6*d**2 + w*d**3 + 0.
d**2*(d - 1)/6
Suppose 5*i + 45 = -s, -3*i + 2*i + 3*s = 25. Let t(w) = w**3 + 10*w**2. Let m be t(i). Solve 2/11*f**2 + m + 2/11*f**3 - 4/11*f = 0 for f.
-2, 0, 1
Let t = 658/9 + -73. Let s(x) be the second derivative of 2/27*x**3 + 0 - 1/18*x**4 - 2*x + t*x**2. Factor s(p).
-2*(p - 1)*(3*p + 1)/9
Solve 2/3*l**4 + 4/3*l - 4/3*l**3 + 0*l**2 - 2/3 = 0.
-1, 1
Suppose 8 = 3*c + c. Let t(n) = -15*n**2 - 30*n - 15. Let w(h) = -3*h**2 - 6*h - 3. Let b(y) = c*t(y) - 11*w(y). Let b(m) = 0. Calculate m.
-1
Suppose -5*j + 24 - 4 = 0. Suppose -3*q + 13 + 12 = 4*y, -j*q = -y - 8. Factor -8*k**y - 2*k**3 + 8*k**3 + 2*k + 6*k**3 + 2*k**5 - k**2 - 7*k**2.
2*k*(k - 1)**4
Let c(s) be the third derivative of s**10/604800 - s**8/80640 - s**5/20 + 2*s**2. Let p(b) be the third derivative of c(b). Factor p(t).
t**2*(t - 1)*(t + 1)/4
Let t be ((-1)/(-2))/((-3)/(-48)). Let r be (t/(-12))/(2/(-9)). Factor 2*u**r + u**3 + 3*u**5 - 2*u**5 + u**2 + 3*u**4.
u**2*(u + 1)**3
Factor -2*b**3 + 2*b**2 + 0*b**2 + 0*b**2 - 4*b**2.
-2*b**2*(b + 1)
Let d(l) = 2 - 18*l**2 + 64*l**2 - 35*l**4 - 1 - 45*l**3 + 27*l. Let f(x) = -71*x**4 - 89*x**3 + 92*x**2 + 53*x + 1. Let h(w) = -7*d(w) + 3*f(w). Factor h(p).
2*(p - 1)*(p + 2)*(4*p + 1)**2
Let o = -8 - -12. Let i = -4 + o. Factor 0 + i*d + 2/5*d**2.
2*d**2/5
Let q(x) be the first derivative of -x**4/44 + 2*x**3/33 + x**2/22 - 2*x/11 + 22. Find k such that q(k) = 0.
-1, 1, 2
Factor 12/7*u - 4/7*u**5 + 4/7 + 8/7*u**2 - 8/7*u**3 - 12/7*u**4.
-4*(u - 1)*(u + 1)**4/7
Suppose -3*v - 2*g + 22 = 0, -v + 2*g = 7*g - 29. Solve -8*h - 9*h**2 + 6*h + 8*h + 3*h**v = 0 for h.
-2, 0, 1
Factor 0 + 1/3*z - 1/9*z**3 + 2/9*z**2.
-z*(z - 3)*(z + 1)/9
Let h(r) = -r - 1. Let t = 13 + -10. Let q(o) = -o**3 - o**2 + 5*o + 5. Let z(i) = t*q(i) + 15*h(i). Factor z(k).
-3*k**2*(k + 1)
Let y = 197 + -115. Let j = y - 572/7. What is h in 0 - 2/7*h + j*h**3 - 2/7*h**2 + 2/7*h**4 = 0?
-1, 0, 1
Let s(d) be the second derivative of -d**7/70 - 7*d**6/25 - 57*d**5/25 - 10*d**4 - 128*d**3/5 - 192*d**2/5 + 19*d. Factor s(q).
-3*(q + 2)**3*(q + 4)**2/5
Suppose 0 = 3*d + l - 38, -2*l = d - 6*d + 67. Factor 3*o - 9*o**2 + 0*o - 5*o + d*o**2.
2*o*(2*o - 1)
Suppose -4*k + 3*y = -18, 5*k - 3*y - 12 = 9. Factor 2/3*u**4 + 0*u**2 + 0*u - 1/3*u**5 + 0 - 1/3*u**k.
-u**3*(u - 1)**2/3
Factor 109*n**2 - 105*n**2 + 8 + 24 + 24*n.
4*(n + 2)*(n + 4)
Let 11*v**2 + 15*v + 2*v**2 - 8*v**2 = 0. What is v?
-3, 0
Let a(r) be the first derivative of -r**5/5 + 3*r**4/4 - r**3 + r**2/2 - 9. Find y such that a(y) = 0.
0, 1
Solve -4/5*i**3 + 22/15*i**2 + 8/15*i - 8/15 = 0.
-2/3, 1/2, 2
Let v = -21824/75 + 291. Let d(h) be the third derivative of 0*h**3 + h**2 - 1/60*h**4 + 0 + v*h**5 - 1/300*h**6 + 0*h. Factor d(o).
