- 3)*(v - 2)/3
Find a such that 0*a + 0 - 69/2*a**3 - 3/2*a**4 + 162*a**2 = 0.
-27, 0, 4
Let g be (-234)/(-14) + 4/14. Suppose 222*n = 223*n - 45. Factor -n*i**2 + 12*i**4 - g*i**4 + 2*i**3 + 4*i**3 + 24*i**3.
-5*i**2*(i - 3)**2
Let a = 77 + -79. Let m be (-51 - -52)*a/(-10). Find k, given that -4/5 - m*k**2 + 4/5*k = 0.
2
Let s(q) = 18*q**2 - 904*q + 7894. Let w be s(39). Find c such that 3*c**4 - 47/4*c**3 - w - 1/4*c**5 + 13*c**2 + 12*c = 0.
-1, 1, 4
Let w be 34*(-357)/(-27)*(-6)/(-7). Let c = w + -385. Factor -c*k**2 + 0 + k**3 + 1/3*k**4 - k.
k*(k - 1)*(k + 1)*(k + 3)/3
Let s(g) be the third derivative of -23*g**2 + 0 + 1/210*g**5 + 0*g + 256/21*g**3 + 8/21*g**4. Let s(h) = 0. What is h?
-16
Suppose -a = -5, 5*x - 2*a + 36 + 24 = 0. Let p be 2 - x/((-3)/(15/35)). Solve -4/7*i**2 + 8/7 - p*i = 0 for i.
-2, 1
Let f be 16/(672/1098) - ((-10)/14)/(-5). Let b(z) be the third derivative of 7/72*z**4 - 1/180*z**5 + 0*z**3 + 0*z + 0 - f*z**2. Determine i so that b(i) = 0.
0, 7
Suppose 2*n + n - 3 = 3*w, 3*n = 2*w + 5. Let r be (0 - n/(-2))*(-5 + 7). Let -2*i + 4*i - 43*i**3 + 18*i**3 - 6*i**4 + 23*i**r - 4 + 10*i**2 = 0. Calculate i.
-1, 2/3, 1
Let j(h) = 57*h**2 + 2106*h - 4202. Let u(f) = -33*f**2 - 1053*f + 2102. Let v(t) = 4*j(t) + 7*u(t). Find p, given that v(p) = 0.
2, 349
Let i(p) = 28 + 34 + 9*p**2 + p**2 + 5*p**3 + 6*p - 4*p**3. Let b be i(-10). Factor 5/2 + 0*x - 5/2*x**b.
-5*(x - 1)*(x + 1)/2
Suppose -8*d + 4*d = g - 180, -4*g = d - 765. Suppose 0 = -56*n + g + 32. Factor -7/6*w**2 + 0 + 7/6*w**n + 1/3*w**3 - 1/3*w.
w*(w - 1)*(w + 1)*(7*w + 2)/6
Let z(s) = -27*s**3 + 68*s**2 - 91*s + 48. Let u(h) = -13*h**3 + 34*h**2 - 46*h + 24. Let o(k) = -13*u(k) + 6*z(k). Factor o(f).
(f - 2)**2*(7*f - 6)
Find x such that -3*x**2 - 24930*x + 8898*x - 16064064 + 2*x**2 - 3*x**2 = 0.
-2004
Let i(t) be the first derivative of -208849*t**3 + 914*t**2 - 4*t/3 - 109. Factor i(o).
-(1371*o - 2)**2/3
Suppose 0 = 3*m + 4*y + 4, -m = -9*y + 10*y. Suppose 2*v - 4*q = 0, 2*q - m = 5*v - 12. Find p, given that 1/5*p + 0*p**v - 1/5*p**3 + 0 = 0.
-1, 0, 1
Suppose 0 = -78*k + 82*k + 24. Let u(q) = -2*q**3 + q**2 + 2*q + 1. Let j(d) = 7*d**3 + 5*d**2 - 7*d - 11. Let y(g) = k*u(g) - 2*j(g). Solve y(i) = 0.
-8, -1, 1
Let r = -1782 - -37423/21. Let c(b) be the second derivative of 0 + 0*b**2 + r*b**4 + 0*b**3 + 3*b - 3/70*b**5. Factor c(j).
-2*j**2*(3*j - 2)/7
Let m(g) be the second derivative of -g**5/12 + 84*g**2 + 2*g + 36. Let k(i) be the first derivative of m(i). Factor k(z).
-5*z**2
Let p(n) be the first derivative of 1/28*n**4 + 9/7*n - 17/14*n**2 + 134 + 1/3*n**3. Factor p(y).
(y - 1)**2*(y + 9)/7
Let f = 99/20 + -293/60. Let z(b) be the first derivative of 0*b**2 - 2 + 0*b + f*b**5 + 1/12*b**4 - 2/9*b**3. Determine n so that z(n) = 0.
