e -i*k + 104*k = -18. Solve -5/7*z - 1/7*z**k + 0 = 0.
-5, 0
Let l(s) be the second derivative of 12*s - 1/30*s**5 + 10/3*s**2 - 1/3*s**3 + 2 - 1/3*s**4. Factor l(t).
-2*(t - 1)*(t + 2)*(t + 5)/3
Suppose -4*o + 6*o = 28. Suppose o = 14*v - 42. Suppose -2*g**5 + 2*g**4 - 6*g**3 - 6*g**2 + v*g**4 + 8*g**2 = 0. What is g?
0, 1
Let v(l) = 4*l**2 + 5463*l + 1871442. Let o(u) = 12*u**2 + 16392*u + 5614320. Let n(g) = -3*o(g) + 8*v(g). Factor n(x).
-4*(x + 684)**2
Let x = -2263 + 1352. Let d = x - -2738/3. Factor d*p**2 - 10/3*p + 0.
5*p*(p - 2)/3
Let z(l) = -l**2 + 9*l + 41. Let m be z(12). Factor -7*q**3 + 4*q**2 - 6*q**4 + 12*q + 4*q**2 - 4*q**2 - q**m - 2*q**3.
-q*(q - 1)*(q + 2)**2*(q + 3)
Suppose 89*l = 78*l - 198. Let t be (29/(-116))/((-5)/l) + 1. Factor 0*a**3 - t*a**4 + 0*a - 1/10 + 1/5*a**2.
-(a - 1)**2*(a + 1)**2/10
Let x = -538 + 557. Suppose -x*u + 12 = -13*u. Solve -2/3*r**u - 2*r - 4/3 = 0.
-2, -1
Let m = 655351/150 + -4369. Let w(f) be the third derivative of -2/15*f**3 - 1/20*f**4 + 32*f**2 + 0*f - m*f**5 + 0. Find c, given that w(c) = 0.
-2, -1
Let l(c) be the second derivative of -c**9/1008 + c**7/70 - 18*c**3 - 9*c - 4. Let b(m) be the second derivative of l(m). Solve b(x) = 0.
-2, 0, 2
Suppose 0*o + 18*o - 270 = 0. Let k be (o + -19 - 4/(-6)) + 4. Factor 0 - 1/3*b**3 + 0*b + b**4 - k*b**2.
b**2*(b - 1)*(3*b + 2)/3
Let t = -191 + 196. Let p be t + -5*3/9. Let 5/3*k - 5/3 + 5/3*k**5 + p*k**2 - 10/3*k**3 - 5/3*k**4 = 0. Calculate k.
-1, 1
Let b(a) be the first derivative of -a**5 + 255*a**4/2 - 8195*a**3/3 - 255*a**2 + 8200*a + 7099. Determine u, given that b(u) = 0.
-1, 1, 20, 82
Suppose 3*a - a - 552 = -4*t, 819 = 3*a - 3*t. Let o = a + -1087/4. Let -27/4*f**2 + 9/4*f**4 - 3/4*f**3 - o*f + 3/2 = 0. What is f?
-1, 1/3, 2
Let w(k) be the second derivative of k**7/21 - 14*k**6/15 + 6*k**5 - 52*k**4/3 + 64*k**3/3 - 70*k + 4. Factor w(g).
2*g*(g - 8)*(g - 2)**3
Suppose 3*b + 201 - 152 = -5*j, -8*b + 3*j + 49 = 0. Factor 3/5*h**5 - 18/5*h**b + 22/5*h**3 - 1/5 + 7/5*h - 13/5*h**4.
(h - 1)**4*(3*h - 1)/5
Let k = -38 - -34. Let i be (2 + k)/(-8 - -7). Find f such that 15*f**4 - 32*f + 2*f**4 - 18*f**4 - 10*f**3 - 32*f**i = 0.
-4, -2, 0
Solve -52*w**3 - 44*w + 1464/5 - 196*w**2 - 4/5*w**4 = 0 for w.
-61, -3, -2, 1
Factor -2468 - 4*f**2 + 3008*f + 1245 + 1223.
-4*f*(f - 752)
Solve -46*m**3 + 128 - 902/3*m + 2/3*m**4 + 218*m**2 = 0.
1, 3, 64
Suppose -4*q + 6 = 2*h - 6, -q + 5*h = 8. Suppose i - 20 = -4*r + 4*i, -2*r = i. Factor 2*o + 0*o + 4*o - 3*o**3 - o**q + 4*o**r.
