l - 136*l + 808 = 262*l. Factor 2*r**3 + l*r**2 + 1/6*r**4 + 8 + 40/3*r.
(r + 2)**3*(r + 6)/6
Suppose 4*n = 7*n - 2*p - 4, -5*n + 15 = 5*p. Let q = 21 + -144/7. Factor 6/7*w**n - 3/7 + q*w.
3*(w + 1)*(2*w - 1)/7
Let y(a) be the first derivative of 4*a**2 + 4/3*a**3 - 8 + 0*a. Factor y(r).
4*r*(r + 2)
Let s(a) be the second derivative of -a**6/180 + a**5/30 + a**4/4 - 7*a**3/6 + 31*a. Let n(r) be the second derivative of s(r). Factor n(f).
-2*(f - 3)*(f + 1)
Suppose -5*r = 4*f + 10, -f + 6*f = 4*r - 33. Suppose -9 = 28*w - 31*w. Factor 0 + 1/4*n**r + 0*n - 1/4*n**w.
-n**2*(n - 1)/4
Let r(m) be the second derivative of m**5/20 - 91*m**4/12 + 1012*m**3/3 + 1058*m**2 + 57*m. Find b, given that r(b) = 0.
-1, 46
Let p be ((-1)/3*(-13 - 95)/12)/12. Factor -a + 1/4*a**3 + p*a**4 + 2 - 3/2*a**2.
(a - 2)*(a - 1)*(a + 2)**2/4
Suppose q + 10 = 2*r, r - 15 = 3*q - 2*r. Suppose q = -2*z - 3*z + 25. Determine m so that -4*m - 1 - 12*m - 2*m**3 - 10*m**2 - z - 2 = 0.
-2, -1
Let s(l) be the third derivative of 1/360*l**5 + 0*l + 0 + 1/36*l**3 - 1/72*l**4 + 12*l**2. Factor s(k).
(k - 1)**2/6
Suppose -10 = -5*o - 10*d + 13*d - 2*d, 0 = -4*d. Solve -24/7*p + 36/7*p**o + 6/7*p**4 + 6/7 - 24/7*p**3 = 0.
1
Let q(x) be the third derivative of -x**7/70 - 43*x**6/20 - 63*x**5/5 - 125*x**4/4 - 83*x**3/2 - 68*x**2 + 2*x. Determine o, given that q(o) = 0.
-83, -1
Let r be 74/(-962)*(-13)/10. Factor -1/5*i**2 - r - 3/10*i.
-(i + 1)*(2*i + 1)/10
Let g = 60/29 + -482/261. Determine d so that -4/9 - 4/9*d**3 - 14/9*d + 4/9*d**4 + g*d**5 - 16/9*d**2 = 0.
-1, 2
Let r = 19 - 7. Suppose -r*s**3 + 3*s**4 + 3*s**2 - 4*s**2 + 8*s + 4*s**5 - 7*s**4 + 5*s**2 = 0. What is s?
-1, 0, 1, 2
Let w(b) be the third derivative of b**9/37800 + b**8/4200 + b**7/2100 + 5*b**4/12 - 7*b**2. Let v(p) be the second derivative of w(p). Factor v(a).
2*a**2*(a + 1)*(a + 3)/5
Let t be -6 + (-30)/(-12) + -5 + 129/14. Factor -t*m - 1/7*m**2 + 6/7.
-(m - 1)*(m + 6)/7
Let g(j) be the second derivative of j**6/30 - 2*j**5/3 + 16*j**4/3 - 64*j**3/3 + 13*j**2 - 14*j. Let x(k) be the first derivative of g(k). Factor x(b).
4*(b - 4)**2*(b - 2)
Let t(i) be the third derivative of 53/450*i**5 + 11/180*i**6 + 0*i + 3/175*i**7 + 2/15*i**4 + 1/504*i**8 + 4/45*i**3 + 0 - 4*i**2. Solve t(f) = 0 for f.
-2, -1, -2/5
Factor 10816/7*o - 4/7*o**4 - 8788/7 - 312*o**2 + 160/7*o**3.
-4*(o - 13)**3*(o - 1)/7
Let c(w) be the first derivative of -w**6/480 - w**5/32 + 3*w**4/16 + 6*w**3 + 2. Let l(f) be the third derivative of c(f). Solve l(d) = 0.
-6, 1
Let d = -13 + 18. Suppose 0 = -2*r + 3 + d. Factor -2*t**r - 5*t**3 - 13*t + 4*t**4 + 4*t**2 + 12*t.
t*(t - 1)**2*(2*t - 1)
Let r(k) be the first derivative of -k**6/6 - 6*k**5/5 + 15*k**4/4 - 8*k**3/3 - 11. Find a such that r(a) = 0.
