. Let h be -2*(-5)/((-30)/b). Solve -3*s + h*s - s**2 + 27 - 35 = 0 for s.
2, 4
Let z(b) = -7*b**3 + 227*b**2 - 1943*b + 4573. Let o(x) = -15*x**3 + 455*x**2 - 3887*x + 9137. Let f(q) = -3*o(q) + 7*z(q). Let f(n) = 0. What is n?
5, 46
Let o = -380175 + 380177. Suppose 3/5*s + 21/5*s**o - 3/5*s**3 - 21/5 = 0. Calculate s.
-1, 1, 7
Let l = 305 - 318. Let h be (-3)/(-2) - (-10)/130*l. Factor 1/6*w**4 - 1/3*w**3 - h*w**2 + 2/3*w + 2/3.
(w - 2)**2*(w + 1)**2/6
Let z(b) be the second derivative of -b**4/6 - 190*b**3 - 81225*b**2 - 32*b - 6. Factor z(g).
-2*(g + 285)**2
Let b(f) be the third derivative of -f**6/40 + 18*f**5/5 - 141*f**4/8 + 35*f**3 - 1056*f**2. Factor b(y).
-3*(y - 70)*(y - 1)**2
Let j(u) be the second derivative of u**4/6 - 7508*u**3/3 + 14092516*u**2 - 2630*u - 1. What is h in j(h) = 0?
3754
Let p be (-100)/40*(-88)/70. Let b = p + -10/21. Factor -4/3*v**2 + 0*v - b*v**4 + 0 + 10/3*v**3 + 2/3*v**5.
2*v**2*(v - 2)*(v - 1)**2/3
Let j(h) be the first derivative of -7*h**4/4 - 2822*h**3/9 - 178*h**2 + 536*h/3 - 2227. Find n, given that j(n) = 0.
-134, -2/3, 2/7
Let w(b) be the first derivative of -b**4/36 - 5*b**3/9 + 11*b**2/6 - 20*b + 42. Let i(g) be the first derivative of w(g). Solve i(j) = 0.
-11, 1
Let z = 7/144 - -47/144. Let l be 45/(-150)*(-10)/24. Factor -l*s**3 - 1/4*s + z*s**2 + 0.
-s*(s - 2)*(s - 1)/8
Determine b, given that 2*b**2 - 6*b**3 - 2*b**3 + 23*b**3 - b**5 - 20*b**3 - b**4 + 5*b**4 = 0.
0, 1, 2
Let y(v) be the first derivative of 2*v**3/15 - 391*v**2/5 - 784*v/5 - 1601. Determine g, given that y(g) = 0.
-1, 392
Let i = 366459/488452 + -30/122113. Factor -i*s - 1/4*s**2 + 1/4*s**4 + 3/4*s**3 + 0.
s*(s - 1)*(s + 1)*(s + 3)/4
Suppose 59*p - 34*p = -3 + 3. Let y(r) be the third derivative of 0*r + r**2 + p - 1/180*r**5 - 1/6*r**3 - 1/18*r**4. Factor y(w).
-(w + 1)*(w + 3)/3
Let o(z) = 12*z**2 + 28*z - 4. Suppose 0 = -95*m + 98*m + 15. Let h(f) = 14*f**2 + 27*f - 5. Let y(g) = m*o(g) + 4*h(g). Factor y(t).
-4*t*(t + 8)
Let n(b) be the first derivative of 65*b**3/9 + 145*b**2/4 - 170*b/3 - 1887. Suppose n(u) = 0. What is u?
-4, 17/26
Let w(p) be the second derivative of -p**7/30 + 16*p**6/15 - 201*p**5/20 + 27*p**4/4 + 4*p**2 + 34*p. Let i(x) be the first derivative of w(x). Factor i(v).
-v*(v - 9)**2*(7*v - 2)
Factor 54*m**5 + 6938*m**3 - 3196*m**2 + 1534*m**2 - 4*m**5 + 968*m - 1140*m**4 - 3354*m**2.
2*m*(m - 11)**2*(5*m - 2)**2
Let r = -224062 - -1120313/5. Let k be 4/(10/3 + 0). Determine a, given that r*a - 3/5*a**2 + k = 0.
-1, 2
Let v(p) be the first derivative of -1/33*p**4 + 0*p + 1/330*p**5 - 20 + 0*p**3 + 25/2*p**2. Let q(f) be the second derivative of v(f). Factor q(l).
2*l*(l - 4)/11
Let v = 810 - 792. Find q, given that 77 - 64*q + v*q - 24*q - 2*q**2 + 71 = 0.
