 1
Let y(i) be the first derivative of i**6/70 - 3*i**5/70 + i**3/7 - 3*i**2/14 - 13*i - 5. Let q(d) be the first derivative of y(d). Factor q(a).
3*(a - 1)**3*(a + 1)/7
Let v be (-3)/(1 + -4 + 2). Let q = 152/9 - 751/45. Factor 0 - q*m**v + 0*m**2 + 4/5*m.
-m*(m - 2)*(m + 2)/5
Suppose -3 + 7*j - 17/4*j**2 - 3/4*j**3 + 5/4*j**4 - 1/4*j**5 = 0. What is j?
-2, 1, 2, 3
Let p(i) be the third derivative of i**8/112 + 9*i**7/70 + 9*i**6/20 - i**5/5 - 3*i**4 + 87*i**2. Suppose p(h) = 0. What is h?
-6, -2, 0, 1
Let n(o) be the first derivative of 1/2700*o**6 + 4 + 1/225*o**5 + 0*o + 1/45*o**4 - 5/3*o**3 + 0*o**2. Let z(d) be the third derivative of n(d). Factor z(v).
2*(v + 2)**2/15
Suppose -9172*t = -9186*t + 112. Factor -4/5*d**3 + t*d**2 + 32/5 - 68/5*d.
-4*(d - 8)*(d - 1)**2/5
Let g = 108 + -108. Let c(x) be the second derivative of g - 11/21*x**3 + 3*x - 2/7*x**2 - 8/21*x**4 - 1/10*x**5. Solve c(u) = 0.
-1, -2/7
Let o = 150 + -148. Suppose -3*x - 1 = -r, -5 = -o*r + 11*x - 8*x. Factor -16/5*a**3 + 0 - 8/5*a - r*a**2 - 4/5*a**4.
-4*a*(a + 1)**2*(a + 2)/5
Let g(q) be the second derivative of 0*q**3 + 1/4*q**5 + 5/6*q**4 + 0*q**2 - 1/6*q**6 + 4*q + 0. Factor g(y).
-5*y**2*(y - 2)*(y + 1)
Suppose -z - 9 = 3*c, c = -6 + 2. Let w(d) = d**3 + 526*d**2 - 2653*d - 6. Let t be w(5). Factor t*m - 16/3*m**z + 44/3*m**2 + 0.
-4*m*(m - 3)*(4*m + 1)/3
Suppose 12*t = 15*t - 36. Factor -l**3 + 2 - 7*l**2 + t*l**2 - l**2 - 5*l.
-(l - 2)*(l - 1)**2
Let d(x) be the second derivative of -x**6/160 + 3*x**5/80 - x**4/16 - x**2/2 + 18*x. Let k(c) be the first derivative of d(c). What is v in k(v) = 0?
0, 1, 2
Let j(z) be the third derivative of 2*z**2 + 1/18*z**4 + 0*z**3 + 0 + 7*z - 2/45*z**5 + 1/90*z**6. Find f such that j(f) = 0.
0, 1
Let b(n) be the third derivative of -n**8/3360 + n**7/980 - n**6/1260 - n**4/4 - 13*n**2. Let v(y) be the second derivative of b(y). Let v(q) = 0. Calculate q.
0, 2/7, 1
What is i in -5*i**4 + 2272*i**3 + 110*i**2 + 120 - 1135*i**3 + 220*i - 1132*i**3 = 0?
-2, -1, 6
Suppose -1/3*j**4 + 5/3*j**3 + 0 + 13/3*j**2 + 7/3*j = 0. Calculate j.
-1, 0, 7
Let g(o) = 5*o**2 + 14*o - 16. Let f(c) = -16*c**2 - 42*c + 48. Let x(u) = -3*f(u) - 10*g(u). Factor x(a).
-2*(a - 1)*(a + 8)
Let h(b) = 12*b - 44. Let a be h(4). Factor 6*v**2 - 68*v**3 + 70*v**3 + v**a - 5*v**2.
v**2*(v + 1)**2
Let x(r) = -2*r**2 + 56*r + 41. Let p(j) = -j**2 + 1. Let k(h) = -20*p(h) + 4*x(h). Suppose k(b) = 0. Calculate b.
-18, -2/3
Let z(o) = -2*o**3 - 2*o**2 + 10*o + 3. Let x(j) = 2*j**3 + 2*j**2 - 12*j - 4. Let y(c) = 3*x(c) + 4*z(c). Factor y(k).
-2*k*(k - 1)*(k + 2)
Let x = 5 - 8. Let t(b) = -5*b**4 - b**3 + 3*b**2 - 3*b - 3. Let l(m) = 16*m**4 + 4*m**3 - 10*m**2 + 10*m + 10. Let y(n) = x*l(n) - 10*t(n). Solve y(p) = 0.