-8, 0, 1
Let -35/2*z - 13/2*z**2 - 1/2*z**3 + 49/2 = 0. Calculate z.
-7, 1
Let k(n) = 37*n - 4*n**2 - 313 + 353 - n**2. Let b(p) = 10*p**2 - 75*p - 80. Let l(g) = -2*b(g) - 5*k(g). Factor l(o).
5*(o - 8)*(o + 1)
Let j(n) be the first derivative of -2*n**5/85 + 2*n**3/17 + 2*n**2/17 + 80. Factor j(b).
-2*b*(b - 2)*(b + 1)**2/17
Let s(x) be the first derivative of 2*x**3/21 + 11*x**2/7 + 238. Factor s(f).
2*f*(f + 11)/7
Let y be (-210)/3990 - (-78)/38. Solve 3/4*l**3 - 6 - 9/2*l**y + 9*l = 0 for l.
2
Let w(l) be the second derivative of -3/140*l**5 + 31*l - 5/28*l**4 + 0*l**2 - 2 - 3/7*l**3. Suppose w(m) = 0. What is m?
-3, -2, 0
Let z(m) be the third derivative of -m**9/12096 - m**8/3360 + m**6/720 + m**5/480 - m**3/6 - 15*m**2. Let o(l) be the first derivative of z(l). Factor o(j).
-j*(j - 1)*(j + 1)**3/4
Factor 40/19 + 96/19*t - 10/19*t**2.
-2*(t - 10)*(5*t + 2)/19
Let w be (72/126)/(204/126). Solve 0 - 4/17*c + w*c**2 + 0*c**3 - 2/17*c**4 = 0 for c.
-2, 0, 1
Let l(r) = -r**2 + 76*r - 1003. Let k be l(17). Suppose 8/3*c**2 - 10/3*c**4 - 4*c**3 + 16/3*c - 2/3*c**5 + k = 0. What is c?
-2, 0, 1
Suppose j - 2*z + 8 = 0, -3*j - 10*z = -15*z + 20. Let 2/5*y**2 + 2/5*y**3 + j*y + 0 = 0. What is y?
-1, 0
Factor 21*m**3 - 3*m**2 + 8*m**4 + 187 - 387 + 188 + 12*m**2 - 2*m**4 - 24*m.
3*(m - 1)*(m + 2)**2*(2*m + 1)
Let d(s) be the second derivative of s**7/210 - s**6/15 + 8*s**5/25 - 13*s**4/30 - 11*s**3/10 + 18*s**2/5 + 437*s. Find t such that d(t) = 0.
-1, 1, 3, 4
Let p = 5137/4 + -1283. Suppose -5/4*n**2 + 5/4*n + 3/4*n**4 - p*n**3 + 1/2 = 0. What is n?
-1, -1/3, 1, 2
Determine d, given that 9/7*d + 0 - 69/7*d**2 = 0.
0, 3/23
Let j(r) = 3*r**4 - 10*r**3 + 2*r**2 + 29*r - 24. Let b(n) = 4*n**4 - 10*n**3 + 2*n**2 + 28*n - 24. Let i(v) = 5*b(v) - 6*j(v). Factor i(x).
2*(x - 1)**2*(x + 3)*(x + 4)
Let i(h) = -h**2 + 4*h + 7. Let x be i(5). Let n be (5 + -9)/((-30)/1). Determine k so that -4/15 + 38/15*k**3 + 14/15*k**4 + n*k + x*k**2 = 0.
-1, 2/7
Let v(d) = -d**2 - 15*d + 19. Let s be v(-16). Factor 8/7*r**s - 32/7*r - 32/7 + 2/7*r**4 + 0*r**2.
2*(r - 2)*(r + 2)**3/7
Suppose 4*d - 3 = 5. Suppose 20 = 2*n + d*n - 5*w, 0 = -3*n + 4*w + 15. Determine c so that 1 - 5*c + 3*c**2 - 4*c + n = 0.
1, 2
Let b = 444/7 + -438/7. Factor 6*j + b*j**3 + 18/7 + 30/7*j**2.
6*(j + 1)**2*(j + 3)/7
Let o(d) be the third derivative of d**6/240 + d**5/40 - d**4/48 - d**3/4 + 29*d**2 + d. Factor o(v).
(v - 1)*(v + 1)*(v + 3)/2
Let z(x) be the third derivative of x**5/150 + x**4/2 + 15*x**3 + 71*x**2 - x. Factor z(a).
2*(a + 15)**2/5
Let q(n) = 11*n**4 - 249*n**3 - 513*n**2 - 271*n - 6. Let v(w) = -100*w**4 + 2240*w**3 + 4615*w**2 + 2440*w + 55. Let a(r) = 55*q(r) + 6*v(r). Solve a(f) = 0.