-2*o*(o - 1)**2/5
Let h(b) be the third derivative of 0*b**3 + 0 - 1/120*b**4 - 3*b**2 + 1/75*b**5 + 0*b. Factor h(t).
t*(4*t - 1)/5
Factor -1/7*a**2 - 4/7*a - 4/7.
-(a + 2)**2/7
Let b be (-15)/(-75) + 14/(-120). Let m(u) be the second derivative of 0 - u - 1/12*u**3 - 1/40*u**5 + 0*u**2 - b*u**4. Let m(r) = 0. What is r?
-1, 0
Let t(b) be the second derivative of -5*b**4/12 + 5*b**3/2 - 19*b. Factor t(c).
-5*c*(c - 3)
Suppose 0 = 3*r - 11 - 1. Let y(v) be the first derivative of -r*v**2 + 8*v + 3 + 2/3*v**3. Factor y(k).
2*(k - 2)**2
Suppose -3*o - 16 = -3*b + 4*b, -4*b - 19 = 3*o. Let i = b - -3. Factor 0 + 1/2*a**i - 1/2*a**4 + 1/2*a - 1/2*a**3.
-a*(a - 1)*(a + 1)**2/2
Let t be (-1 + 0)/(-1) - -4. Let j = -2 + t. Factor 3*k**2 + 17*k - 8*k + 3 + j.
3*(k + 1)*(k + 2)
Let i(k) be the third derivative of k**7/560 + k**6/320 - k**2 - 3. Factor i(t).
3*t**3*(t + 1)/8
Let o be (-4)/6*(-1617)/616. Factor o*m + 3/4 + m**2.
(m + 1)*(4*m + 3)/4
Let s(p) be the second derivative of p**7/126 - p**6/90 - p**5/60 + p**4/36 - 19*p. Find j, given that s(j) = 0.
-1, 0, 1
Let l = -7981/45 - -889/5. Factor -2/3*h - 2/9*h**2 - l.
-2*(h + 1)*(h + 2)/9
Suppose 0 = -v - 2*c + 32 - 22, -2*v + 3*c = 15. Find p such that 3/2*p**3 + v*p + 3/2*p**2 + 0 = 0.
-1, 0
Let u(x) be the second derivative of x**6/180 - x**4/12 - 2*x**3/9 + x**2/2 - 3*x. Let l(w) be the first derivative of u(w). Solve l(j) = 0.
-1, 2
Let k be 1*-1 - 56/(-42). Factor -2/3 + 1/3*b + k*b**2.
(b - 1)*(b + 2)/3
Let g(r) be the second derivative of 4*r**4/9 - r**3/9 - 25*r. Determine a so that g(a) = 0.
0, 1/8
Let c = 3154/9 + -350. Factor 88/9*m**2 - 38/9*m + c.
2*(4*m - 1)*(11*m - 2)/9
Let d(k) be the third derivative of k**6/210 + 2*k**5/105 + k**4/42 - 16*k**2. Find b such that d(b) = 0.
-1, 0
Let d(v) = 201*v**3 - 695*v**2 + 357*v - 53. Let z(a) = -a**3 - a**2 - a + 1. Let p(u) = d(u) + 5*z(u). Factor p(q).
4*(q - 3)*(7*q - 2)**2
Let n(h) be the first derivative of -26/3*h**6 + 0*h**4 - 7 + 8/5*h**5 + 0*h + 0*h**3 + 0*h**2. Factor n(k).
-4*k**4*(13*k - 2)
Let i = 34/3 - 232/21. Let 0 + 0*p**2 - 2/7*p**3 + i*p = 0. What is p?
-1, 0, 1
Let a(g) be the first derivative of g**5/60 - 5*g + 5. Let s(z) be the first derivative of a(z). Factor s(p).
p**3/3
Let f(v) = 5*v**4 + 5*v**3 - 24*v**2 - 24*v. Let n(i) = 5*i**4 + 5*i**3 - 23*i**2 - 23*i. Let m(a) = -3*f(a) + 4*n(a). Determine u so that m(u) = 0.
-2, -1, 0, 2
Let h(z) be the first derivative of -3 + 2*z - z**4 + 10/3*z**3 - 4*z**2. Solve h(q) = 0.
1/2, 1
Suppose 11 = -2*h + 15. Suppose -v + 5 = 0, -2*n - 2*v = h*v - 24. Let -10/3*t**3 + 10/3*t - 4/3 + 4/3*t**n = 0. Calculate t.
-1, 2/5, 1
Let s = -296/85 + 66/17. Factor 1/5 - 2/5*b**2 + 1/5*b**5 - s*b**3 + 1/5*b + 1/5*b**4.
(b - 1)**2*(b + 1)**3/5
Let p = -13 - -11. Let m be ((-2)/(-4))/(p/(-3)). Factor -1/4 - m*b - 3/4*b**2 - 1/4*b**3.
