 t(k) be the third derivative of k**6/600 + k**5/100 - k**4/5 + 19*k**3/2 + k**2 - 49. Let x(f) be the first derivative of t(f). Factor x(b).
3*(b - 2)*(b + 4)/5
Factor 24970*c**2 - 1246700/3*c + 1300/3*c**3 + 5/3*c**4 + 4598405/3.
5*(c - 7)**2*(c + 137)**2/3
Let m = -167 + 172. Factor 7*n**m - 10*n**3 + 10*n**2 - 5*n**3 + 2*n**5 - 4*n**5.
5*n**2*(n - 1)**2*(n + 2)
Let m(v) be the second derivative of v**5/30 + 10*v**4/3 + v + 517. Factor m(w).
2*w**2*(w + 60)/3
Suppose -179*m - 4 = -171*m - 4. Let c(y) be the first derivative of m*y + 1/5*y**5 - 1/2*y**4 + 0*y**2 - y**3 + 31. Let c(l) = 0. What is l?
-1, 0, 3
Let a(h) be the first derivative of 35/3*h**3 + 22 + 5/4*h**4 + 0*h + 15*h**2. Solve a(r) = 0 for r.
-6, -1, 0
Let d(x) be the second derivative of x**7/2520 - x**6/90 - 3*x**5/40 + 27*x**4/4 - 3*x - 11. Let b(q) be the third derivative of d(q). Factor b(n).
(n - 9)*(n + 1)
Suppose -2 = -4*b + 2*b + 2*j, b - 9 = -j. Find a, given that 15*a**4 - 15*a**2 - a**3 + 15*a**5 - 5*a**b - 5*a - 4*a**3 = 0.
-1, -1/2, 0, 1
Let 21169*v**4 - 21171*v**4 + 16*v**2 + 10*v**3 + 43*v - 139*v = 0. What is v?
-3, 0, 4
Let o be 116/357 + 304/(-7752). Factor -2*k**2 - 16/7 + o*k**3 + 4*k.
2*(k - 4)*(k - 2)*(k - 1)/7
Determine k, given that -3541*k + 2*k**4 + 3108*k**2 + 126224 - 3543*k - 14314*k - 16943*k + 5805*k - 130*k**3 = 0.
14, 23
Let r = -7142/11 + 21778/33. Factor 88/3*o - r - 10/3*o**3 - 16/3*o**2.
-2*(o - 2)*(o + 4)*(5*o - 2)/3
Let t(f) be the second derivative of 3*f**5/20 + 9*f**4 + 251*f**3/2 + 324*f**2 - 7*f + 251. Suppose t(u) = 0. What is u?
-27, -8, -1
Let l(d) be the first derivative of d**7/147 - 8*d**6/105 + d**5/10 - 39*d - 154. Let j(x) be the first derivative of l(x). Factor j(h).
2*h**3*(h - 7)*(h - 1)/7
Let b(r) be the first derivative of 0*r**3 + 27/5*r**5 + 0*r**2 - 1/2*r**6 + 0*r + 132 - 6*r**4. Factor b(q).
-3*q**3*(q - 8)*(q - 1)
Let c = 849 - 847. Factor -h**c + 18 - 8*h - 9*h + 14*h.
-(h - 3)*(h + 6)
Solve 18/5*o + 35 - 1/5*o**2 = 0.
-7, 25
Suppose 915/8*l**4 - 141/2 + 9/4*l**5 - 191/2*l + 1911/8*l**2 + 821/2*l**3 = 0. Calculate l.
-47, -3, -2/3, 1/2
Suppose 0 = 19*r - 5*r - 126. Solve 511*g**3 - 4*g**5 - 517*g**3 + r*g**4 + g**5 = 0 for g.
0, 1, 2
Let y(q) = q**2 + 30*q - 19. Let v be y(-31). Let x be ((-4)/v - (-2)/(-3)) + 4. Factor 20*r + 0*r**3 - 10*r**2 - 24 + 64 - 5*r**x.
-5*(r - 2)*(r + 2)**2
Let j(n) be the first derivative of -n**4/54 + 4*n**2/9 + 43*n - 75. Let l(p) be the first derivative of j(p). Factor l(x).
-2*(x - 2)*(x + 2)/9
Let v = 54334/3 - 380326/21. Factor -12/7*y + 8/7 + v*y**2.
4*(y - 2)*(y - 1)/7
Let z(j) = -2*j**2 - 35*j - 54. Let b be z(-16). Let o be b/12 + (-18)/(-4). Factor 0 + 0*n**2 + 2/3*n**5 - 4/3*n**3 + 0*n - 2/3*n**o.