-1, 0, 53
Let u(m) be the first derivative of 0*m - 2/3*m**3 + 2*m**2 + 25 + 2/5*m**5 - m**4. Find c, given that u(c) = 0.
-1, 0, 1, 2
Let d(k) be the first derivative of -5*k**6/6 + 21*k**5 - 95*k**4/2 - 10*k**3/3 + 195*k**2/2 - 95*k - 18. Suppose d(t) = 0. What is t?
-1, 1, 19
Let o(q) = -17*q**2 + 88*q - 1960. Let r(x) = -2*x**2 - 3. Let y(j) = -3*o(j) + 24*r(j). Determine b so that y(b) = 0.
44
Solve 10/9*q**2 - 2*q**3 - 4/9*q**4 + 0*q + 0 = 0.
-5, 0, 1/2
Suppose -d = -0 + 3. Let z be 16/(-20) - d - 2/1. Determine s so that 0 + 2/5*s**2 - 1/5*s - z*s**3 = 0.
0, 1
Suppose -159 - 3 = -54*f. Factor -6/11*x**f + 0 + 0*x + 2/11*x**2.
-2*x**2*(3*x - 1)/11
Let f = -1/16587 + -5075617/82935. Let z = 837/10 + f. Factor -z*a + 5/2*a**3 - 15/2*a**2 - 25/2.
5*(a - 5)*(a + 1)**2/2
Let h(y) = -2*y**2 + 15*y + 6. Let x be h(7). Let a be x/12 + (-1)/(-4). What is w in 0 + 2*w**4 - 10/3*w**2 + 8/3*w**3 - a*w = 0?
-2, -1/3, 0, 1
Suppose 1126 = 4*i - 2*p, 0 = i + p - 33 - 244. Factor -i*h + 35*h**4 + 10*h**3 + 280*h.
5*h**3*(7*h + 2)
Let z be ((-3)/12)/(1/(-7) - (-2336)/(-896)). Solve -1/11*t**4 + 0 + z*t**2 - 2/11*t + 2/11*t**3 = 0.
-1, 0, 1, 2
Let r = 525 - 1047/2. Let u(z) be the second derivative of -1/4*z**4 - r*z**2 + 0 - z**3 - 3*z. Find p, given that u(p) = 0.
-1
Suppose -4*s - 7 = -3*y, 15 = 3*y + 5*s - 10. Let j(k) be the first derivative of 3*k - 3/4*k**4 + y + 3*k**3 - 9/2*k**2. Factor j(b).
-3*(b - 1)**3
Factor -52/7*w + 22/7*w**2 - 2/7*w**3 + 32/7.
-2*(w - 8)*(w - 2)*(w - 1)/7
Find h, given that -192/5*h**2 - 512/5 - 32/5*h**3 - 2/5*h**4 - 512/5*h = 0.
-4
Let u(h) be the second derivative of 0 + 1/60*h**6 - 30*h - 1/12*h**3 + 1/8*h**4 + 0*h**2 - 3/40*h**5. Factor u(m).
m*(m - 1)**3/2
Suppose -12 = 6*x - 36. Let m(y) be the first derivative of -1/4*y**3 + 0*y + 9/20*y**5 + 3/8*y**x + 3 + 0*y**2. Factor m(o).
3*o**2*(o + 1)*(3*o - 1)/4
Find w, given that -25/6*w - 1/6*w**3 + 0 + 5/3*w**2 = 0.
0, 5
Let q(a) = a**3 - 6*a**2 + 5*a + 2. Let p be q(5). Suppose 0 = -p*y - 2*y + 2*y. Factor -1/2*o**3 + 0*o + 1/2*o**4 + y*o**2 + 0.
o**3*(o - 1)/2
Let f(b) be the first derivative of 2*b**5/35 + 131*b**4/14 + 3784*b**3/7 + 79376*b**2/7 - 170368*b/7 - 166. What is p in f(p) = 0?
-44, 1
Let 368/5*q + 16928/5 + 2/5*q**2 = 0. Calculate q.
-92
Factor -217*h**3 - 5*h**5 + 115*h**2 - 115*h**2 - 28*h**3 + 70*h**4.
-5*h**3*(h - 7)**2
Let o(z) be the second derivative of -z**4/36 - 20*z**3/9 + 41*z**2/6 + 2*z - 5. Solve o(p) = 0 for p.
-41, 1
Let j(n) be the second derivative of -n**5/40 - n**4/24 + n**3/2 + 15*n + 3. Find v, given that j(v) = 0.
-3, 0, 2
Suppose -b + 0 = -3*k - 15, -5*b + k = -19. Factor -4*w**2 - b - 186*w + 192*w + w**2.
-3*(w - 1)**2
Let b(q) be the third derivative of 7/8*q**4 - 38*q**2 + 0 + 5*q**