g = 4*z + 9. Let b be (8 - (-330)/(-40))/(z - 1). Let -1/2*k + b*k**2 - 2 = 0. What is k?
-2, 4
Let o(m) be the first derivative of m**4/14 + 34*m**3 + 4368*m**2 - 66248*m - 4200. Factor o(a).
2*(a - 7)*(a + 182)**2/7
Let y be 5/2 - (20 + 18/(216/(-246))). Factor -t - 1/4*t**y + 0 - 5/4*t**2.
-t*(t + 1)*(t + 4)/4
Let l be 232/(-290) - (-2 + 28/(-35)). Factor -3/7*a**l - 27/7 + 18/7*a.
-3*(a - 3)**2/7
Let p(y) be the third derivative of -5 + 1/180*y**5 - 1/12*y**4 - 4*y**2 - 7/18*y**3 + 0*y. Suppose p(b) = 0. Calculate b.
-1, 7
Let q(f) be the first derivative of -f**4/36 + 16*f**3/9 - 128*f**2/3 - 77*f + 53. Let p(g) be the first derivative of q(g). Determine d so that p(d) = 0.
16
Let t(x) be the third derivative of x**8/2184 - x**7/1365 - 11*x**6/780 + 3*x**5/130 + 3*x**4/26 - 575*x**2. Suppose t(u) = 0. Calculate u.
-3, -1, 0, 2, 3
Factor 25581*i**2 - 6601*i**2 + 125280*i + 35314 + 197966 + 149*i**3 + 5*i**4 + 431*i**3.
5*(i + 4)**2*(i + 54)**2
Let c(s) = s - 4 - 48 - 2*s - 105*s**2 + 106*s**2. Let q be c(8). Solve 0 - 3/2*g**2 - g**3 + 1/2*g**q + 0*g = 0 for g.
-1, 0, 3
Let j(f) be the second derivative of -f**5/20 - 25*f**4/12 + 31*f**3 - 3636*f. Factor j(w).
-w*(w - 6)*(w + 31)
Factor -800/7*c**2 + 1040/7*c + 1/7*c**5 - 40/7*c**4 + 40*c**3 - 512/7.
(c - 32)*(c - 2)**4/7
Suppose 36*q - 30*q = -1326. Let m = -221 - q. Suppose m + 0*c**2 - 2/11*c + 2/11*c**3 = 0. Calculate c.
-1, 0, 1
Let r(s) be the third derivative of -s**8/378 + 37*s**7/945 - 61*s**6/540 - 23*s**5/270 + 65*s**4/108 - 14*s**3/27 - 10767*s**2. What is a in r(a) = 0?
-1, 1/4, 1, 2, 7
Let o be (-340)/2805*(-55)/20. Factor o*a**3 + 1/3*a**2 + 1 - 5/3*a.
(a - 1)**2*(a + 3)/3
Let i(v) = 3 - 2*v + 2 - 7 - 2*v. Let b be i(-2). Factor -69*f**5 - b*f**4 + 135*f**5 - 69*f**5 - 3*f**3.
-3*f**3*(f + 1)**2
Factor -123/4 - 625/4*s**5 - 77375/4*s**4 - 9235/2*s**2 - 30825/2*s**3 - 2461/4*s.
-(s + 123)*(5*s + 1)**4/4
Let q(x) = x**2 - 34. Let m be q(6). Determine b so that -6 + 445*b**2 - b + b**3 - 466*b**m + 27 = 0.
-1, 1, 21
Let q(u) be the first derivative of u**5 + 75*u**4/2 + 220*u**3 + 445*u**2 + 375*u - 12121. Factor q(y).
5*(y + 1)**2*(y + 3)*(y + 25)
Factor -1/3 + 1/9*f**2 - 2/9*f.
(f - 3)*(f + 1)/9
Let x(v) = 3*v**2 + 9*v - 6. Let q(d) = 2*d**2 + 10*d - 7. Let u(y) = 4*q(y) - 3*x(y). Let t be u(1). Factor -2 - l - 1/8*l**t.
-(l + 4)**2/8
Let h(o) = 15*o**2 + 1240*o + 25225. Let a(g) = -5*g**2 - 413*g - 8408. Let t = 280 + -270. Let v(p) = t*a(p) + 3*h(p). Determine w, given that v(w) = 0.
-41
Let u(i) = 15*i**2 + 190*i + 1610. Let w(g) = -g**2 - g + 1. Let n = -81 + 71. Let m(q) = n*w(q) - u(q). Suppose m(r) = 0. What is r?
-18
Let n(r) be the third derivative of -16/9*r**4 + 4/315*r**7 + 0*r + 0*r**3 - 2/15*r**6 + 18 + 7*r**2 - 8/9*r**5 + 1/252*r**8. Find c, given that n(c) = 0.
