 2)/5
Let h(m) = 3*m**3 + 6*m**2 + 1505*m + 3013. Let s be h(-2). Suppose 0 + 20/17*n**2 - 32/17*n - 2/17*n**s = 0. What is n?
0, 2, 8
Let f(d) = 4*d + 173. Let r be f(-40). Solve 20 + r*l**3 - 3*l**3 - 40*l + 4*l**2 + 7*l**2 + 4*l**2 - 5*l**4 = 0.
-2, 1, 2
Let r(q) be the first derivative of -2*q**6/21 + 17*q**5/35 - 65*q**3/21 + 32*q**2/7 - 12*q/7 + 628. Let r(a) = 0. Calculate a.
-2, 1/4, 1, 2, 3
Let u(v) = -3*v - 4. Let g = 28 + -32. Let n be u(g). Solve 6*b**2 - 8 - 4*b**3 - 8*b - 3*b**4 + n*b**3 + b**4 = 0 for b.
-1, 2
Suppose 6*l + 5 - 23 = 0. Factor -l*c + 3*c**5 - 20 + 6*c**4 - 28 + 48 - 6*c**2.
3*c*(c - 1)*(c + 1)**3
Let u(p) be the third derivative of p**5/240 + 115*p**4/8 + 1379*p**3/24 - 6*p**2 + 24. Factor u(a).
(a + 1)*(a + 1379)/4
Suppose 3*o + 27 = 3*y, 4*y + 4*o = -7 + 3. Let j = 11557 + -57766/5. Factor 70*z**2 - 125 + 1/5*z**5 + j*z**y + 25*z + 26*z**3.
(z - 1)*(z + 5)**4/5
Factor -121 - 57 - 199 - 83 - 555*v + 25*v**2.
5*(v - 23)*(5*v + 4)
Let v = 1143 - 1832. Let w = -4819/7 - v. Factor -8/7*x**4 + 0 + 0*x - w*x**5 + 0*x**2 - 4/7*x**3.
-4*x**3*(x + 1)**2/7
Suppose -41*a = -46*a + 20. Factor -y**4 + 42*y**3 + 3*y**3 - 35*y**2 - 198*y - 27*y - 6*y**4 + 2*y**a - 140.
-5*(y - 7)*(y - 4)*(y + 1)**2
Let i = 706 - 704. Let 13*l**2 + 2 - 2 - 56*l**2 + 7*l**i - 3*l**3 = 0. Calculate l.
-12, 0
Let b(l) be the third derivative of -20/3*l**4 + 1/5*l**5 + 0*l + 0 + 1/30*l**6 - 23*l**2 + 0*l**3. Factor b(u).
4*u*(u - 5)*(u + 8)
Let 110/9*d**3 + 50 + 1/9*d**5 + 355/3*d + 752/9*d**2 - 26/9*d**4 = 0. What is d?
-2, -1, 15
Let z(y) be the first derivative of 48*y**5/35 - 738*y**4/7 - 495*y**3/7 - 93*y**2/7 - 14017. Factor z(h).
3*h*(h - 62)*(4*h + 1)**2/7
Suppose 0 = -907*w - 901 + 2715. Factor -2187/4 + 5103/4*m - 1863/2*m**w + 447/2*m**3 + 3/4*m**5 - 87/4*m**4.
3*(m - 9)**3*(m - 1)**2/4
Let o(w) be the second derivative of 0 + 0*w**3 + 0*w**2 + 1/21*w**7 + 4/15*w**6 + 1/2*w**5 + 18*w + 1/3*w**4. Let o(b) = 0. Calculate b.
-2, -1, 0
Suppose -50*l + 12 = -44*l. Determine h, given that 5*h**2 - 28 - 2*h**l + 2*h**2 - 30*h - 10*h**2 + 3*h**2 = 0.
-14, -1
Let y(l) be the second derivative of -l**5/20 - 11*l**4/6 - 37*l**3/6 + 30*l**2 + 2383*l. Suppose y(n) = 0. What is n?
-20, -3, 1
Let g(b) be the second derivative of -b**6/144 - b**5/4 + 119*b**2 - 11*b. Let z(s) be the first derivative of g(s). Determine o, given that z(o) = 0.
-18, 0
Suppose 106 = -55*i + 271. Let -98/11*x**5 + 96/11 + 128*x**2 - 712/11*x - 162/11*x**i - 532/11*x**4 = 0. Calculate x.
-4, -3, 2/7, 1
Let l(j) be the second derivative of -j**4/108 + 103*j**3/27 - 205*j**2/18 + 31*j + 8. Determine u, given that l(u) = 0.
1, 205
Let f(x) be the first derivative of -16/5*x**5 - 54 - 8*x**2 + 16/3*x**3 + 3*x**4 + 0*x + 2/3*x**6. What is l in f(l) = 0?