-2, 0, 1
Let z(v) be the second derivative of 0*v**2 + 0 - 1/4*v**4 + 3/25*v**5 + 0*v**3 + 81*v + 1/50*v**6. Suppose z(i) = 0. What is i?
-5, 0, 1
Let g(n) be the first derivative of n**6/6 + 6*n**5/5 - 9*n**4 + 40*n**3/3 - 939. What is f in g(f) = 0?
-10, 0, 2
Suppose -72/5*c**2 + 54/5*c**4 - 3*c - 6/5*c**3 + 21/5*c**5 + 18/5 = 0. Calculate c.
-2, -1, 3/7, 1
Let u(c) be the first derivative of -c**6/240 - 7*c**5/40 - 49*c**4/16 + 2*c**3/3 + 22*c - 68. Let l(k) be the third derivative of u(k). Solve l(r) = 0.
-7
Let a be 175/15*(1 - 55/(-110)). Factor 9 - 1/2*v**3 + a*v + 8*v**2.
-(v - 18)*(v + 1)**2/2
Let y(g) be the second derivative of 81*g**2 - 5/6*g**4 + 1/30*g**5 - 5 + 12*g + 3*g**3. Find a, given that y(a) = 0.
-3, 9
Let l be ((-4)/20)/((-135)/(-1200)*-188 + 21). Find m, given that l*m**3 - 4/3 - 4/3*m + m**2 + 1/3*m**4 = 0.
-2, -1, 1
Let m = 492472/809439 + 10/35193. Find v, given that 12/23 - m*v**2 + 38/23*v = 0.
-2/7, 3
Let a(i) be the second derivative of -i**5/25 + 283*i**4/60 - 511*i**3/3 + 735*i**2/2 - 54*i + 4. Let a(b) = 0. What is b?
3/4, 35
Find a such that -1/4*a**3 + 373321/2 - 370877/4*a - 305*a**2 = 0.
-611, 2
Let y = -188 - -190. Find n, given that n**y - 37*n + 61*n - 27*n = 0.
0, 3
Determine m, given that -440*m**2 - 60*m + m**3 - 494*m**2 + 993*m**2 = 0.
-60, 0, 1
Let m(o) be the first derivative of -11*o**4/21 - 8*o**3/3 - 24*o**2/7 + 62*o + 72. Let k(y) be the first derivative of m(y). Factor k(d).
-4*(d + 2)*(11*d + 6)/7
Solve 223 + 369 - 804 + 638*d - 6*d**2 = 0 for d.
1/3, 106
Let w be 5/(195/6) + 1140/26. Let y = -38 + w. Let -4*i**4 - 3 + 0*i**4 + y*i**2 + 6*i**4 - 5*i**4 = 0. What is i?
-1, 1
Let i = -318 - -321. Factor 171*w**3 - 84*w**i - 82*w**3 - 50*w**2.
5*w**2*(w - 10)
Let b = 48/4051 - -502180/12153. Suppose -b*t + 1922/3 + 2/3*t**2 = 0. What is t?
31
Let z(g) be the first derivative of 7*g**5/15 + 267*g**4/4 + 22276*g**3/9 - 6090*g**2 + 13456*g/3 - 3572. Determine m, given that z(m) = 0.
-58, 4/7, 1
Let x = 443 - 399. Factor 367 - x + 267 + t**2 + 71 - 46*t - 132.
(t - 23)**2
Let w(f) be the first derivative of -f**4/12 - 43*f**3/3 - 127*f**2/3 + 1563. Suppose w(k) = 0. Calculate k.
-127, -2, 0
Suppose 0 = 615*n - 610*n - 3*j - 58, 0 = -4*n + 3*j + 53. Let -3/5*x**4 + 0*x + 0 - 3/5*x**n + 3/5*x**3 + 3/5*x**2 = 0. Calculate x.
-1, 0, 1
Let l be (-2592)/(-672) + ((-720)/(-84) - 9). Factor 36/7 + l*c**2 - 3/7*c**3 - 57/7*c.
-3*(c - 4)*(c - 3)*(c - 1)/7
Let s = -100356 + 100356. Suppose -20/3*a**2 - 20/3*a**3 + 0 + 5/3*a**4 + s*a + 5/3*a**5 = 0. Calculate a.
-2, -1, 0, 2
Suppose -5*k + 2*l - 80 = -7*k, -k + 43 = 2*l. Solve -17 + 26*g**2 + 8*g - g**2 + k*g + 7 = 0 for g.
-2, 1/5
Let z(t) be the first derivative of -4*t**3/3 + 1384*t**2 + 2772*t - 3418. Factor z(y).
