
-2, 1, 16
Let b(p) be the first derivative of -p**6/1260 + 13*p**5/210 + 9*p**4/28 + p**3 - 2*p - 122. Let i(n) be the third derivative of b(n). Factor i(u).
-2*(u - 27)*(u + 1)/7
Let m(i) be the first derivative of i**4/4 + 3*i**3/7 + 1136. Factor m(y).
y**2*(7*y + 9)/7
Let h = 108250 - 974194/9. Factor 2/9*n**4 + h*n**2 + 20/9*n**3 + 0 + 16/3*n.
2*n*(n + 2)**2*(n + 6)/9
Let n = 28222 - 28220. Let y be (6/5)/(9/140). Factor 2/3 + y*p**3 + 19/3*p + 19*p**n + 16/3*p**4.
(p + 1)*(p + 2)*(4*p + 1)**2/3
Let c = 34751 - 34747. Suppose -28/3*q**3 - 4/3*q**5 + 0 + 0*q + 20/3*q**4 + c*q**2 = 0. What is q?
0, 1, 3
Suppose 0 = 2*s - 10, 5*t + 2*s - 19 - 11 = 0. Let p(v) be the second derivative of 10/3*v**3 + 3*v - 1/5*v**5 - 1/3*v**t + 0 - 6*v**2. Factor p(m).
-4*(m - 1)**2*(m + 3)
Let y(d) be the second derivative of d**6/105 + 194*d**5/7 + 235225*d**4/7 + 456336500*d**3/21 + 55330800625*d**2/7 + 664*d + 1. Factor y(n).
2*(n + 485)**4/7
Let y(q) = -6*q**3 + 102*q + 22*q**2 + 190 - 80*q**2 - 244. Let u(k) = -2*k**3 - 19*k**2 + 34*k - 18. Let o(i) = -16*u(i) + 5*y(i). Factor o(d).
2*(d - 1)**2*(d + 9)
Let n(j) be the third derivative of 3*j**7/140 - 61*j**6/180 + 2*j**5/3 + j**4 - 7*j**3 + 2*j**2 + j. Let k(s) be the first derivative of n(s). Factor k(q).
2*(q - 6)*(q - 1)*(9*q + 2)
Suppose -7 = -2*h - 1. Let m = 38113 + -724131/19. Factor 14/19*v**2 - m*v - 2/19*v**h - 32/19.
-2*(v - 4)**2*(v + 1)/19
Let q(y) = 37*y**3 - 1683*y**2 - 1635*y + 17. Let w(v) = 26*v**3 - 1202*v**2 - 1168*v + 12. Let m(n) = 12*q(n) - 17*w(n). Find a such that m(a) = 0.
-118, -1, 0
Let n = -88196/3 - -29400. Factor -2/3*v**5 - 8/3*v**4 + 0 - n*v**2 + 0*v - 10/3*v**3.
-2*v**2*(v + 1)**2*(v + 2)/3
Let o(q) = -30157*q + 30168. Let g be o(1). Factor -34/3*j - 1/3*j**2 - g.
-(j + 1)*(j + 33)/3
Suppose 2*t = -288*y + 286*y + 8, 4*y = 6*t - 14. Factor 0 + 27*v**2 + 21*v + 45/7*v**t + 3/7*v**4.
3*v*(v + 1)*(v + 7)**2/7
Find v, given that 1/6*v**4 - 24*v**2 + 0*v - 5/3*v**3 + 0 = 0.
-8, 0, 18
Let g(j) be the first derivative of -5*j**3/3 + 315*j**2/2 + 990*j - 29. Factor g(m).
-5*(m - 66)*(m + 3)
Let p(u) be the first derivative of -161*u**3 + 60 - 343/10*u**5 + 65*u**2 - 12*u + 1323/8*u**4. Suppose p(s) = 0. What is s?
2/7, 3
Let h = -2321759/35 - -331682/5. Factor -30/7*b + h*b**2 - 33/7.
3*(b - 11)*(b + 1)/7
Let p = -715776 - -715778. Factor -42*s - 1029 - 3/7*s**p.
-3*(s + 49)**2/7
Factor -612*f + 300*f**2 - 47*f**3 - 25*f**3 + 382*f**2 + 4085*f**4 - 4083*f**4.
2*f*(f - 18)*(f - 17)*(f - 1)
Let h(g) be the second derivative of 5*g**7/14 - 19*g**6/3 + 167*g**5/4 - 115*g**4 + 200*g**3/3 + 160*g**2 - 1475*g. Find b, given that h(b) = 0.
-1/3, 1, 4
Suppose 5*p - 98 = -2*k, 2*k + 3*k - 75 = -4*p. Factor 30 - p*g + 7*g**3 - 5 + 5*g**4 - 4*g**3 - 30*g**2 + 17*g**3.
