918*r + 9905. Let n(w) = w**2 + 3689*w + 7430. Let s(j) = -11*n(j) + 8*u(j). Factor s(m).
5*(m - 249)*(m + 2)
Let i(p) be the third derivative of -11*p**5/48 - 5*p**4/96 + 5*p**3/2 - 11*p**2 + 1. Factor i(v).
-5*(v - 1)*(11*v + 12)/4
Let o(d) = 58*d**2 + 24*d + 24. Let x be o(-5). Let y = x - 1352. Solve -45/2 - 5/2*a**y + 15*a = 0 for a.
3
Let u = -142/31 + 1454/155. What is o in 86/5*o**2 - 32 - u*o**3 - 48/5*o + 2/5*o**4 = 0?
-1, 4, 5
Let d(q) = q + 83. Let v be d(-29). Let y be (-96)/v + (7 - 5). Factor 0 - 1/9*w**4 - y*w**3 + 1/9*w**2 + 2/9*w.
-w*(w - 1)*(w + 1)*(w + 2)/9
Factor -203/8*y + 0 + 1/8*y**2.
y*(y - 203)/8
Suppose 5*x - 2*j - 17 = 0, -j = 3*x - 2*j - 10. Let r(k) be the first derivative of -2*k**2 - 2*k + 11 - 2/3*k**x. Let r(n) = 0. Calculate n.
-1
Suppose -1738*y + 1736*y - 7*c = 6, 4*y - 5*c - 102 = 0. Let b = 5 + -3. Find t, given that -y*t - 15*t**b - 27/5 = 0.
-3/5
Let u = -270 - -328. Suppose u*d - 58 = 29*d. Factor 15/4*r**3 - 1/2 - 3/4*r + 7/2*r**d.
(r + 1)*(3*r + 1)*(5*r - 2)/4
Let w be (-9)/6 + (-6)/(-4). Suppose 0*k = -k - 5*r + 2, w = -3*k - r + 6. Suppose 6*l - k*l - 4 + 0*l + 3*l**2 - 4*l**2 = 0. What is l?
2
Let z = -2955 - -115247/39. Let a(r) be the second derivative of 0 - 1/13*r**2 - z*r**3 - 9*r - 1/78*r**4. Factor a(s).
-2*(s + 1)**2/13
Let f(x) = 5*x**2 - 7*x - 1. Let q(g) = 5*g + 14. Let s be q(-2). Let a(r) = 2*r**2 - 2*r. Let j(c) = s*f(c) - 11*a(c). Factor j(d).
-2*(d + 1)*(d + 2)
Suppose 0 = 2*t - 41 - 19. Let m be (t/(-35))/(4/(-14)). Factor 1412*v + v**5 + 5*v**4 + 8*v**m - 1412*v + 4*v**2.
v**2*(v + 1)*(v + 2)**2
Let a(z) be the first derivative of z**4/4 - 19*z**3/2 - 30*z**2 - 133*z + 5. Let l(y) be the first derivative of a(y). Factor l(f).
3*(f - 20)*(f + 1)
Let w be (-433 + 415 - (-219)/13)/(3/(-2)). Determine x, given that 18/13 + 2/13*x**5 + w*x**4 + 4/13*x**3 - 6/13*x - 28/13*x**2 = 0.
-3, -1, 1
Let n(s) be the second derivative of -s**4/30 + 176*s**3/15 + 2*s + 15. Factor n(j).
-2*j*(j - 176)/5
Let b = -478222 - -478234. Factor -24 + 9/2*r**2 - 3/8*r**4 - 3/2*r**3 + b*r.
-3*(r - 2)**2*(r + 4)**2/8
Let s(y) be the first derivative of -2*y**5/75 - 77*y**4/5 - 105794*y**3/45 + 35728*y**2/5 - 107648*y/15 + 639. Factor s(w).
-2*(w - 1)**2*(w + 232)**2/15
Factor -16/3*q**4 + 704/3*q**2 + 0 + 3872/15*q + 2/15*q**5 + 208/5*q**3.
2*q*(q - 22)**2*(q + 2)**2/15
Let k(p) = 188*p - 28949. Let t be k(154). Factor 0 - 18/7*b - 2/7*b**t - 20/7*b**2.
-2*b*(b + 1)*(b + 9)/7
Let v(z) be the third derivative of z**5/630 - 4*z**4/21 + 215*z**3/63 + 697*z**2. Factor v(n).
2*(n - 43)*(n - 5)/21
Let r(k) = -3*k**3 - 342*k**2 + 12*k + 306. Let p(o) = o**3 + 168*o**2 - 5*o - 152. Let g(l) = 9*p(l) + 4*r(l). Factor g(t).