-3*o*(o - 2)*(o + 1)
Let r(x) = x**3 + 16*x**2 - 20*x - 28. Let n be r(-17). Determine q, given that -269*q + 357*q - 21*q**3 - 13*q**2 + 17*q**3 - n*q**2 = 0.
-11, 0, 2
Suppose w - 3*w = -4. Let m be ((-1002)/(-198) + -5)*(-121)/(-44). Let -m*v**w - 3/2 + v = 0. What is v?
3
Let d = 414167 + -414165. Factor 64/9*g + 2/9*g**4 - 10/9*g**3 - 4/3*g**d + 64/9.
2*(g - 4)**2*(g + 1)*(g + 2)/9
Suppose 3*d = -3*j + 4*d + 1671, -5*d + 557 = j. Let q = 560 - j. Find r such that 5/2*r**4 + 5/6*r**5 - 35/6*r**2 + 0*r + 10/3 - 5/6*r**q = 0.
-2, -1, 1
Let b(k) be the third derivative of k**4/4 + k**3/2 - 15*k**2 - 2*k. Let u be b(0). Solve -20*z + 5/2*z**u - 5/2*z**2 + 30 = 0.
-3, 2
Suppose 80*g - 86*g = 18. Let f be (g + 7)/(19 + -6). What is m in 80/13*m + 34/13*m**2 + f*m**3 + 32/13 = 0?
-4, -1/2
Let n(d) = d - 1. Let m(u) = 5*u**2 - 11*u - 24. Let r = -5 + 7. Suppose -4*k + 9 = -p, -2 = p - r*k + 3. Let q(c) = p*m(c) + 4*n(c). Factor q(b).
-5*(b - 4)*(b + 1)
Factor 1839*b**2 + 325593999 - 3023*b**3 + 2454*b**2 + 3020*b**3 - 2047761*b.
-3*(b - 477)**3
Let y(a) be the third derivative of 3*a**2 + 0 - 1/210*a**5 + 14*a + 1/84*a**4 - 1/420*a**6 + 1/21*a**3. Solve y(k) = 0 for k.
-1, 1
Suppose -1870*m + 53 = -1867*m + 4*t, 4*t - 62 = -6*m. Factor m*n**3 + 0*n - 3/2*n**2 - 3/2*n**4 + 0.
-3*n**2*(n - 1)**2/2
Let i(l) be the first derivative of -l**3/9 + 102*l**2 - 611*l/3 + 7587. Determine r so that i(r) = 0.
1, 611
Let f(w) be the third derivative of 0*w - 1/945*w**7 + 0*w**4 + 84*w**2 - 1/270*w**5 + 0 - 1/270*w**6 + 0*w**3. Factor f(c).
-2*c**2*(c + 1)**2/9
Let r(q) be the first derivative of 23 + 0*q - 9*q**2 - 5/8*q**4 + 0*q**3 - 1/12*q**5. Let l(w) be the second derivative of r(w). Solve l(i) = 0 for i.
-3, 0
Suppose -75*t**2 + 1 - 26*t**3 - 1 - 21*t**2 - 1206*t**4 + 1208*t**4 = 0. What is t?
-3, 0, 16
Let f be ((-83)/(-3))/(17/(-13 - 463)). Let r = f - -778. Factor 6 - 8/3*a - r*a**2.
-2*(a - 1)*(5*a + 9)/3
Let x(u) be the first derivative of u**6/9 - 4*u**5/15 - 4*u**4/3 - 4*u**3/9 + 7*u**2/3 + 8*u/3 - 12. Determine h so that x(h) = 0.
-1, 1, 4
Let v(s) be the first derivative of s**3/6 - 1339*s**2/4 + 1337*s + 4660. Factor v(j).
(j - 1337)*(j - 2)/2
Suppose 48*q = -7*q + 165. Let k(c) be the first derivative of 1/6*c**q + 0*c**2 - 1/2*c + 12. Factor k(o).
(o - 1)*(o + 1)/2
Let c(p) = 5*p**3 - 87*p**2 - 24*p + 7. Let z be c(18). Let f = 553 - z. Factor -f*d - 1/2*d**2 - 18.
-(d + 6)**2/2
Let n = 159 - 158. Let b(s) = 12*s**4 - 16*s**2 - 6*s + 10. Let w(v) = -v**4 + v**2 + v - 1. Let t(j) = n*b(j) + 10*w(j). Factor t(z).