-4*(y - 693)*(y + 1)
Let f be (49/(-14) - -2) + 13/2. Let k be 135/(-54)*(-4)/f. Factor -16/5*y**3 + 8*y**k + 3/5 + 23/5*y.
-(y - 3)*(4*y + 1)**2/5
Let b(p) = p**4 - p**3 + 3*p + 1. Let z(h) = -12*h**5 + 59*h**4 + 109*h**3 - 552*h**2 - 138*h + 2. Let v(u) = 2*b(u) - z(u). Suppose v(r) = 0. What is r?
-3, -1/4, 0, 4
Let z be (-1 + -1 - -5)/(2 + -6)*(-7 - -3). Solve -2/3*u**z + 1/3*u**5 + 1/3*u + 0 + 0*u**4 + 0*u**2 = 0 for u.
-1, 0, 1
Let n(v) be the third derivative of -1/195*v**5 + 2/39*v**3 - 66*v**2 + 0 + 1/156*v**4 - 1/780*v**6 + v. Determine q, given that n(q) = 0.
-2, -1, 1
Suppose -2*j + 9 = 4*n - 3*j, 3*n - 4 = -2*j. Factor -5*l + 23*l + 4*l**3 + 5*l**n - 12*l - 5*l.
l*(l + 1)*(4*l + 1)
Let f(p) = p**4 - 2*p**3 + p**2 + 3*p - 2. Let i(n) = 52*n**4 - 120*n**3 + 580*n**2 + 696*n - 112. Let a(t) = -56*f(t) + i(t). Factor a(s).
-4*s*(s - 11)*(s + 1)*(s + 12)
Suppose -200*y - 18 = -209*y. Let u(c) be the third derivative of -1/6*c**4 + 0 + 1/30*c**6 + 1/210*c**7 + 1/30*c**5 + 0*c - 1/2*c**3 + 13*c**y. Factor u(i).
(i - 1)*(i + 1)**2*(i + 3)
Let h(q) be the third derivative of -q**8/168 + 8*q**7/105 - 17*q**6/60 - q**5/15 + 2*q**4 + 362*q**2. Determine n, given that h(n) = 0.
-1, 0, 2, 3, 4
Suppose 165*f - 41*f = 60*f - 62 + 190. Determine v, given that -8/7*v**4 + 2/7*v + 0 - 8/7*v**f + 2/7*v**5 + 12/7*v**3 = 0.
0, 1
Let k(c) be the second derivative of -1/110*c**5 + 0*c**4 - 2*c + 0*c**2 + 10 + 3/11*c**3. Solve k(h) = 0 for h.
-3, 0, 3
Let o(v) = -4*v + 25. Let d be o(15). Let n = 39 + d. Factor 3*u**4 - 3*u**n + 3*u**2 - 3*u**4.
-3*u**2*(u - 1)*(u + 1)
Solve -6272*g**4 - 14250312723*g - 6206*g**4 + 12481*g**4 + 25431849*g**2 - 15129*g**3 = 0.
0, 1681
Factor -2/11*b**2 - 764/11*b + 1536/11.
-2*(b - 2)*(b + 384)/11
Let m(l) be the second derivative of l**6/10 - 81*l**5/4 + 4347*l**4/4 + 14283*l**3/2 - 3026*l. Factor m(o).
3*o*(o - 69)**2*(o + 3)
Solve 389 - 558*s + 185 - 825 - 167*s - 5*s**2 - 1179 = 0.
-143, -2
Let h = 166408 - 166406. Factor 1/3*m**5 - 2/3*m**3 - 2/3*m**h + 1/3*m**4 + 1/3 + 1/3*m.
(m - 1)**2*(m + 1)**3/3
Let j = -63/3797 + 53347/11391. Determine b, given that -10/3*b**2 - 2 - j*b - 2/3*b**3 = 0.
-3, -1
Let c(b) be the second derivative of 4*b - 175/3*b**3 - 3 - 125/12*b**4 - 245/2*b**2. Factor c(l).
-5*(5*l + 7)**2
Let u(b) be the first derivative of -b**6/180 - b**5/6 - 25*b**4/12 - b**3 + 5*b + 57. Let j(h) be the third derivative of u(h). Let j(z) = 0. Calculate z.
-5
Let d(a) be the first derivative of -13/2*a**4 - 2*a**2 + 22/3*a**3 + 8/5*a**5 + 0*a + 36. Factor d(s).
2*s*(s - 2)*(s - 1)*(4*s - 1)
Let j(u) = 5*u**4 - 80*u**3 + 290*u**2 - 385*u + 175. Let v(n) = 5*n**4 - 78*n**3 + 289*n**2 - 384*n + 