-3*(t - 48)*(t - 1)*(t + 1)
Let x(r) = 5*r**3 + r**2 + r + 1. Let i(f) = -2*f**4 - 13*f**3 + 85*f**2 + 151*f + 11. Let m(h) = 2*i(h) - 22*x(h). Suppose m(j) = 0. Calculate j.
-35, -1, 0, 2
Let b(g) be the second derivative of 0 + 1/4*g**4 - 13/2*g**3 + 18*g**2 + 49*g. Factor b(a).
3*(a - 12)*(a - 1)
Let n(f) be the first derivative of -17 - 1/12*f**4 + 0*f**2 + 1/3*f**3 - 14*f. Let j(y) be the first derivative of n(y). Factor j(d).
-d*(d - 2)
Let x(h) be the third derivative of h**5/20 + 41*h**4/8 - 225*h**3 - 5056*h**2. Factor x(d).
3*(d - 9)*(d + 50)
Find z such that 712/17*z + 33922/17*z**3 - 15628/17*z**4 - 182/17*z**5 - 19528/17*z**2 + 704/17 = 0.
-88, -2/13, 2/7, 1
Factor -1/8*p**2 - 124609/2 + 353/2*p.
-(p - 706)**2/8
Let v(w) be the third derivative of w**6/60 + 13*w**5/6 - 11*w**4/2 - 18*w**2 + 5. Factor v(l).
2*l*(l - 1)*(l + 66)
Suppose w - 13 = -i, -538*w = -539*w - 3*i + 29. Find v such that w*v + 8/3 - 1/3*v**3 + 2*v**2 = 0.
-1, 8
Factor 9004*d**5 - d**2 + 68*d**3 - 789*d**4 - 12206*d**4 + 159*d**3 + 3765*d**5.
d**2*(d - 1)*(113*d - 1)**2
Suppose -5*w - 11 = -3*a, -2*w - 1 = -2*a + 1. Let r be (1 - 70/75)/((-1)/a). Solve -4/5 - r*o**2 + 4/5*o = 0.
2
Suppose 0 = -21*x + 33 + 9. Factor -11*q**4 + x*q**3 + 20*q + 6*q**4 - 12*q**3 + 20 - 10*q**3 - 15*q**2.
-5*(q - 1)*(q + 1)*(q + 2)**2
Suppose -5*k = 4 - 14. Suppose 5*w + 0*v = v + 145, -k*w = -3*v - 71. What is p in 4*p**2 - 3*p**2 + w*p - 30*p = 0?
0, 2
Factor -102*f**2 - 794*f**4 + 2381*f**4 - 793*f**4 - 144*f - 9*f**3 - 791*f**4.
3*f*(f - 8)*(f + 2)*(f + 3)
Let d(i) = 44*i**2 - 1312*i + 1284. Let t(z) = 16*z**2 - 438*z + 428. Let m(o) = -3*d(o) + 8*t(o). What is r in m(r) = 0?
1, 107
Let r = 350 - 331. Suppose -r + 70 = 17*t. Factor 324/5*f - 48/5 - 504/5*f**2 - 147/5*f**t.
-3*(f + 4)*(7*f - 2)**2/5
Let x(v) be the second derivative of -55/3*v**3 + 200*v**2 - 1/3*v**4 + 0 + 1/10*v**5 - 24*v. Determine k, given that x(k) = 0.
-8, 5
Let f(s) be the third derivative of 1/300*s**6 + 0 + 1/15*s**5 + 12*s**2 + 1/1680*s**8 - 9*s + 1/3*s**3 - 1/175*s**7 - 9/40*s**4. Factor f(a).
(a - 5)*(a - 1)**3*(a + 2)/5
Let v be (27645/532 - 52)*-8. Solve 3042/7 - 156/7*d + v*d**2 = 0 for d.
39
Let k(o) be the second derivative of 0 + 1/4*o**5 + 5/2*o**3 + 45/2*o**2 - 25/12*o**4 - 17*o. Solve k(p) = 0.
-1, 3
Suppose 8*d = 7*d + 7. Let t be d - (20/2 - 5). Factor 0*o + 0 - 1/2*o**t - 1/2*o**3 + 1/2*o**4 + 1/2*o**5.
o**2*(o - 1)*(o + 1)**2/2
Suppose 51/4*s**2 + 3/4*s**3 - 60 + 93/2*s = 0. Calculate s.
-10, -8, 1
Let w(k) = -61133*k + 183402. Let d be w(3). Solve -240*t - 4/3*t**4 - 80/3*t**d - 108 - 472/3*t**2 = 0.
-9, -1
Find p such that -1805/4*p + 0 - 95/2*p**2 - 5/4*p**3 = 0.
-19, 0
Let o(u) be the third derivative of -u**7/1680 + u**6/120 - 3*u**5/80 + 15*u**4/8 - 40*u**2. Let r(h) be the second derivative of o(h). What is d in r(d) = 0?