-2, 0, 4
Let u = 10620 - 10618. Solve 10/19*b**3 - 8/19*b - 28/19*b**u + 48/19 = 0.
-6/5, 2
Let 4008/11*u**2 + 3456/11 - 28/11*u**4 + 2/11*u**5 - 7200/11*u - 238/11*u**3 = 0. Calculate u.
-12, 1, 12
Let w(r) = r**2 + 7*r + 2. Let k be w(-7). Let h = 2128 - 2126. Factor k*j - h*j**3 - 3*j**4 + 7*j + 3*j**5 + 3*j**2 - 3*j - 7*j**3.
3*j*(j - 2)*(j - 1)*(j + 1)**2
Solve 52*v**3 - 9341*v + 61*v**2 + 9485*v + 4*v**4 + 33*v**2 + 98*v**2 = 0 for v.
-6, -1, 0
Let x = 598850 - 598832. Suppose 0 + 0*s + 21/5*s**5 + 6*s**2 - x*s**4 - 81/5*s**3 = 0. What is s?
-1, 0, 2/7, 5
Suppose -64*v = -4*w - 60*v - 16, 0 = 4*v - 24. Let c(d) be the first derivative of 2/5*d**4 - 2 - 2/5*d**3 + 0*d + 0*d**w - 2/25*d**5. Factor c(g).
-2*g**2*(g - 3)*(g - 1)/5
Find o such that -4/9*o**4 + 32/3 + 280/9*o + 64/3*o**2 + 10/3*o**3 = 0.
-2, -1/2, 12
Suppose -20307*k = -20316*k + 54. Let b(l) be the third derivative of 0*l - l**3 + 33*l**2 - 1/12*l**4 + 0 + 1/10*l**5 + 1/60*l**k. Suppose b(y) = 0. What is y?
-3, -1, 1
Let t be (276/(-21) - -15 - 16) + 19. Determine q, given that t*q**2 + 2/7*q**4 - 20/7*q + 0 - 16/7*q**3 = 0.
0, 1, 2, 5
Let t(r) be the second derivative of r**6/420 + r**5/105 - r**4/28 - 223*r**2/2 + 331*r. Let y(d) be the first derivative of t(d). Factor y(w).
2*w*(w - 1)*(w + 3)/7
Suppose -18*s = -135 - 117. Suppose 4*c = t + s, -22 + 6 = 2*t - 5*c. Factor 0 + n + 5/6*n**t - 1/6*n**3.
-n*(n - 6)*(n + 1)/6
Suppose 0 - 2/11*j**5 + 0*j - 40/11*j**2 - 14/11*j**4 + 56/11*j**3 = 0. What is j?
-10, 0, 1, 2
Factor 45763618 - 63*w**2 - 57*w**2 + 247213*w + 223187*w + 1800*w**2 + 2*w**3 - 1859618.
2*(w + 280)**3
Suppose 2*p - 5*l + 14 = 0, 3*p + 4*l - 52 = -73. Let u be (-1)/p*10/10. Let -u*c**2 - 2/7 + 3/7*c = 0. Calculate c.
1, 2
Let b(j) be the first derivative of -j**5/4 + 5*j**4/12 + 5*j**3/3 - 39*j + 13. Let r(c) be the first derivative of b(c). Let r(x) = 0. What is x?
-1, 0, 2
Let y(m) be the third derivative of 7*m**5/60 - 23*m**4/2 + 39*m**3/2 + 35*m**2 + 17*m. Factor y(c).
(c - 39)*(7*c - 3)
Factor 4*m**3 + 2434 + 2592 - 164*m**2 + 736*m - 5602.
4*(m - 36)*(m - 4)*(m - 1)
Let c = -325702 - -325706. Factor -8 - c*k - 4/9*k**2.
-4*(k + 3)*(k + 6)/9
Let x = 3/10 + -2/15. Suppose -3*q = 985 - 961, 0 = w + 4*q + 30. Solve -2*m - m**3 - x*m**4 - 13/6*m**w - 2/3 = 0.
-2, -1
Let t be (-17 - 35/(525/(-243)))*(-10)/4. Solve -4/7*x**4 + 0*x + 16/7*x**t + 12/7*x**3 + 0 = 0.
-1, 0, 4
Suppose 30*c - 3 = 23 + 64. Suppose -t**c - 7/2*t - 1 - 7/2*t**2 = 0. What is t?
-2, -1, -1/2
Let y(z) be the third derivative of z**8/2352 + z**7/70 + 67*z**6/420 + 143*z**5/210 + 83*z**4/56 + 11*z**3/6 - 5*z**2 - 2*z - 612. Factor y(w).