-1, 0, 1, 2
Let t be (3 - (46/(-14) + 7))*(-152)/380. Factor -54/7 + 6/7*m**2 + 18/7*m - t*m**3.
-2*(m - 3)**2*(m + 3)/7
Suppose -724*b - 2164/3*b**2 - 8/3 = 0. What is b?
-1, -2/541
Let s(v) be the third derivative of -v**5/30 - 23*v**4/12 - 30*v**3 + 818*v**2. Factor s(h).
-2*(h + 5)*(h + 18)
Suppose -14 = -m - 4*f, -19 = 3*m - 5*f - 10. Find d, given that -20*d**2 + 135*d - 9*d**2 - 135 - 16*d**2 + 12*d**m + 5*d**3 - 12*d**2 = 0.
3
Let b be -4*8/64*-10. Factor 1810*o**4 + 185*o**3 + 11*o**b - 1895*o**4 - 161*o**2 - 20 - 34*o**2 + 47*o + 4*o**5 + 53*o.
5*(o - 2)*(o - 1)**3*(3*o - 2)
Let r(u) = 15*u**3 - 223*u**2 - 212*u + 1023. Let t(b) = 84*b**3 - 1116*b**2 - 1060*b + 5116. Let x(n) = -16*r(n) + 3*t(n). Determine h so that x(h) = 0.
-17, -3, 5/3
Let r be ((-5)/40)/(30/(-48)). Suppose 0 - r*c**4 + 0*c - 4*c**3 - 20*c**2 = 0. Calculate c.
-10, 0
Let w(z) = z**4 + 4*z**3 + 11*z**2 - 4*z - 4. Let k(b) = -b**3 - b**2 + b. Suppose 0 = 13*v - 46 + 7. Let x(s) = v*w(s) + 24*k(s). Factor x(n).
3*(n - 2)**2*(n - 1)*(n + 1)
Factor 4084/5 + 4092/5*t**2 - 8172/5*t - 4/5*t**3.
-4*(t - 1021)*(t - 1)**2/5
Let x(b) = 2*b**4 - 6*b**3 + 4*b**2. Let w(g) be the third derivative of -g**7/105 + 7*g**6/120 - g**5/12 + 27*g**2. Let n(o) = 4*w(o) + 5*x(o). Factor n(k).
2*k**3*(k - 1)
Factor -14/9*t**2 - 20/3*t + 0 + 2/9*t**3.
2*t*(t - 10)*(t + 3)/9
Suppose 50*h = 46*h - 512. Let p = 405 + h. Find a, given that -5*a**3 + 38*a - p*a**2 - 13*a + 287*a**2 - 30 = 0.
-2, 1, 3
Let j be 8/3 - 2 - (-119)/72. Let f = j + -13/24. Factor -f*m + 0 - 8/3*m**2 - 2/9*m**4 - 4/3*m**3.
-2*m*(m + 2)**3/9
Suppose -5*l - v = -18 + 6, -v - 15 = -4*l. Let w = 94307/17146 + -2/8573. Find u, given that -l + 5/6*u**4 + w*u**3 + 5/2*u + 61/6*u**2 = 0.
-3, -1, 2/5
Suppose -96 + 26*a**3 - a**4 - 316/3*a**2 - 1/3*a**5 + 168*a = 0. What is a?
-12, 2, 3
Let d be 6*(34958/660)/227. Let 1/10*b**5 + 0 - 1/5*b**4 - 6/5*b**3 - d*b**2 - 1/2*b = 0. What is b?
-1, 0, 5
Suppose 3*v = -178*z + 177*z, -2 = z + 5*v. Let u(s) be the first derivative of -4/3*s**z + 0*s - 2*s**2 + 4. Factor u(w).
-4*w*(w + 1)
Let h(t) = 3*t - 17. Let m be h(11). Let y be -8 - (-248)/m - 7. Factor -y*l**4 + 0 + 3/2*l**3 + 0*l + 2*l**2.
-l**2*(l - 4)*(l + 1)/2
Factor -1/5*v**2 + 186/5*v + 187/5.
-(v - 187)*(v + 1)/5
Factor -155*k + 81 - 261 + 125 - 13 - 388 - k**2.
-(k + 3)*(k + 152)
Factor -2/3*v**2 - 148*v + 446/3.
-2*(v - 1)*(v + 223)/3
Let s be 36/14*(30 + (-528)/18). What is z in -s*z**3 + 12/7*z**2 - 3/7*z**4 + 0*z + 3/7*z**5 + 0 = 0?
-2, 0, 1, 2
Let q(a) = -a**5 - a**4 - a**3 + a**2. Let p(y) = 5*y**5 + 3*y**4 - 5*y**3 - 3*y**2. Let l = -128 + 125. Let t(w) = l*q(w) - p(w). Solve t(b) = 0 for b.