1, 3
Let g(a) be the third derivative of 0*a**3 + 0*a**4 + 7/540*a**6 - 123*a**2 + 0*a**5 + 1/1512*a**8 + 0*a + 8/945*a**7 + 0. Factor g(f).
2*f**3*(f + 1)*(f + 7)/9
Let v(t) be the third derivative of -7/16*t**4 - 243*t**2 - 3/2*t**3 - 1/40*t**5 + 0 + 0*t. Factor v(h).
-3*(h + 1)*(h + 6)/2
Let g be 7/(-204)*166 - 38/(-228) - -6. Let m be 0 + (32/34)/2. Factor -g*q - m - 2/17*q**2.
-2*(q + 2)**2/17
Let f(i) = -3*i**3 - 423*i**2 + 810*i - 429. Let j(h) = -2*h**2 + h - 2. Let a(d) = f(d) - 15*j(d). Factor a(q).
-3*(q - 1)**2*(q + 133)
Let f(p) = 117*p**2 + 15*p - 435. Let w(t) = -8*t**2 + 4*t - 1. Let b(u) = -f(u) - 15*w(u). Solve b(x) = 0.
10, 15
Let s(c) be the first derivative of -c**6/12 + 3*c**5/5 - 3*c**4/8 - 13*c**3/3 + 6*c**2 + 812. Determine z so that s(z) = 0.
-2, 0, 1, 3, 4
Suppose 150*m - 115*m - 18 = 26*m. Factor 153*b + 60 + 15/2*b**m.
3*(b + 20)*(5*b + 2)/2
Let f(j) = 2*j**2 + 5*j + 13. Let n be f(-3). Solve 10*g - 22 + 58 - 2*g**2 - 26 - n - 2*g**3 = 0.
-3, 1
Suppose 16*q - 12*q = 276. Let k be 342/38 - q/9. Factor -1/3*d**4 - d**2 - 4/3*d**3 + k + 4/3*d.
-(d - 1)*(d + 1)*(d + 2)**2/3
Let h(t) = -2*t + 8. Let j be h(3). Suppose 3*u**j + 14*u - 18*u - 4 + u**2 - 4 = 0. What is u?
-1, 2
Let s(d) be the first derivative of 15 - 54925/2*d**4 - 156*d**2 - 16/5*d - 3380*d**3. Suppose s(v) = 0. Calculate v.
-2/65
Let g(j) = -8*j + 24. Let h be g(3). What is o in 371*o + h*o**2 + 5*o**2 - 371*o = 0?
0
Let q be 0 + ((-148)/(-703))/(291/57 - 5). Let 3/2*b**4 + 0*b + 0 + 3/2*b**5 + 0*b**q + 0*b**3 = 0. Calculate b.
-1, 0
Let c be (3 - (-148)/(-48))/(8/(-520)*5). Let a(q) be the first derivative of -15 - 1/18*q**6 - c*q**4 - 2/3*q**2 + 2/5*q**5 + 0*q + 4/3*q**3. Factor a(p).
-p*(p - 2)**2*(p - 1)**2/3
Factor -38598*r**2 + 77199*r**2 - 38600*r**2 - 67*r.
r*(r - 67)
Let l(j) = j**3 + 2*j**2 + j + 2. Let n(g) = -28*g**3 - 1158*g**2 + 2078*g + 500. Let y(u) = -10*l(u) - n(u). Factor y(t).
2*(t - 2)*(t + 65)*(9*t + 2)
Suppose -4*p = 2*d - 20, -5*d = -10*d + 2*p - 10. Suppose -v + 116 = -b + 117, 4*v - 38 = -3*b. Factor 0 + d*i**4 + 0*i**2 + 3/7*i**v + 0*i - 3/7*i**3.
3*i**3*(i - 1)*(i + 1)/7
Suppose 2/5 + 19/5*n - 133/5*n**3 + 132/5*n**4 - 36/5*n**5 + 16/5*n**2 = 0. What is n?
-1/6, 1, 2
Let v(x) = 367*x - 16513. Let q be v(45). Find f, given that 0 + f**4 - 1/2*f**3 - f**q + 0*f + 1/2*f**5 = 0.
-2, -1, 0, 1
Suppose 131/4 + 65/2*h - 1/4*h**2 = 0. Calculate h.
-1, 131
Let x(f) be the first derivative of 2*f**3/27 - 68*f**2/3 + 406*f/9 + 202. Factor x(l).
2*(l - 203)*(l - 1)/9
Factor 2 + 17*t - 22367*t**3 + 43*t**2 + 22353*t**3 - 48*t.
-(t - 2)*(t - 1)*(14*t - 1)
Solve -3798*k - 3606201 + 893*k**2 - 1794*k**2 + 900*k**