such that -12*k + 12*k**2 + 8 + 0*k - 8*k**n = 0.
1, 2
Let f(l) = -2*l**3 - 4*l**2 + 19*l + 7. Let x(m) = -2*m**2 + 20*m + 7 - 2*m**3 + 10 - 2*m**2 - 1 - 6. Let z(b) = 6*f(b) - 5*x(b). Factor z(n).
-2*(n - 1)**2*(n + 4)
Suppose 5*g = 40 + 40. Factor 26*s**2 - 5*s - 3*s + g*s**3 + 2*s**2.
4*s*(s + 2)*(4*s - 1)
Let n = 473 - 225. Let m = -140 + n. Determine t, given that -3*t**4 - 3*t**5 - m + 12*t**2 + 108 + 12*t**3 = 0.
-2, -1, 0, 2
Let r be 123/(-287) + 9/21. Let p be (1 - r)/((-13)/(-26)). Factor 8/3 - 2*j - 14/3*j**p.
-2*(j + 1)*(7*j - 4)/3
Let p(c) be the third derivative of -c**6/18 + 8*c**5/45 + 5*c**4/18 - 16*c**3/9 + 4*c**2 - 27*c. Factor p(w).
-4*(w - 1)*(w + 1)*(5*w - 8)/3
Determine j, given that 3 - 27*j**2 - 11/2*j**3 - 61/2*j = 0.
-3, -2, 1/11
Suppose -15 = -4*f + z, 3*f + 2*z - 8 = 6. Let -4 - 2*a - 4*a**3 + a**2 + 11*a**2 + 2*a**4 - 6*a**2 + 6*a**3 - f*a**4 = 0. What is a?
-1, 1, 2
Let u be (46/230)/(1/25). Let t(r) be the first derivative of 1/27*r**6 + 0*r - 2/45*r**u + 2/27*r**3 + 0*r**2 - 1/18*r**4 + 1. Factor t(p).
2*p**2*(p - 1)**2*(p + 1)/9
Factor -197164*o**3 - 9219*o + 48005*o**2 - 35886*o + 5*o**4 - 94090 + 196189*o**3.
5*(o - 97)**2*(o - 2)*(o + 1)
Let h = 6120/7 - 874. Factor 6/7*y - h*y**4 + 10/7*y**2 + 2/7*y**3 + 0.
-2*y*(y - 3)*(y + 1)**2/7
Suppose -2*l - 2*l + 56 = -2*h, 4*l + 5*h = 28. Suppose l*d - 14*d = -4. Suppose 1/5*o**d + 0 + 1/5*o**3 + 0*o = 0. Calculate o.
-1, 0
Let b(v) be the second derivative of 38*v + 0*v**3 - 1/4*v**2 + 1/96*v**4 + 0. Determine q, given that b(q) = 0.
-2, 2
Let r(c) = 246*c + 4676. Let g be r(-19). Factor -5 - 1/5*j**g + 2*j.
-(j - 5)**2/5
Let o(c) = -7 + 5 + 2 - 52 + 3*c. Let b be o(18). Factor 1/4*p**5 + 0 - 1/4*p**3 - 1/2*p**4 + 1/2*p**b + 0*p.
p**2*(p - 2)*(p - 1)*(p + 1)/4
Solve -2/15*u**2 - 301056/5 + 896/5*u = 0.
672
Let x be (-1)/(-2)*(-16)/(-24). Let l = 7864/3 - 2616. Find z, given that -8/3*z - x*z**2 - l = 0.
-4
Let r(s) = 3*s**3 - 166*s**2 + 2233*s - 40. Let n be r(23). Let 21*p - 3/7*p**5 + n*p**2 + 0 - 6*p**4 - 144/7*p**3 = 0. What is p?
-7, -1, 0, 1
Let b(t) = 7*t**2 - 7*t - 1. Let j(c) = -29*c**2 - 83*c + 116. Let q(x) = -12*b(x) - 3*j(x). Suppose q(o) = 0. Calculate o.
-112, 1
Let s = -188740 + 1317748/7. Let r = -489 - s. Factor 0 + 3/7*j**5 - r*j**3 + 12/7*j + 6/7*j**4 - 12/7*j**2.
3*j*(j - 1)**2*(j + 2)**2/7
Find i, given that 13/3*i**2 + 2/3*i**4 - 11/3*i**3 - 4/3*i + 0 = 0.
0, 1/2, 1, 4
Determine v so that 38/3*v**2 + 4/3*v**5 - 86/3*v**3 + 82/3*v - 40/3 + 2/3*v**4 = 0.
-5, -1, 1/2, 1, 4
Let d(g) be the third derivative of -1/504*g**8 - 17/180*g**6 - 17/90*g**5 + 0*g**3 - 2*g + 69*g**2 + 0 - 1/6*g**4 - 1/45*g**7. Find h such that d(h) = 0.