-37, 2
Find a, given that 171*a**2 + 4*a**3 - 354*a**2 + 42*a**2 - 396*a - 7*a**3 = 0.
-44, -3, 0
Let s = 1670 + -1670. Find p, given that s*p**2 + 2/5*p**5 + 0*p - 12/5*p**3 + 0 - 2*p**4 = 0.
-1, 0, 6
Suppose 5666 + 17630 = -14*o. Let a = o - -1666. Factor 3/2*h**3 - 1/2 + h**4 - 1/2*h**a - 3/2*h.
(h - 1)*(h + 1)**2*(2*h + 1)/2
Suppose -2*z + 532 - 1808 = 3*m, -5*z - 3179 = 2*m. Let j = 1273/2 + z. Factor -a - j*a**2 + 5/4*a**3 + 2 - 1/4*a**4.
-(a - 2)**3*(a + 1)/4
Let o = -100242 - -100246. Let 9*b + 0 - 3*b**o + 33/2*b**2 - 9/2*b**3 = 0. What is b?
-3, -1/2, 0, 2
Let l(a) be the second derivative of 0 + 0*a**2 - 16/3*a**4 + 203*a + 11*a**3 - 1/10*a**5. Determine w, given that l(w) = 0.
-33, 0, 1
Let z(q) be the second derivative of -q**7/42 + 21*q**6/2 - 24963*q**5/20 + 24649*q**4/12 - 44*q + 3. Suppose z(n) = 0. Calculate n.
0, 1, 157
Let i(p) be the second derivative of -1 - 13/18*p**3 + 1/36*p**4 + 11/3*p**2 + 2*p. Let i(f) = 0. Calculate f.
2, 11
Solve 7/2*w**2 + 9*w - 1/4*w**4 - 45/4 - w**3 = 0.
-5, -3, 1, 3
Let l(y) be the third derivative of -y**7/42 + 9*y**6/8 - 67*y**5/4 + 1085*y**4/24 + 1225*y**3 + 3*y**2 - 687*y - 2. Factor l(q).
-5*(q - 15)*(q - 7)**2*(q + 2)
Let i(u) be the first derivative of -7*u**6/57 - 184*u**5/19 - 1149*u**4/38 + 6136*u**3/57 + 2756*u**2/19 - 2016*u/19 - 2099. Let i(y) = 0. What is y?
-63, -4, -1, 2/7, 2
Suppose -h + 73 = -m, -2*m - 64 - 152 = -3*h. Suppose -116 = -2*c - 2*c. Factor -c*d**2 + 31 - 24*d + 21*d**3 + 35 - h.
(d - 2)*(3*d + 1)*(7*d + 2)
Suppose -252 = -2*q - 3*q - 2*h, -4*h + 4 = 0. Suppose q*p - 45*p = 0. Suppose p*y + 0 + 8/3*y**2 - 14/3*y**4 + 8*y**3 = 0. What is y?
-2/7, 0, 2
Let s(n) be the first derivative of n**3/8 - 12675*n**2/8 + 53551875*n/8 + 7230. Suppose s(x) = 0. What is x?
4225
Let x be (4/3)/((-6)/(-225)). Let r = x - 40. Factor -5*b**3 + 6*b**2 + 1 - b**3 + 4*b + b**4 + r*b**3.
(b + 1)**4
Let a be 3 - 12*12/8. Let n(g) = -9*g**2 + 28*g - 11. Let x(h) = -35*h**2 + 110*h - 45. Let m(f) = a*n(f) + 4*x(f). Factor m(w).
-5*(w - 3)*(w - 1)
Let a(b) = -18*b**3 - 130*b**2 - 379*b - 337. Let j(y) = 100*y**3 + 716*y**2 + 2084*y + 1852. Let h(c) = 28*a(c) + 5*j(c). Suppose h(w) = 0. What is w?
-11, -2
Let o(s) = 195*s**4 + 15*s**3 - 195*s**2 - 35*s. Let n(x) = 2*x**3 + 0*x**3 + x + x - 7*x + 28*x**4 - 28*x**2. Let h(g) = 20*n(g) - 3*o(g). Factor h(k).
-5*k*(k - 1)*(k + 1)*(5*k + 1)
Suppose 2*f - 3 = -5*d - 14, -f - 1 = d. Factor -10*k + 9*k**f + 9 - 2*k - 15*k**2 + 9*k**2.
3*(k - 3)*(k - 1)
Let j(y) = 6*y**2 + 180*y + 120. Let i(c) = -2 - 5741*c**2 + 5740*c**2 - 26*c - 15. Let x(g) = -27*i(g) - 4*j(g). Factor x(r).