-2, 0, 2
Let z(x) = -x**4 - 60*x**3 - 363*x**2 - 639*x - 335. Let j(k) = k**4 + 90*k**3 + 545*k**2 + 957*k + 501. Let n(y) = 5*j(y) + 7*z(y). Factor n(h).
-2*(h - 20)*(h + 1)*(h + 2)**2
Let s = 175674/11 - 15966. Find k such that 0 + 56/11*k**2 - s*k - 6/11*k**4 - 12/11*k**3 + 2/11*k**5 = 0.
-3, 0, 2
Let y = -167/13 + 1121/65. Suppose -26/5*r - 8/5 - 4/5*r**3 - y*r**2 = 0. Calculate r.
-4, -1, -1/2
Let d = -117127 + 1288398/11. Factor d*k**3 - 6/11*k + 3/11*k**2 - 8/11.
(k - 2)*(k + 1)*(k + 4)/11
Factor 3/7*i**3 - 306/7 + 195/7*i + 108/7*i**2.
3*(i - 1)*(i + 3)*(i + 34)/7
Suppose -50 = -3*b - 137. Let u = 33 + b. Factor u*c**2 - 3*c**2 + 654*c - 653*c.
c*(c + 1)
Let p(n) be the first derivative of -2523*n**5/5 + 72993*n**4/2 - 700557*n**3 - 145986*n**2 - 10092*n + 7036. Suppose p(o) = 0. Calculate o.
-2/29, 29
Determine g so that 416784*g + 415872 + 1825/2*g**2 + 1/2*g**3 = 0.
-912, -1
Suppose 4*w - 9 = -2*p + 121, -5*p + 312 = -3*w. Let v = p - 49. Suppose 7*t - v*t**3 - 11*t + 4*t**4 - 4*t**2 + 18*t**3 = 0. What is t?
-1, 0, 1
Let x(b) = 3*b - 28. Let t be x(11). Suppose -2*u + 22 = -3*n, u = -3*n + 7 - t. Factor 2*g**3 + u*g - 8*g**3 - 10*g**2 + 8*g**3.
2*g*(g - 4)*(g - 1)
Let u(f) be the second derivative of 2/3*f**3 + 3*f**2 - 1/6*f**4 + 69*f + 0. Factor u(b).
-2*(b - 3)*(b + 1)
Let f(i) be the first derivative of 2/3*i**3 - 10/3*i + 1/12*i**4 - 4 + 1/2*i**2. Solve f(v) = 0 for v.
-5, -2, 1
Let 60/7*m**2 + 0 - 4/7*m**3 - 104/7*m = 0. What is m?
0, 2, 13
Let g(f) be the second derivative of -f**4/3 + 904*f**3/3 - 102152*f**2 - 6*f + 26. Find d, given that g(d) = 0.
226
Let q = -1018409 - -319780925/314. Let t = q - 14/157. Factor 0 - t*k - 1/4*k**2.
-k*(k + 6)/4
Solve 2/7*x**2 + 4*x + 80/7 = 0 for x.
-10, -4
Let i(q) be the first derivative of 10/9*q**3 - 3*q**2 - 5 + 8/3*q. Factor i(p).
2*(p - 1)*(5*p - 4)/3
Let h(d) be the first derivative of -d**6/360 + d**5/24 - d**4/6 + d**3/3 - 10*d - 22. Let i(o) be the third derivative of h(o). Solve i(r) = 0.
1, 4
Let p(h) be the second derivative of -h**9/7560 - h**8/300 - 7*h**7/300 + 37*h**3/6 - 132*h. Let j(m) be the second derivative of p(m). Factor j(s).
-2*s**3*(s + 7)**2/5
Determine m so that 20/9*m - 22/9*m**3 - 2/3*m**2 + 0 + 2/9*m**5 + 2/3*m**4 = 0.
-5, -1, 0, 1, 2
Let 55488 + 3*s**2 - 1734*s + 86196 - 39518 - 5711 + 154108 = 0. What is s?
289
Suppose -17*r + 13*r = v - 9, -5*r - v + 11 = 0. Suppose -5*f + 23 = -12. Factor 5*p**r + 7348 - 7358 + f*p - 2*p.
5*(p - 1)*(p + 2)
Let h(x) be the first derivative of -x**6/40 + 2*x**5/5 - 15*x**4/8 + x**2/2 - 29*x - 64. Let r(k) be the second derivative of h(k). Find o such that r(o) = 0.
0, 3, 5
Let b(m) be the third derivative of m**8/312 - m**7/273 - 37*m**6/780 - 31*m**5/390 - m**4/26 + 223*m**2. Let b(v) = 0. C