5*(g - 1)**2*(g + 1)*(g + 5)
Let o = 110 - 106. Factor -2*t**5 + 32*t**4 - 20*t**4 - 22*t**o.
-2*t**4*(t + 5)
Let c be -2 + 0/1 + (224 - 222). Suppose 3*x = -c*x + 12. Solve 0 + 10/9*w**3 - 4/9*w**2 + 0*w + 8/9*w**x - 2/3*w**5 = 0 for w.
-1, 0, 1/3, 2
Let v(u) be the third derivative of u**6/60 - 59*u**5/30 - 257*u**4/12 + 105*u**3 - 8*u**2 - 57. Factor v(k).
2*(k - 63)*(k - 1)*(k + 5)
Let c = -375 + 370. Let u(n) = 9*n**3 + 40*n**2 + 436*n + 1724. Let o(h) = 11*h**3 + 41*h**2 + 437*h + 1723. Let p(k) = c*u(k) + 4*o(k). Factor p(z).
-(z + 12)**3
Let h(o) be the third derivative of 18*o**2 - 1/168*o**6 + 0 - 1/1470*o**7 + 5/21*o**3 + 6*o + 1/140*o**5 + 17/168*o**4. Factor h(c).
-(c - 2)*(c + 1)**2*(c + 5)/7
Suppose -5*a + 1734 = -431. Let g = a + -1291/3. Factor 10/3*h**2 - 8*h + g.
2*(h - 2)*(5*h - 2)/3
Let c(w) = -5*w**2 - 69*w + 17. Let x be c(-14). Determine u, given that 0*u**4 - 125*u**2 - 40*u - 2883*u**x - 10*u**4 + 2788*u**3 = 0.
-8, -1, -1/2, 0
Let z be (13/819*-371 - (-40)/(-36)) + 7. Solve z*w + 16/3*w**2 - 14/3*w**3 + 0 = 0.
0, 8/7
Suppose 27*t - t - 104 = 0. Factor -58*x**4 - 53*x**t - 54*x**4 + 168*x**4 - 42*x**2 - 15*x**3.
3*x**2*(x - 7)*(x + 2)
Suppose -129693 - 72771 = -9*x. Suppose x + 15*i**3 - 65*i**2 - 22496 + 20*i = 0. Calculate i.
0, 1/3, 4
Let q be 849/198*2 - (11 + 1216/(-57) - -10). Suppose -q*n - 30/11*n**3 - 2/11*n**4 - 126/11*n**2 + 0 = 0. What is n?
-7, -1, 0
Let i = -146/1659 + 10574/1659. Solve -4/7*f**3 + 180/7 - 156/7*f + i*f**2 = 0.
3, 5
Let m = -280862/43 - -6532. Let x = 156/215 - m. Factor 0 + 6/5*q**2 - 4/5*q - x*q**3.
-2*q*(q - 2)*(q - 1)/5
Let c(u) be the third derivative of 1/12*u**4 - 3*u + 4/9*u**3 + 0 - 14*u**2 + 1/180*u**5. Find o such that c(o) = 0.
-4, -2
Let b(c) = 3*c**5 - c**3 + c + 2. Let y(f) = 8*f**5 + 109*f**4 - 111*f**3 + 3*f + 6. Let p(s) = -3*b(s) + y(s). Suppose p(k) = 0. What is k?
0, 1, 108
Find d such that -2/5*d**5 + 6/5*d**4 + 16/5 + 14/5*d**3 - 22/5*d**2 - 12/5*d = 0.
-2, -1, 1, 4
Let h = 1255 + -1254. Let g be (2 + 0)*h/((-120)/(-100)). Find w, given that -1/3*w**5 + 0 + g*w**2 - 1/3*w**4 + 2/3*w + w**3 = 0.
-1, 0, 2
Let x(p) be the second derivative of p**5/70 - 267*p**4/14 + 800*p**3/21 - 5890*p. Factor x(r).
2*r*(r - 800)*(r - 1)/7
Let j = 35 - 31. Factor 3*n**2 - 8*n**4 - 6*n**3 + 26*n**4 - 15*n**j.
3*n**2*(n - 1)**2
Let w(b) = -10*b**3 - b**2 - 3*b - 2. Let z be w(-1). Let a be (4 + -2 + 0)/(13/546). Factor -18*n**2 + 32 - 8*n**4 + z*n**4 + 20*n**3 + a*n**2 + 80*n.
2*(n + 1)**2*(n + 4)**2
Let d(q) be the first derivative of q**6/120 - 11*q**4/48 - 3*q**3/4 - q**2 - 26*q - 111. Let l(a) be the first derivative of d(a). Factor l(n).
