e (-4)/6 - 16/12. Let u be 3/(q + 7/2). Factor u*l**2 - l + l**5 - 1 - l**4 + 3*l**5 + 2*l**3 - 5*l**5.
-(l - 1)**2*(l + 1)**3
Factor 10*q**3 + 8*q + 6*q**4 + 0 - 64/3*q**2.
2*q*(q + 3)*(3*q - 2)**2/3
Suppose 15 = 3*v - 6. Let 16*l**2 - 10*l**2 - l - v*l**2 = 0. What is l?
-1, 0
Let p(i) be the third derivative of -i**6/280 - i**5/210 + i**4/168 + i**2. Factor p(o).
-o*(o + 1)*(3*o - 1)/7
Let h be -7 - 205/(-30) - 6/(-4). Factor h*a + 1/3*a**3 + 0 + 4/3*a**2.
a*(a + 2)**2/3
Let a(v) be the first derivative of v**7/420 - v**6/20 + 9*v**5/20 - 9*v**4/4 - 4*v**3/3 + 1. Let n(w) be the third derivative of a(w). Factor n(o).
2*(o - 3)**3
Let -5/2*n + 1/2*n**3 - 1/2*n**2 - 3/2 = 0. What is n?
-1, 3
Let u be 2*4*5/10. Let o(d) be the first derivative of -1/4*d**u + 2 + 1/3*d**3 - d + 1/2*d**2. Factor o(p).
-(p - 1)**2*(p + 1)
Suppose -7*s = -3*s. Factor 2/9*i**2 + 0*i + s.
2*i**2/9
Let l(r) be the first derivative of 5*r**2 - 2*r - 3 - 8/3*r**3. Factor l(k).
-2*(k - 1)*(4*k - 1)
Let s be -5*(2 + 1 + -4). Let h be (2/1)/(30/s). Factor 2/3 - p**2 + h*p.
-(p - 1)*(3*p + 2)/3
Determine s so that 1404*s**2 + 6480*s + 58*s**3 + 5184 + 66*s**3 + 3*s**4 - 13*s**3 = 0.
-12, -1
Let u(r) be the second derivative of 0 - 3/80*r**5 - 1/16*r**4 - 1/24*r**3 - 1/120*r**6 + 0*r**2 + 2*r. Factor u(a).
-a*(a + 1)**3/4
Let a(d) be the first derivative of -4*d**5/5 + 7*d**4/5 + 4*d**3/5 - 14*d**2/5 + 8*d/5 + 41. Find o, given that a(o) = 0.
-1, 2/5, 1
Let t(d) be the first derivative of d**3/12 + 7*d**2/8 + 3. Solve t(c) = 0.
-7, 0
Let t(v) = -2*v**3 + 33*v**2 - 60*v + 43. Let p(i) = 15*i**3 - 265*i**2 + 480*i - 345. Let o(b) = 3*p(b) + 25*t(b). Let o(z) = 0. Calculate z.
2
Let i = 958/11 + -87. Let b(k) be the first derivative of 4/33*k**3 - 2/55*k**5 - i*k**4 - 2 + 1/11*k**2 + 1/33*k**6 - 2/11*k. Factor b(u).
2*(u - 1)**3*(u + 1)**2/11
Let z = 49 - 49. Let u(j) be the third derivative of z*j + 0*j**6 + 0 - 1/30*j**5 - 1/24*j**4 + j**2 + 1/336*j**8 + 0*j**3 + 1/105*j**7. Solve u(o) = 0 for o.
-1, 0, 1
Let q be (-26)/(-9) + (-8)/36. Factor -16/3*t**3 + 2*t**4 + 0*t + 0 - q*t**2 + 6*t**5.
2*t**2*(t - 1)*(3*t + 2)**2/3
Let 0 - 45/4*g**2 + 5*g = 0. Calculate g.
0, 4/9
Suppose m + 4*w = 1 - 5, 5*m = -3*w - 3. Suppose -5*x + 3*i + 6 = 0, 4*x - 9 = i - m. Factor 2/9*u - 2/9*u**2 + 0 - 2/9*u**x + 2/9*u**4.
2*u*(u - 1)**2*(u + 1)/9
Let m(u) = -u**2 - 6*u + 18. Let d be m(-8). Let g(x) be the first derivative of 0*x - 1/3*x**3 + 1/2*x**d + 2. Suppose g(p) = 0. What is p?
0, 1
Let f be (-9)/(-2)*(-12)/(-9). Factor 8*t**2 + 0*t**5 - 8*t - 4*t**4 - 3*t**5 - 2*t**5 + f*t**3 + 3*t**5.
-2*t*(t - 1)**2*(t + 2)**2
Let s(m) be the second derivative of -m**4/24 - m**3/3 - 3*m**2/4 + 5*m. Factor s(b).