-3, -2, -1, 0
Let z(s) be the first derivative of -s**4/4 - 50*s**3 + 153*s**2/2 + 302*s - 4089. Factor z(o).
-(o - 2)*(o + 1)*(o + 151)
Suppose 256762*s + 168 = 256818*s. Let 1/4*r**5 - 2 + 3/2*r**4 + 1/2*r**2 - 3*r + 11/4*r**s = 0. What is r?
-2, -1, 1
Determine t, given that -1488*t - 2*t**2 + 0*t**2 + 0*t**2 + 1531*t + 977*t - 130050 = 0.
255
Factor 8919/2*c**2 - 7/4*c**3 + 811538 - 2841657*c.
-(c - 1274)**2*(7*c - 2)/4
Let 27/5*h**2 + 0 - 3/5*h**3 + 156/5*h = 0. Calculate h.
-4, 0, 13
Let j be (-97)/9 - (195/(-5) - -28). Let 1/3 - j*h - 1/9*h**2 = 0. What is h?
-3, 1
Let n(j) be the third derivative of 1/4*j**4 + 0 - 2*j - 11/60*j**6 + 2*j**2 + 0*j**3 - 1/6*j**5 - 1/35*j**7. Factor n(l).
-2*l*(l + 1)*(l + 3)*(3*l - 1)
Let h be 12/66*1397/635. Factor -h*d**4 + 0 - 4/5*d**3 + 0*d**2 + 0*d.
-2*d**3*(d + 2)/5
Let l = -86/133 + -542515/399. Let j = -1359 - l. Let -2*p + j + 2/3*p**2 = 0. Calculate p.
1, 2
Let b(s) be the first derivative of s**3 - 669*s**2/2 - 3420*s - 6965. Solve b(n) = 0.
-5, 228
Let v(p) be the first derivative of 11/8*p**3 - 47 + 8*p - 7*p**2 + 1/40*p**5 + 7/16*p**4. Suppose v(c) = 0. Calculate c.
-8, 1
Let g(v) be the third derivative of -v**5/110 - 13*v**4/44 - 40*v**3/11 - v**2 + 146*v + 2. What is y in g(y) = 0?
-8, -5
Let w(t) be the third derivative of t**6/60 - 2299*t**5/10 + 5285401*t**4/4 - 12151136899*t**3/3 + 7851*t**2. Factor w(s).
2*(s - 2299)**3
Let x(b) = 2*b**2 - 15*b - 118. Let o be x(28). Let -134*k**2 - 174*k**2 + 7110*k + 4*k**3 - o*k - 198 - 5578 = 0. What is k?
1, 38
Suppose -4*b - v + 5 = 0, b + 4*v + 156 = 176. Let w(g) be the second derivative of -1/8*g**4 + 19*g - 9/80*g**5 + b*g**3 + 0*g**2 + 0 - 1/40*g**6. Factor w(j).
-3*j**2*(j + 1)*(j + 2)/4
Let g(a) be the third derivative of 2*a**6/75 - 14*a**5/15 - 149*a**4/40 - 57*a**3/10 - 2283*a**2. Let g(r) = 0. What is r?
-3/4, 19
Factor -48/5*d**2 + 693/5*d + 1/5*d**3 - 2646/5.
(d - 21)**2*(d - 6)/5
Let n(z) = 5*z + 143. Let d be n(-19). Find r such that 22*r**5 - 6*r**5 - 10*r**5 - 5*r**5 + d*r**3 - 11*r**2 + 75*r**2 - 15*r**4 = 0.
-1, 0, 8
Let f(g) be the third derivative of -1/27*g**3 + 1/1890*g**7 - 1/180*g**5 + 0 - 5/216*g**4 + g + 1/1080*g**6 + 6*g**2. Factor f(i).
(i - 2)*(i + 1)**3/9
Let u(w) be the first derivative of -3*w**5/5 - 2067*w**4/4 - 5648. Factor u(g).
-3*g**3*(g + 689)
Let t be (-1 - 0)*(-2 - -8)*43. Let x = -255 - t. Factor 16/3*q - 32/3 + 2/3*q**x + 14/3*q**2.
2*(q - 1)*(q + 4)**2/3
Let v(k) = -k**2 + 27*k - 25. Let i be v(25). Suppose 56 = i*u + 6. Solve 4/5 + 14/5*s - 8/5*s**3 - 2*s**u = 0 for s.
-2, -1/4, 1
Let a(l) = -l - 184. Let i be a(-9). Let s be (340/i + 2)*7. Factor -s*d**2 + 8/5 - 6/5*d.
-2*(d - 1)*(d + 4)/5
Let j = 123601/186165 + -1528/1773. Let z = -1/135 - j. Let 2/21*m**2 + 0 - 4/21*m - 2/21*m**4 + z*m**3 = 0. Calculate m.