0, 1
Let l(q) be the first derivative of 5 - 3/5*q**5 - 3/8*q**4 - 1/4*q**6 + 0*q**3 + 0*q**2 + 0*q. Factor l(m).
-3*m**3*(m + 1)**2/2
Suppose -4*a + 36 = -3*a. Factor 352*q**3 + a*q + 350*q**3 + 2*q**4 - 6*q**2 - 710*q**3.
2*q*(q - 3)**2*(q + 2)
Let k(l) = l**3 + 4*l**2 + 8*l + 67. Let y be k(-5). Factor 1/2*i**y + 1/2*i + 0.
i*(i + 1)/2
Let i(t) = t**2 - 5*t - 9. Let k be i(-2). Let s be k/(-30) - (-20)/24. Suppose -s*l + 0 + 2/3*l**2 = 0. What is l?
0, 1
Let k(a) be the first derivative of -3*a**5/5 - 21*a**4/2 + 31*a**3 - 24*a**2 - 195. Factor k(o).
-3*o*(o - 1)**2*(o + 16)
Let n be 275/(-5)*(-4)/(-50). Let k = -21/5 - n. Factor -2/5*x + k + 1/5*x**2.
(x - 1)**2/5
Suppose -a + 5 = -6*a + 3*o, -3*a - 4*o = -26. Factor 0 + 1 + 2 - 5 - 3*x - x**a.
-(x + 1)*(x + 2)
Let q(d) be the second derivative of d**6/45 + d**5/5 - 4*d**4/9 - 2*d**3/3 + 7*d**2/3 + 305*d. Suppose q(z) = 0. Calculate z.
-7, -1, 1
Let k = 1 - 24. Let c = -17 - k. Let -h - 10 - c*h + 5*h**2 + 2*h = 0. Calculate h.
-1, 2
Let j(l) be the first derivative of -2*l**2 + 8*l - 26 - 4/3*l**3. Determine g, given that j(g) = 0.
-2, 1
Let b(h) be the second derivative of -10*h**4/3 - 12*h**3 - 81*h**2/5 + 184*h. Find r such that b(r) = 0.
-9/10
Let g(f) be the first derivative of 4*f**3/3 - 76*f**2 + 148*f - 129. Determine c so that g(c) = 0.
1, 37
Let 80 - 8 + 25*d**4 - 163*d**5 + 51*d**3 + 166*d**5 - 114*d - 37*d**2 = 0. What is d?
-4, -3, 2/3, 1
Suppose 2*x - 7 = -3. Suppose 43*s**3 - 22*s**3 - 23*s**3 + 2*s**4 - 2*s**x + 2*s**5 = 0. Calculate s.
-1, 0, 1
Let z(v) be the third derivative of -v**7/420 + 37*v**6/900 - 7*v**5/150 + 13*v**3/6 - 7*v**2. Let n(w) be the first derivative of z(w). Factor n(f).
-2*f*(f - 7)*(5*f - 2)/5
Suppose q = -2*q + 21. Let b(s) = -9*s**2 - 36*s - 80. Let r(g) = 17*g**2 + 73*g + 160. Let y(u) = q*b(u) + 4*r(u). Factor y(h).
5*(h + 4)**2
Let h(p) = 2*p**3 + 16*p**4 - 28*p**4 + 15*p**4 - p**2. Let j(d) = -25*d**4 - 16*d**3 + 7*d**2. Let y(c) = -51*h(c) - 6*j(c). Factor y(m).
-3*m**2*(m - 1)*(m + 3)
Let z(u) be the second derivative of -2*u**6/135 + 4*u**5/45 - 32*u**3/27 + 32*u**2/9 + 3*u - 30. Find p such that z(p) = 0.
-2, 2
Let r be ((-4)/(-3))/((-16)/(-48)). Let c(q) be the first derivative of -1/3*q**3 - q**2 - q - r. Factor c(g).
-(g + 1)**2
Let y(b) be the first derivative of -2 - 1/10*b**2 - 7/15*b**3 - 2/5*b**4 + 16/25*b**5 + 0*b. Factor y(m).
m*(m - 1)*(4*m + 1)**2/5
Let x(g) be the first derivative of 2*g**3/21 + 102*g**2/7 + 5202*g/7 - 2. Suppose x(b) = 0. Calculate b.
-51
Let v(j) be the third derivative of -j**6/10 + 28*j**5/15 + 7*j**4/2 - 20*j**3/3 + 4*j**2 + 74. Determine r, given that v(r) = 0.
-1, 1/3, 10
Let u be 23/(115/(-66)) - -14. Let -8/5*t**3 + u*t - 8/5 + 16/5*t**2 - 8/5*t**4 + 4/5*t**5 = 0. Calculate t.