-(b + 1)*(b + 3)/2
Let t be 1/(10/3 - 3). Let q be t*1 - (-45)/(-20). Suppose j**3 + q*j**2 - 1/4*j + 0 = 0. What is j?
-1, 0, 1/4
Let q(c) be the first derivative of 4*c - 13/2*c**4 + 6/5*c**5 - 11*c**2 + 3 + 38/3*c**3. Find a such that q(a) = 0.
1/3, 1, 2
Let s be (-12)/15*15/2. Let a be (-16)/s*18/84. Factor a*k - 2/7*k**2 - 2/7.
-2*(k - 1)**2/7
Suppose -3*p = 2 - 20. Let y(a) be the second derivative of 0*a**2 - 1/15*a**p + 0 + 1/10*a**5 - 1/21*a**7 + 1/6*a**4 - 2*a + 0*a**3. Factor y(r).
-2*r**2*(r - 1)*(r + 1)**2
Let w(i) be the second derivative of i**5/40 - i**4/12 - 7*i**3/12 - i**2 + 2*i + 32. Factor w(l).
(l - 4)*(l + 1)**2/2
Let i(h) be the third derivative of 1/24*h**4 - 2*h**2 + 0*h**3 + 1/30*h**5 + 0*h + 1/120*h**6 + 0. Factor i(q).
q*(q + 1)**2
Let d(n) be the first derivative of 5*n**3 + 0*n - 1 - 3*n**4 + 3/5*n**5 - 3*n**2. Solve d(g) = 0 for g.
0, 1, 2
Let o be 10/3 - 5*4/10. Let -2/3*h + o*h**3 + 4/9*h**4 + 4/9 - 8/9*h**2 - 2/3*h**5 = 0. Calculate h.
-1, 2/3, 1
Let h be 161/237 + 12/(-18). Let i = h + 625/553. Suppose -2/7*j**2 + i*j - 8/7 = 0. What is j?
2
Let d(o) = o**2 - o - 1. Let w(x) = x**2 - 6*x + 20. Let u(h) = -h + 4. Let a(g) = 22*u(g) - 4*w(g). Let v(i) = -a(i) - 6*d(i). Let v(b) = 0. What is b?
1
Let n be 18/(-24) - (1 - 2). Solve 1/4*j**3 + n*j + 0 - 1/2*j**2 = 0.
0, 1
Let z(b) be the first derivative of -3*b**5/5 - 21*b**4/4 - 18*b**3 - 30*b**2 - 24*b + 17. Factor z(q).
-3*(q + 1)*(q + 2)**3
Let m(u) be the second derivative of -u**7/84 + u**6/15 - u**5/8 + u**4/12 - 8*u. Factor m(j).
-j**2*(j - 2)*(j - 1)**2/2
Let o(f) be the second derivative of -f**7/70 + f**6/40 - 5*f**2/2 - 4*f. Let s(q) be the first derivative of o(q). What is g in s(g) = 0?
0, 1
Let y(z) be the third derivative of 4*z**7/525 - 11*z**6/300 + 3*z**5/50 - z**4/60 - z**3/15 - 6*z**2. Factor y(r).
2*(r - 1)**3*(4*r + 1)/5
Let p(c) be the third derivative of -c**5/90 + c**4/12 + 3*c**2. Find b such that p(b) = 0.
0, 3
Let o = -5 + 5. Suppose 5*p - s = 5, 4*p + 5*s + 1 + 24 = o. Factor 0*f - 3/2*f**4 + p + 0*f**3 + 3/2*f**2.
-3*f**2*(f - 1)*(f + 1)/2
Let q(m) be the third derivative of m**7/840 + m**6/480 - m**5/20 - 7*m**4/24 - 2*m**3/3 + 20*m**2. Factor q(y).
(y - 4)*(y + 1)*(y + 2)**2/4
Find l, given that -14/3*l**2 + 4 - 10/3*l**3 + 2/3*l**4 + 10/3*l = 0.
-1, 1, 6
Suppose 2 = 2*y - 4. Let d(i) be the third derivative of 0 - 1/210*i**5 + 0*i + y*i**2 + 2/21*i**3 - 1/84*i**4. Factor d(g).
-2*(g - 1)*(g + 2)/7
Let z(q) be the second derivative of 0*q**3 + 0 + 1/4*q**4 + q - 3/2*q**2. Factor z(k).
3*(k - 1)*(k + 1)
Suppose 23 + 7 = 15*h. Solve 23/4*z + 7/4*z**h + 3/2 = 0.
-3, -2/7
Let w(n) be the first derivative of n**6/6 - n**5/5 - n**4/2 + 2*n**3/3 + n**2/2 - n + 3. Let w(a) = 0. Calculate a.
