - 4/7*y.
2*y*(y - 1)*(y + 1)*(y + 2)/7
Let w(u) be the third derivative of u**7/840 + u**6/180 - u**5/40 + 7*u**3/6 - 7*u**2. Let r(d) be the first derivative of w(d). Solve r(o) = 0 for o.
-3, 0, 1
Let s(t) = 12*t**5 - 12*t**4 - 16*t**3 + 16*t**2 - 7*t - 4. Let x(v) = v**5 - v**4 - v**3 + v**2 - v. Let i(l) = -2*s(l) + 22*x(l). Solve i(d) = 0 for d.
-2, -1, 1, 2
Let k be -6*1/2*-9. Suppose -5*o + 2*n + 13 = -n, -7 = -5*o - 3*n. Factor 20*z + k + 15*z + 3*z + 9*z**o + z**3 - 11*z.
(z + 3)**3
Let w(a) = a - 61. Let c(v) = -30. Let k(p) = 5*c(p) - 2*w(p). Let n be k(-14). Factor -8/5*i**3 + n*i**2 - 2/5*i**5 + 0*i - 8/5*i**4 + 0.
-2*i**3*(i + 2)**2/5
Let g(l) be the third derivative of l**6/360 - l**5/60 + l**4/24 - 17*l**3/3 - 17*l**2. Let n(r) be the first derivative of g(r). Let n(q) = 0. What is q?
1
Let f = 8361692/35 - 238940. Let i = 174/5 + f. Factor 4/7*x**3 + 0 - i*x - 2/7*x**2.
2*x*(x - 1)*(2*x + 1)/7
Let t(y) = 4*y**4 - 180*y**3 + 140*y**2 + 164*y - 176. Let l(g) = -g**4 + 60*g**3 - 46*g**2 - 54*g + 59. Let p(b) = -8*l(b) - 3*t(b). Let p(c) = 0. What is c?
-1, 1, 14
Find z such that -156/7*z - 225/7*z**2 + 51/7*z**4 - 90/7*z**3 - 36/7 + 36/7*z**5 = 0.
-1, -3/4, -2/3, 2
Let v = 181 - 542/3. Let k = 13 + -9. What is r in 0 + v*r**2 - 1/3*r**3 - 1/3*r**k + 1/3*r = 0?
-1, 0, 1
Suppose 6*g = 1050 - 366. Factor 7*o**2 + 110*o**4 + 9*o**2 - g*o**4.
-4*o**2*(o - 2)*(o + 2)
Suppose 6*z - 9 = 3. Let f be (-16)/96 - z/(-12). Factor 0*i + 0*i**4 + 2/7*i**3 + f*i**2 + 0 - 2/7*i**5.
-2*i**3*(i - 1)*(i + 1)/7
Let y = -422 - -424. Let p(n) be the third derivative of 0*n + 0 + 1/18*n**3 - 1/36*n**4 + 1/180*n**5 - y*n**2. Suppose p(j) = 0. Calculate j.
1
Let m be (10 - 12) + 1/(-3) + 5. Suppose 2 - m*i + 2/9*i**4 - 4/9*i**2 + 8/9*i**3 = 0. What is i?
-3, 1
Let i(k) = -5*k**4 + 77*k**3 + 234*k**2 + 235*k + 80. Let l(q) = -9*q**4 + 153*q**3 + 468*q**2 + 471*q + 160. Let h(b) = 10*i(b) - 6*l(b). Factor h(j).
4*(j - 40)*(j + 1)**3
Let d = 20933/31413 - -3/10471. Find z such that -d*z**5 - 2/3*z