2*n**3*(n - 2)*(n + 1)/3
Let l(v) be the first derivative of -4*v**3/3 + 624*v**2 - 97344*v + 2339. Suppose l(b) = 0. Calculate b.
156
Let d(x) be the second derivative of -3*x**5/20 - 23*x**4/4 - 107*x**3/2 - 255*x**2/2 - 3419*x. Find w, given that d(w) = 0.
-17, -5, -1
What is p in -7*p + 7*p - 3218*p**2 + 2*p**3 + 1480*p**2 = 0?
0, 869
Let c(t) = -t**3 - 5*t**2 + 17*t - 11. Let h be c(-8). Suppose 15 = -2*i + h. Determine b, given that -15 - 16*b**2 + 18 - 52*b - i = 0.
-3, -1/4
Let c(a) be the first derivative of 10/3*a**2 - 8*a - 244 + 4/9*a**3. Factor c(p).
4*(p - 1)*(p + 6)/3
Let i be (-164)/(-2) + 1099756/(-13671). Determine v so that 2/9*v**4 + 0 + 28/9*v**2 + 16/9*v + i*v**3 = 0.
-4, -2, -1, 0
Let o = 392 - 390. Determine l so that 115 + 84*l - 253 + 318 - 4*l**o - 4*l**3 = 0.
-3, 5
Let p(k) be the second derivative of k**4/30 + 3568*k**3/15 + 3182656*k**2/5 + 4*k - 648. What is b in p(b) = 0?
-1784
Let c = 4036 + -4036. Let g(i) be the second derivative of 2/5*i**5 + 3*i**3 - 2*i**2 - 2*i**4 - 18*i + c. Let g(m) = 0. What is m?
1/2, 2
Let v be 178/267 + -1 + (-19)/(-3). Let i be -2 - (-7 + -1 + 4). Let -5*n + 10*n**2 + v*n**i - 11*n**2 = 0. Calculate n.
0, 1
Factor 2806*j + 1167*j**2 - 3*j**3 - 1946*j + 1486*j.
-3*j*(j - 391)*(j + 2)
Let s(z) be the first derivative of 2*z**3/33 + 1554*z**2/11 - 3110*z/11 - 4697. Solve s(u) = 0.
-1555, 1
Let j = 175/51 - -721/102. Factor j*i**2 - 41/2*i + 6 + 12*i**3 + 2*i**4.
(i + 3)*(i + 4)*(2*i - 1)**2/2
Let r be 10*((-1273)/(-76) + -17) - -3. Find k such that 5*k - 25/2 - r*k**2 = 0.
5
Factor 1092/5*u**3 + 4332/5*u**2 + 0 + 3/5*u**4 + 864*u.
3*u*(u + 2)**2*(u + 360)/5
Let g(q) be the first derivative of -q**6/60 + 3*q**5/4 - 28*q**4/3 - 5*q**3/2 + 225*q**2/4 - 50*q - 89. Let y(d) be the first derivative of g(d). Factor y(h).
-(h - 15)**2*(h - 1)*(h + 1)/2
Let n be ((-8)/2)/4 - 11. Let c = 17 + n. Factor -10*j**3 + 16*j**2 - j**c + j**3 - 8*j**3 - 6*j + j**2 + 7*j**4.
-j*(j - 3)*(j - 2)*(j - 1)**2
Let u be 3/3 - 12/(-348)*-29. Let l(q) be the third derivative of -1/600*q**6 - 44*q**2 + 0 + 0*q**3 + 0*q + u*q**4 + 1/300*q**5. Factor l(f).
-f**2*(f - 1)/5
Let q(k) = 2*k**2 + 12*k - 23. Let b be q(-11). Factor 0*t**4 - b*t**5 - 4*t**2 + 5*t**4 + 5*t**3 + 82*t**5 - t**2.
-5*t**2*(t - 1)**2*(t + 1)
Factor 1/4*m**5 + 101/4*m**4 + 1349/2*m**3 + 7301/4*m + 2401/4 + 3749/2*m**2.
(m + 1)**3*(m + 49)**2/4
Let j(s) be the second derivative of 1010025*s**4/4 - 2010*s**3 + 6*s**2 - 308*s + 3. Factor j(o).
3*(1005*o - 2)**2
Let p(t) be the third derivative of t**6/180 + 2*t**5/9 + 17*t**4/36 - 38*t**3/9 - 3*t**2 - 244. Factor p(s).
2*(s - 1)*(s + 2)*(s + 19)/3
Suppose -3*o - 114 = -3*c, -3*o - c - 50 = 52. Let h be 240/o + 6 - 185/(-175). Determine r so that 3/5*r + h*r**3 - 1/5*r**4 + 0 + r**2 = 0.