-1, 1
Suppose 5*c = 2*c + 90. Find x such that -34*x**3 + 2*x + 0*x - 7*x**2 + c*x**3 = 0.
-2, 0, 1/4
Let j be (-4)/(-14) + 52/14. Let k(h) be the first derivative of 0*h + 1/8*h**j + 1/8*h**2 - 1/4*h**3 + 3. Factor k(d).
d*(d - 1)*(2*d - 1)/4
Let c(t) be the first derivative of 6*t**6 + 0*t - 8*t**4 - 16/3*t**3 - 3 + 0*t**2 + 12/5*t**5. Factor c(x).
4*x**2*(x - 1)*(3*x + 2)**2
Suppose 4*s = -4*g + 32, g - 5*s + 10 = -0*g. Determine n, given that 0*n**3 + 3/2*n + 0 - 3*n**2 + 3*n**4 - 3/2*n**g = 0.
-1, 0, 1
Let i(z) be the first derivative of -z**7/14 - z**6/3 - 3*z**5/5 - z**4/2 - z**3/6 + 3*z + 6. Let y(h) be the first derivative of i(h). What is q in y(q) = 0?
-1, -1/3, 0
Let s(t) be the third derivative of t**7/105 + t**6/30 + t**5/30 - 7*t**2. Determine d, given that s(d) = 0.
-1, 0
Let u(p) = 4*p**5 - 4*p**3 - 8*p**2 - 9*p - 1. Let t(b) = b**5 - b**4 - b**3 + b**2 + b + 1. Let o(f) = -3*t(f) + u(f). Suppose o(k) = 0. What is k?
-2, -1, 2
Let n(r) = -4*r**2 - 12*r - 11. Let w(k) = -12*k**2 - 36*k - 32. Let t(f) = 8*n(f) - 3*w(f). Factor t(m).
4*(m + 1)*(m + 2)
Suppose -6*w = -17 - 7. Suppose -j = 5*h - w - 1, 3*j = 5*h - 25. Factor -n - 1/2*n**h - 1/2.
-(n + 1)**2/2
Let k(a) = 15*a**5 + 5*a**4 + 10*a**3 - 30*a**2 - 5*a - 15. Let h(n) = -n**5 + n**2 + 1. Let w(z) = -20*h(z) - k(z). Determine g so that w(g) = 0.
-1, 1
Let k be 55/(-88) + (-2)/(-3). Let s(y) be the first derivative of 0*y**2 + k*y**6 - 2 - 1/10*y**5 + 0*y + 0*y**4 + 0*y**3. Suppose s(o) = 0. Calculate o.
0, 2
Suppose r = -4*r - 4*s + 6, 0 = -2*r - 4*s. Let o(x) be the first derivative of 2 - 4/21*x**3 + 1/14*x**4 + 0*x + 0*x**r. Factor o(l).
2*l**2*(l - 2)/7
Let i be (((-4)/(-7))/1)/((-6)/(-21)). Determine u, given that 1/3*u**5 - u**3 + 0*u + 0 - 2/3*u**i + 0*u**4 = 0.
-1, 0, 2
Let r(n) be the third derivative of -n**5/210 + n**3/21 + 8*n**2. Factor r(a).
-2*(a - 1)*(a + 1)/7
Let q(i) be the first derivative of -2*i**3/57 - 3*i**2/19 - 4*i/19 + 2. Solve q(n) = 0.
-2, -1
Suppose -q + 8 = 3*q, 3*g = -q + 14. Solve 8/5 - 4/5*c**3 - 6/5*c**2 + 2/5*c**g + 8/5*c = 0.
-1, 2
Suppose -3*w = 3*l - 15, -3*w = -7*w + 8. Suppose 1 - 19 = -l*h. Factor 0*i**2 - 4/3*i**3 + 0 + 0*i + h*i**4.
2*i**3*(9*i - 2)/3
Let x(d) be the third derivative of -1/16*d**4 - 5*d**2 + 1/120*d**5 + 0*d + 0*d**3 + 0. Factor x(o).
o*(o - 3)/2
Suppose 0 = 3*q - 7*q + 3*x + 1513, 740 = 2*q + 4*x. Let y = -1874/5 + q. Factor y*f + 1/5 + 9/5*f**2.
(3*f + 1)**2/5
Suppose 0 = x + 5*n - 4, -3*x - 2*x - 2*n - 26 = 0. Let d be 4/x - 30/9. Let m(g) = 5*g**2 - 5. Let c(i) = -6*i**2 + 6. Let f(a) = d*c(a) - 5*m(a). Factor f(h).
-(h - 1)*(h + 1)
Let m(d) = 7*d**4 - 92*d**3 + 669*d**2 - 1283*d - 2045. Let g(i) = 8*i**4 - 92*i**3 + 668*i**2 - 1284*i - 2044. Let x(v) = -3*g(v) + 4