-1, 0, 1, 2
Factor -125/4*f - 5/4*f**2 - 105.
-5*(f + 4)*(f + 21)/4
Solve 70*h**5 + 2355*h**3 + 2315/2*h**4 - 1450*h - 3845/2*h**2 - 210 = 0.
-14, -3, -2/7, -1/4, 1
Suppose 167*s - 21 = -3*z + 170*s, -5*s - 3 = 11*z. Factor 4/3*f**z + 0 - 1/3*f**3 + 5/3*f.
-f*(f - 5)*(f + 1)/3
Let k(r) be the third derivative of -119*r**2 + 7/12*r**4 - 2 + 0*r + 3/20*r**5 + 1/120*r**6 + 0*r**3. Factor k(h).
h*(h + 2)*(h + 7)
Let f = 486 + -470. Let p be (-126)/(-24)*f/30. What is v in 4/5 - 4/5*v**4 - 2/5*v**5 + p*v + 4/5*v**3 + 16/5*v**2 = 0?
-1, 2
Suppose 0 = -4*k - 4*y + 40, -4*y = -4*k + y + 49. Determine t, given that -5*t**2 + 3*t**4 - k*t**4 + 13*t**4 = 0.
-1, 0, 1
Suppose 0 = 58*g + 29709 - 29825. Let b(j) be the third derivative of -2/15*j**3 - 1/40*j**4 + 0 - j**g + 1/300*j**5 - 6*j. Factor b(f).
(f - 4)*(f + 1)/5
Let m = 473 + -467. Let l(h) = 4*h. Let n be l(1). Let z**n - 4*z**4 + m + 6*z**2 - 9 = 0. Calculate z.
-1, 1
Suppose 113*x = 2533*x - 4840. Solve 40*l**3 + 2/11 - 40/11*l + 22*l**4 + 156/11*l**x = 0 for l.
-1, 1/11
Let l(q) be the third derivative of -q**8/1344 - q**7/420 + 3*q**6/32 - 71*q**5/120 + 43*q**4/24 - 3*q**3 + 554*q**2. Factor l(x).
-(x - 2)**3*(x - 1)*(x + 9)/4
Let 106/5*g + 0 + 1/5*g**2 = 0. What is g?
-106, 0
Let m = -5189 - -197183/38. Let p(s) be the first derivative of 1/19*s**2 - m*s**4 + 4/57*s**3 + 19 - 4/19*s. Factor p(i).
-2*(i - 2)*(i - 1)*(i + 1)/19
Let m = -286 - -280. Let x(l) = 69*l**2 - 107*l + 30. Let w(f) = -70*f**2 + 105*f - 30. Let t(c) = m*w(c) - 5*x(c). Factor t(y).
5*(3*y - 2)*(5*y - 3)
Let j(c) = 5*c**2 + 673*c + 1263. Let g(u) = -10*u**2 - 1347*u - 2507. Let l(d) = -3*g(d) - 7*j(d). Factor l(x).
-5*(x + 2)*(x + 132)
Let a(l) = 13*l**4 - 57*l**3 - 54*l**2 + 43*l - 18. Let y(v) = -7*v**4 + 27*v**3 + 26*v**2 - 20*v + 8. Let r(x) = -4*a(x) - 9*y(x). Find u, given that r(u) = 0.
-1, 0, 4/11, 2
Suppose -2*x + 7*k - 12*k + 13 = 0, 3*k = -5*x + 42. Let c(h) = -h + 11. Let l be c(x). Factor -1/3*m - 1/6 - 1/6*m**l.
-(m + 1)**2/6
Factor -3670*o - 6*o**2 + 6*o**2 + 250 + 3745*o + 4*o**2 + o**2.
5*(o + 5)*(o + 10)
Let v(n) be the second derivative of -3*n**5/20 + 56*n**4 - 223*n**3/2 + n + 1232. Factor v(f).
-3*f*(f - 223)*(f - 1)
Let f(p) be the second derivative of p**4/54 + 38*p**3/27 - 215*p**2/9 + 871*p. Factor f(l).
2*(l - 5)*(l + 43)/9
Let p(t) be the second derivative of -t**7/5040 + t**5/15 - 53*t**4/4 - 129*t. Let g(j) be the third derivative of p(j). Suppose g(d) = 0. What is d?
-4, 4
Factor -216*u + 1/5*u**2 + 58320.
(u - 540)**2/5
Let l(p) = -46*p - 40*p + 188*p - 200 - 38*p - 39*p. Let x be l(8). Factor -4/13*m**2 + 0 + 6/13*m**3 + x*m.
2*m**2*(3*m - 2)/13
Let o(b) = 8*b**2 + b + 1. Let u(h) = -55*h**2 + 33*h + 34. Let k(f) = 