(w + 1)**3*(w + 7)*(w + 11)/7
Let r = 505 + -503. Factor 134*h**r + 147*h**3 - 104*h - 31*h - 152*h**3 + 6*h**2.
-5*h*(h - 27)*(h - 1)
Let v(q) = -5*q**2 - 552*q - 12. Let p(m) = -20*m**2 - 2210*m - 50. Let i(x) = -6*p(x) + 25*v(x). Factor i(n).
-5*n*(n + 108)
Let u(x) = 5*x + 23. Let f be u(-7). Let o be ((-5)/10)/(3/f). Factor -3*d**2 - 4*d**4 + 433*d + 9*d**o - d**5 + 8*d**2 - 413*d - d**3 + 8.
-(d - 2)*(d + 1)**2*(d + 2)**2
Let z(o) be the first derivative of o**5/40 + o**4/4 + 11*o**3/12 + 3*o**2/2 - 98*o + 226. Let i(r) be the first derivative of z(r). Factor i(j).
(j + 1)*(j + 2)*(j + 3)/2
Let i(v) be the first derivative of 2*v**5/35 - v**4/14 - 8*v**3/7 - 4*v**2/7 + 32*v/7 + 479. Let i(l) = 0. Calculate l.
-2, 1, 4
Let i(q) = -q**3 + 267*q**2 - 19035*q + 149769. Let g(c) = -8*c. Let l(p) = -45*g(p) + 5*i(p). Factor l(d).
-5*(d - 129)**2*(d - 9)
Suppose -83*b + 82*b = -4. Factor 8*r**b - 23*r**3 + 53*r**3 - 2*r**5 - 2*r - 42*r**3 + 8*r**2.
-2*r*(r - 1)**4
Let x be (27915/1490)/(225/20). Let h = x + 1/745. Factor -8/3 - h*t**2 + 22/3*t.
-(t - 4)*(5*t - 2)/3
Factor -77/8*r + 1/8*r**2 - 79/4.
(r - 79)*(r + 2)/8
Let w = 51/107 - 2953/6420. Let c(k) be the third derivative of -w*k**5 + 0 - 1/10*k**3 + 1/600*k**6 + 0*k + 7/120*k**4 - 34*k**2. Determine z so that c(z) = 0.
1, 3
Let u(t) be the third derivative of -1/210*t**7 + 11 - 1/40*t**6 + 1/60*t**5 + 1/8*t**4 + 0*t**3 + 3*t**2 + 0*t. Factor u(m).
-m*(m - 1)*(m + 1)*(m + 3)
Let n(g) be the second derivative of 2 - 1/6*g**3 + 1/20*g**5 - 5/12*g**4 + 5/2*g**2 - 81*g. Factor n(v).
(v - 5)*(v - 1)*(v + 1)
Let x = -499 + 504. Let -9*d**2 + 14*d**4 + 27*d**2 - 491*d**x + 493*d**5 + 30*d**3 = 0. What is d?
-3, -1, 0
Let -9/2 + 1/4*b**2 + 7/4*b = 0. What is b?
-9, 2
Let w be (3 + 304/(-88))/(384/(-528)). Suppose -13/4*y**3 - w*y**4 + 21/4*y + 9/8 - 5/2*y**2 = 0. What is y?
-3, -1/5, 1
Let g(u) = u**3 + 18*u**2 + 115*u + 1684. Let h be g(-17). Let r(y) be the first derivative of 1/2*y**2 - 1/4*y**4 + h - 2/3*y**3 + 2*y. Factor r(f).
-(f - 1)*(f + 1)*(f + 2)
What is t in -9*t**2 + 17*t**3 - 4*t**4 - 3*t**4 + 0*t**4 - 561*t + 561*t - t**5 = 0?
-9, 0, 1
Let w = -294/23 - -2748/161. Determine m, given that -8/7*m**2 - w*m + 8/7 = 0.
-4, 1/4
Let g(b) be the first derivative of 3/40*b**5 - 9/16*b**2 + 56 - 3/4*b + 9/32*b**4 + 1/8*b**3. Factor g(z).
3*(z - 1)*(z + 1)**2*(z + 2)/8
Let s be 6/(-3)*(-15)/6. Let m(j) = j**3 + 4*j**2 - 8*j - 10. Let a be m(-4). Factor -a*o**5 + 12*o**s - o**3 + 11*o**5.
o**3*(o - 1)*(o + 1)
Let q(u) be the third derivative of u**8/112 + 9*u**7/70 + 3*u**6/4 + 23*u**5/10 + 33*u**4/8 + 9*u**3/2 + 152*u**2 + 5*u. Let q(s) = 0. Calculate s.
-3, -1
Let x(z) be the first derivative of 5*z**3/3 - 7810*z**2 + 12199220*z + 942. Suppose x(i) = 0. Calcul