-(b + 1)**3/4
Solve 4 + 19*l - 8*l**2 - 1 + 9*l**3 + 41*l**2 = 0.
-3, -1/3
Factor 8/3*w + 4/3*w**3 + 2/3 + 10/3*w**2.
2*(w + 1)**2*(2*w + 1)/3
Let q(u) = 6*u**5 - 6*u**4 - 19*u**3 + 7*u**2 + 7*u. Let g(y) = -2*y**5 + 2*y**4 + 6*y**3 - 2*y**2 - 2*y. Let h(l) = -7*g(l) - 2*q(l). Solve h(i) = 0.
-1, 0, 2
What is n in 0*n + 1/2*n**2 + 0 + 1/2*n**3 = 0?
-1, 0
Suppose -2/3 + 1/3*x**2 + 1/3*x = 0. What is x?
-2, 1
Let i be 14/(-35)*(-11 + 0 + 6). What is f in -f**4 - 1/2*f + 3*f**i - 1 - 1/2*f**3 = 0?
-2, -1/2, 1
Let x = 394/5 - 386/5. Solve x + 2/5*l**2 - 8/5*l = 0 for l.
2
Factor -5*k + 5/2*k**2 - 20.
5*(k - 4)*(k + 2)/2
Let g(l) be the third derivative of -l**7/1155 + l**6/660 + 3*l**2. Factor g(p).
-2*p**3*(p - 1)/11
Solve -8/5*g**5 + 0*g + 0*g**2 + 0 + 2/5*g**3 + 6/5*g**4 = 0.
-1/4, 0, 1
Suppose 4 + 32 = 9*m. Let q(t) be the first derivative of -44*t**2 + 16*t + 567/2*t**m - 60*t**3 + 2. Suppose q(s) = 0. What is s?
-2/7, 2/9
Let k(n) = -n**2 + 4*n + 5. Let l = -13 - -18. Let c be k(l). What is a in 1/2*a**4 - 1/4*a**3 + 0*a - 1/4*a**5 + c + 0*a**2 = 0?
0, 1
Let x(i) be the second derivative of 0 + 3/10*i**6 + i**2 - i + 11/4*i**4 + 5/2*i**3 + 29/20*i**5. Let x(m) = 0. Calculate m.
-1, -2/9
Let h(g) = -g. Suppose -2*k - 4 = -y, k - y + 20 = -5*y. Let v be h(k). Find i such that 24*i**3 + 2 - 26*i**4 - 24*i**5 - 3 + 3 - v + 28*i**2 = 0.
-1, -1/3, 1/4, 1
Let n be 8*((-4)/4)/(-4). Let m(f) be the second derivative of 0 - f**2 - 5/6*f**3 - 7/30*f**6 - n*f + 3/4*f**4 + 1/4*f**5. Factor m(d).
-(d - 1)**2*(d + 1)*(7*d + 2)
Let i(a) be the second derivative of 1/18*a**4 + 2*a + 0 - 4/9*a**3 + 4/3*a**2. Factor i(v).
2*(v - 2)**2/3
Suppose -2*u - 120 = -6*u. Let i = u - 28. Suppose 3/5*a - 2/5 - 1/5*a**i = 0. Calculate a.
1, 2
Suppose 0 = 7*x - 5*x + 3*z + 8, 4*x + 4*z + 8 = 0. Factor 6/11*j + 4/11*j**x + 2/11.
2*(j + 1)*(2*j + 1)/11
Let k(z) = -z**2 - z - 1. Let d(s) = 8*s**2 - 14*s - 62. Let c(f) = -2*d(f) - 20*k(f). Solve c(b) = 0.
-6
Let u(f) be the second derivative of -f**4/84 - f**3/21 - f**2/14 + 10*f. Factor u(s).
-(s + 1)**2/7
Let f = 21/8 + -89/40. Determine x, given that -f*x + 0 - 6/5*x**3 + 2/5*x**4 + 6/5*x**2 = 0.
0, 1
Factor -32/5*h + 28/5*h**4 - 72/5*h**3 + 16*h**2 + 0 - 4/5*h**5.
-4*h*(h - 2)**3*(h - 1)/5
Let n = 0 + 0. Let t = -7 - -9. Factor n + 4/3*w + 2*w**t - 10/3*w**3.
-2*w*(w - 1)*(5*w + 2)/3
Let h be 17/(-18) + 2 - (1 - 0). Let r(s) be the second derivative of 0*s**2 - 1/18*s**4 - h*s**3 - 1/60*s**5 + 2*s + 0. Factor r(t).
-t*(t + 1)**2/3
Suppose 7*d = 4*d + 3. Let s = d + 1. Factor 1/3*i**5 + 0 + 1/3*i + 0*i**4 + 0*i**s - 2/3*i**3.
i*(i - 1)**2*(i + 1)**2/3
Let h(x) 