3*(r - 7)*(r + 1)
Factor -100/13*x**2 + 2/13*x**3 + 0 + 66*x.
2*x*(x - 39)*(x - 11)/13
Suppose 3739*n + 28 = 3735*n + 5*j, -n - 2*j = -19. Suppose 86/9*c - 44/9 - 40/9*c**2 - 2/9*c**n = 0. Calculate c.
-22, 1
Let m(v) be the second derivative of 5*v**4/12 - 3320*v**3/3 + 1102240*v**2 - 2*v + 4457. Let m(n) = 0. What is n?
664
Let m(k) be the second derivative of k**9/12096 - k**7/840 + 3*k**3/2 - k**2 + 124*k. Let u(r) be the second derivative of m(r). Solve u(p) = 0.
-2, 0, 2
Let d = 3/298400 - -1210907173/2685600. Let o = 451 - d. Factor -o*r**3 + 0*r - 1/3*r**2 + 4/9.
-(r - 1)*(r + 2)**2/9
Let r(q) = -5*q**3 + 141*q**2 - 2175*q + 3. Let z(m) = 11*m**3 - 285*m**2 + 4349*m - 7. Let a(c) = -14*r(c) - 6*z(c). Find h, given that a(h) = 0.
0, 33
Let b(d) be the third derivative of d**7/42 - 11*d**6/2 + 789*d**5/2 - 10395*d**4/2 + 59535*d**3/2 - 2*d**2 + 3*d - 17. Solve b(o) = 0.
3, 63
Let j(f) be the first derivative of -110224*f**3/3 + 664*f**2 - 4*f - 1578. Factor j(v).
-4*(166*v - 1)**2
Let g(i) be the third derivative of i**7/168 + 5*i**6/18 + 3*i**3 + 105*i**2. Let b(n) be the first derivative of g(n). Let b(o) = 0. Calculate o.
-20, 0
Let s(n) be the first derivative of -n**6/6 - 24*n**5/5 - 21*n**4/4 + 46*n**3/3 + 4084. Factor s(p).
-p**2*(p - 1)*(p + 2)*(p + 23)
Let y(q) = -2*q**4 - 28*q**3 + 6*q**2 + 96*q + 62. Let g(o) = -7*o**4 - 58*o**3 + 13*o**2 + 192*o + 123. Let a(k) = 2*g(k) - 5*y(k). Solve a(r) = 0.
-1, 4
Let p(u) be the first derivative of -u**6/1980 + u**5/55 - 76*u**3/3 + 22. Let s(o) be the third derivative of p(o). Let s(m) = 0. What is m?
0, 12
Let y(r) be the second derivative of 1/12*r**4 + 0 + 30*r + 3/2*r**3 + 9*r**2. Factor y(d).
(d + 3)*(d + 6)
Let c(i) be the third derivative of i**5/60 - 7*i**4/12 + 13*i**3/3 - 24*i**2. Let x be c(12). Factor -4 - g**2 - 73*g + 3*g**2 + 75*g + 0*g**x.
2*(g - 1)*(g + 2)
Let l(t) be the second derivative of 2*t**7/35 - 16*t**6/75 - 121*t**5/25 - 122*t**4/15 + 304*t**3/5 + 1152*t**2/5 - 2468*t. Determine u so that l(u) = 0.
-3, -4/3, 2, 8
Factor 45*i**2 + 7/2*i**3 + 108 + 162*i.
(i + 6)**2*(7*i + 6)/2
Let x(i) be the third derivative of 14/3*i**3 + 3/5*i**5 + 0 + 0*i - 119*i**2 + 5/2*i**4 + 1/30*i**6. Find n such that x(n) = 0.
-7, -1
Let j(z) be the second derivative of -z**7/2310 - z**6/1320 - 32*z**2 - 154*z. Let h(f) be the first derivative of j(f). Let h(t) = 0. Calculate t.
-1, 0
Determine y so that -34/9*y**3 - 196/9 - 2/9*y**4 - 62/3*y**2 - 350/9*y = 0.
-7, -2, -1
Suppose -5*z = -b + 7, 0 = -4*b - z - 7 - 7. Let k be 10 + 33/b + 13/5. What is x in 14/5*x**3 - 2/5*x + k*x**4 + 0 + 4/5*x**2 = 0?
-1, 0, 1/4
Let p(x) be the second derivative of -5*x**4/12 - 520*x**3/3 - 3075*x**2/2 - 1605*x. Factor p(h).
-5*(h + 3)*(h + 205)
Suppose -37*h + 4*w + 69 = -38*h, -4*h + 5*w + 102 = 0. Determine d so that -51/4*d**2 + 12