-1, 1, 2
Let f = 5754 - 5752. Factor 0*a - 18/5*a**3 + 18/5*a**f + 0 + 6/5*a**4 - 2/15*a**5.
-2*a**2*(a - 3)**3/15
Let y(k) be the first derivative of -k**7/7 - 2*k**6/3 - k**5 + 5*k**3/3 + 2*k**2 - 19*k + 6. Let g(p) be the first derivative of y(p). What is d in g(d) = 0?
-1, 2/3
Suppose 0*u - 15 = 5*u. Let a be 2 + (5/u - (7 - 7)). Factor 0*q**2 - a*q + 0 + 1/3*q**3.
q*(q - 1)*(q + 1)/3
Let o(l) be the second derivative of l**6/6 - 5*l**5/4 + 5*l**4/6 + 50*l**3/3 - 60*l**2 + 25*l - 1. Factor o(g).
5*(g - 3)*(g - 2)**2*(g + 2)
Let n(r) = -2*r**2 + r - 1. Let l(w) = w**2 - 4*w + 19. Let s(h) = -l(h) - n(h). Factor s(t).
(t - 3)*(t + 6)
Let n = -103 - -103. Let w(g) be the third derivative of g**2 + 0*g**4 - 8/735*g**7 + 0 - 1/420*g**6 + 0*g + 1/105*g**5 - 5/1176*g**8 + n*g**3. Factor w(d).
-2*d**2*(d + 1)**2*(5*d - 2)/7
Suppose 139*s - 4 = 137*s. Let f = 5 + -1. Factor -g**2 + s*g**4 + 19*g**3 - 6*g**4 - 17*g**3 + 3*g**f.
-g**2*(g - 1)**2
Let q = 1336 - 33397/25. Let p(w) be the first derivative of 0*w**4 - 3/5*w + 0*w**2 + 2/5*w**3 - q*w**5 - 9. Factor p(y).
-3*(y - 1)**2*(y + 1)**2/5
Let 2*j**5 - 19*j**3 + 10*j - 16*j**2 + 7*j**3 + 32*j**2 - 12 - 4*j**4 = 0. Calculate j.
-2, -1, 1, 3
Let u(w) be the first derivative of 2*w**4 + 4/3*w**3 + 4*w + 1/3*w**6 - 5*w**2 - 8/5*w**5 - 51. Factor u(g).
2*(g - 2)*(g - 1)**3*(g + 1)
Let n(s) be the second derivative of s**5/12 + 25*s**4/12 + 125*s**3/6 - 45*s**2/2 + 14*s. Let w(d) be the first derivative of n(d). Factor w(u).
5*(u + 5)**2
Let m(x) be the third derivative of -x**9/272160 + x**8/45360 - x**7/22680 + x**5/15 - 9*x**2. Let l(w) be the third derivative of m(w). Factor l(h).
-2*h*(h - 1)**2/9
Factor 8*v**3 + 2*v**4 + 3*v - 1/3*v**5 + 26/3*v**2 + 0.
-v*(v - 9)*(v + 1)**3/3
Factor 50*t**3 - 5*t**4 + 35*t**2 + 19050*t - 18870*t - 200*t**2.
-5*t*(t - 4)*(t - 3)**2
Let q(a) be the first derivative of -a**4/14 + 8*a**3/21 + 11*a**2/7 + 12*a/7 - 122. Determine r so that q(r) = 0.
-1, 6
Factor -306/5*u + 303/5*u**2 + 3/5.
3*(u - 1)*(101*u - 1)/5
Factor 0 + 78/5*k**2 - 339/5*k**3 + 0*k + 231/5*k**4.
3*k**2*(7*k - 2)*(11*k - 13)/5
Factor -1/3*z**4 - 4/3 - 4/3*z + 2/3*z**3 + z**2.
-(z - 2)**2*(z + 1)**2/3
Suppose 0 = 5*q - 9 + 4. Solve 5*c**2 - q - 14 + 5*c - 15 = 0.
-3, 2
Let j be (30512/(-14))/(-4) - -2. Let f = j - 546. Solve -2/7*g**4 + f*g + 4/7 - 2/7*g**2 - 6/7*g**3 = 0.
-2, -1, 1
Let g(l) be the third derivative of -l**6/40 + 21*l**5/20 + l**4/8 - 21*l**3/2 - l**2 + 160*l. Find k such that g(k) = 0.
-1, 1, 21
Let y(t) be the first derivative of -t**6/18 + 13*t**5/15 - 4*t**4 + 4*t**3 - 70. Factor y(c).
-c**2*(c - 6)**2*(c - 1)/3
Factor 208*c**5 - 206*c**5 + 206*c - 260*c**2 + 144*c**3 - 60 