(n - 4)*(n + 1)**2*(n + 2)/4
Let i be (-18 + (-3088)/(-176))*((-22)/5 - -4). Factor i*k**3 - 2/11*k**4 + 10/11*k**2 + 6/11*k + 0.
-2*k*(k - 3)*(k + 1)**2/11
Let c(k) be the first derivative of 5*k**4/8 - 35*k**3 - 1685*k**2/4 - 735*k + 2709. Factor c(u).
5*(u - 49)*(u + 1)*(u + 6)/2
Let w = -5397 - -5397. Let a(n) be the second derivative of -55/6*n**3 + n**5 + 8*n + 15/2*n**2 + w + 10/3*n**4. Factor a(m).
5*(m + 3)*(2*m - 1)**2
Let r(z) be the third derivative of z**6/480 - 391*z**5/80 + 114465*z**4/32 + 344569*z**3/24 + 843*z**2. Let r(q) = 0. What is q?
-1, 587
Let 21/5*j + 0 - 1/10*j**2 = 0. Calculate j.
0, 42
Suppose -5*p = r - 5, -2*p + 4*p + 11 = -3*r. Find j, given that -4*j + 3*j**p + j**5 + j**4 - 4*j - 5*j**3 + 8*j = 0.
-3, 0, 1
Let s = -31 - -33. Suppose -3*c = 6, s*x + 5 - 15 = 3*c. Factor -49/4*l**3 - 77/4*l**x - 8*l - 1.
-(l + 1)*(7*l + 2)**2/4
Let s(b) be the first derivative of 2*b**6/15 - 38*b**5/5 + 69*b**4/5 + 2*b**3/15 - 46*b**2/5 - 152. Let s(k) = 0. What is k?
-1/2, 0, 1, 46
Suppose r - 6*i - 2 = -3*i, -2 = -r + 2*i. Suppose 3*y**5 - 2582*y**4 - r*y**5 + 2581*y**4 = 0. What is y?
0, 1
Determine o so that -18*o**3 - 18*o**4 - 20*o**2 + 144*o + 15*o**4 + 2*o**3 - 123 + 7*o**4 - 21 = 0.
-3, 2, 3
Let c(g) be the first derivative of -2*g**3/3 - 40*g**2 + 258*g + 860. Let c(k) = 0. Calculate k.
-43, 3
Let m = -62338 + 124679/2. Factor m - 1/6*g**2 + 4/3*g.
-(g - 9)*(g + 1)/6
Let n(k) be the first derivative of -6 + 0*k - 2*k**2 - 1/3*k**3. Factor n(z).
-z*(z + 4)
Let c = -6244 + 18736/3. Let o(b) be the first derivative of -16 - c*b**3 + b**2 + 2*b. Factor o(s).
-2*(s - 1)*(2*s + 1)
Let c(n) be the third derivative of 0 - 7*n**2 - 1/8*n**6 + 1/140*n**7 + 0*n**3 + 0*n**5 + n + 0*n**4. Determine f so that c(f) = 0.
0, 10
Let h(y) = 11*y**3 + 2280*y**2 + 185351*y - 53126. Let v(l) = -12*l**3 - 2280*l**2 - 185356*l + 53123. Let t(b) = -10*h(b) - 8*v(b). Factor t(n).
-2*(n + 163)**2*(7*n - 2)
Suppose 1624*l**2 - 15*l + 760 - 1628*l**2 - 20*l - l = 0. What is l?
-19, 10
Let r(p) be the third derivative of 27/4*p**3 + 149/60*p**5 + 1/672*p**8 + 0*p + 1/20*p**7 + 23/40*p**6 + 87/16*p**4 - 190*p**2 + 0. Factor r(v).
(v + 1)**3*(v + 9)**2/2
Let p = 565354/9 + -62814. Find l, given that -88/9 - 272/9*l**2 - p*l**3 + 388/9*l = 0.
-11, 2/7, 1
Let 0 - 438/17*l + 2/17*l**2 = 0. Calculate l.
0, 219
Let n = 89944 + -989382/11. Factor 0*z + 4/11*z**2 + 10/11*z**3 + 8/11*z**4 + n*z**5 + 0.
2*z**2*(z + 1)**2*(z + 2)/11
Let t(y) be the third derivative of 0 + 9*y + 0*y**3 - 1/60*y**6 + 1/180*y**5 - 5*y**2 - 1/630*y**7 + 1/12*y**4. Find a, given that t(a) = 0.
-6, -1, 0, 1
Let o(b) = -955*b**2 - 5745*b + 32915. Let y(s) = 37*s**2 + 221*s - 1266. Let x(l) = 6*o(l) + 155*y(l). Factor x(p).
5*(p - 36)*(p - 7)
Let m be ((-88 + -30)*1