-1, 0, 3
Let b(c) = -15*c**3 - 19*c**2 + 15*c + 4. Let n(r) = -7*r**3 - 8*r**2 + 7*r + 2. Let z(j) = -2*b(j) + 5*n(j). Factor z(w).
-(w - 1)*(w + 1)*(5*w + 2)
Find i such that -186553*i**3 - 4176*i**5 + 4175*i**5 - 2281024*i**2 - 5249888 - 7140512 + 868*i**4 - 9236480*i + 3465*i**3 = 0.
-4, 440
Let z(s) = -20*s**3 + 5420*s**2 - 3*s - 5328. Let a(j) = 5*j**3 - 1355*j**2 + j + 1331. Let v(c) = 23*a(c) + 6*z(c). Determine t so that v(t) = 0.
-1, 1, 271
Let q(s) = 2*s**2 - 3*s - 34. Let z(o) = -o**2 + 2*o + 17. Let c(y) = 2*q(y) + 5*z(y). Let l be c(6). Factor -l*r**3 - 7*r + 13 - 9*r**2 - 15 - 2*r**4 + r**4.
-(r + 1)**3*(r + 2)
Suppose 7 = -13*h + 33. Suppose -h*p = -3*r + 22, -r + 0*r - 3*p - 11 = 0. What is q in 3/2*q**2 - q**r - 1/2 + 1/2*q**3 - 1/2*q = 0?
-1, -1/2, 1
Let i(k) be the third derivative of -k**6/300 + k**5/150 + 14*k**4/15 - 476*k**2. Suppose i(v) = 0. Calculate v.
-7, 0, 8
Let x(f) be the third derivative of -f**6/60 + 226*f**5/15 - 75*f**4 - 11650*f**2. Determine c, given that x(c) = 0.
0, 2, 450
Let a(h) be the second derivative of h**4/16 + 85*h**3/8 + 63*h**2/2 - 412*h - 2. Factor a(g).
3*(g + 1)*(g + 84)/4
Let v = -101985 + 101987. Factor 46*d + 40/3 - 7/3*d**v.
-(d - 20)*(7*d + 2)/3
Suppose n + w - 4 = 0, 0 - 16 = -4*n - 3*w. Suppose 103 = n*h - 5. Factor -18*l**3 + h*l + 9 - 12*l**2 - 15*l**4 + 4*l**2 - 6*l + 14*l**2 - 3*l**5.
-3*(l - 1)*(l + 1)**3*(l + 3)
Let w(y) = 11*y - 32. Let t be w(12). Factor -121*g**2 + 4*g - 5*g + t*g**2.
-g*(21*g + 1)
Let k be (-23)/(-6) + (-30)/(-180). Solve -213*h**3 - 7*h**2 + 38*h**3 - 23*h**2 + 0*h**2 - 180*h**k = 0.
-3/4, -2/9, 0
Let u(s) be the third derivative of -s**6/120 + s**5/4 + 17*s**4/24 - 7*s**3/3 + 6*s**2. Let p be u(16). Factor -9 + 9*d + 15 + 3*d**3 - 9*d**p - 9.
3*(d - 1)**3
Let p be (-2 - 145/(-87))*(3 + -4). Determine v so that 0 - p*v - 37/3*v**3 - 20*v**4 - 12*v**5 - 10/3*v**2 = 0.
-1/2, -1/3, 0
Let f(z) = 167*z**2 - 333*z - 2. Let m be f(2). Suppose -1/2*s**2 + 1/2*s**4 + m*s + 0 + 1/4*s**3 - 1/4*s**5 = 0. What is s?
-1, 0, 1, 2
Let n = 159643 - 1117495/7. Factor -4/7*w - 2/7*w**2 + n.
-2*(w - 1)*(w + 3)/7
Find u such that 12 - 25/2*u**3 - 15/2*u**2 - 9/2*u**4 + 13*u - 1/2*u**5 = 0.
-4, -3, -2, -1, 1
Let c(v) be the third derivative of v**6/40 - 23*v**5/20 + 7*v**4 + 40*v**3 - 109*v**2. Factor c(m).
3*(m - 20)*(m - 4)*(m + 1)
Suppose 36*v - 99 = 3*v. Let b(y) = 2*y**3 + 4*y**2 + 8*y - 16. Let c(z) = z**3 + 4*z**2 + 8*z - 16. Let s(m) = v*b(m) - 4*c(m). Factor s(k).
2*(k - 2)**2*(k + 2)
Let m be 27*728/(-2457) + -1 + 13 + -2. Solve -6 + 27/7*c - 3/7*c**m = 0 for c.
2, 7
Suppose 5*k + 6 = -4*l, 3*l + 8 = 2*k + 2*l. Suppose 0 = 4*g - 3*i - 43, -k*i + 0*i - 22 = -2*g. What is h