2*z*(z - 1)**2*(z + 2)
Let z(c) = -63*c**2 - 187*c + 8. Let f be z(-3). Let n(m) be the first derivative of -5/4*m**4 - 5*m**f + 0*m - 8 + 5*m**3. Factor n(a).
-5*a*(a - 2)*(a - 1)
Suppose -494 + 178 = -117*x + 38*x. Let v(w) be the second derivative of 1/6*w**x - 1/3*w**3 - 27*w + 0 - 2*w**2. Find o such that v(o) = 0.
-1, 2
Let p be (1/1)/2 - 18/(-4). Suppose -2*y - l + 9 = 0, -11 = -p*y - 4*l + 19. Find a, given that 2*a**3 + 942*a**y + 4*a**4 - 3*a**4 - 941*a**2 = 0.
-1, 0
Let g = 106 + -102. Factor 4 + 6 - 7*i**3 + 3*i**3 - 8*i**2 + 4*i + 0 + 2*i**4 - g.
2*(i - 3)*(i - 1)*(i + 1)**2
Let n(c) be the second derivative of -c**5/5 + 20*c**4/3 + 8*c**3/3 - 160*c**2 + 2194*c. Factor n(z).
-4*(z - 20)*(z - 2)*(z + 2)
Let q be 11*(10 + (-20)/4). Let b(t) = -5*t**2 - 57*t + 58. Let k(w) = 135*w**2 + 1540*w - 1565. Let z(o) = q*b(o) + 2*k(o). Factor z(i).
-5*(i - 1)*(i + 12)
Let p = -1012 + 984. Let h be ((-2)/p)/(11 + (-1374)/126). Let -9/2*n**2 + 0 - h*n**3 - 15/4*n = 0. Calculate n.
-5, -1, 0
Let l(z) = z**2 - 5*z - 9. Let y be l(-2). Factor -1271*m**4 + 3*m**2 - y*m**2 + 1273*m**4.
2*m**2*(m - 1)*(m + 1)
Let s(f) = 47*f**2 + 2590*f + 1677033. Let p(u) = 23*u**2 + 4. Let x(t) = 4*p(t) - 2*s(t). Solve x(w) = 0 for w.
-1295
Solve 71033 + 5*l**2 - 71393 + 0*l**2 - 5*l = 0 for l.
-8, 9
Let s be (-5 + (-84)/(-18))*-30. Find b, given that 22*b**2 - 5*b**2 - 19*b**2 + 28 + s*b = 0.
-2, 7
Let n = 75 - 68. Let g(k) = 2*k**3 - 54*k**2 + 92*k - 68. Let l(o) = o**3 - 36*o**2 + 61*o - 46. Let q(d) = n*l(d) - 5*g(d). Suppose q(a) = 0. What is a?
1, 2, 3
Let -2/17*o**4 + 90/17 + 12/17*o**3 - 172/17*o + 72/17*o**2 = 0. What is o?
-5, 1, 9
Let r = 15923837/11 + -1447621. Let -2/11*l**2 - r*l + 0 = 0. What is l?
-3, 0
Determine x, given that 6 + 45*x**3 + 5*x - 196/3*x**2 + 28/3*x**4 = 0.
-6, -1/4, 3/7, 1
Let t = 4327/8565 - 22/571. Let g(m) be the first derivative of t*m**5 - 13/6*m**2 + 22/9*m**3 + m - 3/2*m**4 + 1 - 1/18*m**6. Solve g(w) = 0.
1, 3
Let u = -26019/2 - -13011. Suppose 5/2*r - 9/2*r**3 + 1/2 + u*r**2 = 0. What is r?
-1/3, 1
Let w(s) be the first derivative of s**3/15 - 157*s**2/10 + 152*s - 953. Solve w(m) = 0.
5, 152
Suppose 52*u - 2477 - 4184 = 619. Factor -17/2*l**4 + 241/2*l**2 + u*l + 43/2*l**3 + 1/2*l**5 + 50.
(l - 10)**2*(l + 1)**3/2
Let k(l) be the third derivative of l**9/453600 - l**8/15120 + l**7/1512 + 4*l**5/5 + 22*l**2. Let h(a) be the third derivative of k(a). Factor h(j).
2*j*(j - 5)**2/15
Let h(c) be the third derivative of c**8/57120 - 2*c**7/5355 + 11*c**4/6 - 2*c**2 - 2. Let m(u) be the second derivative of h(u). Let m(i) = 0. Calculate i.
0, 8
Let f(k) be the third derivative of -10*k**2 + 1/100*k**5 - 4*k**3 - 10 + 0*k - 9/20*k**4. Let f(q) = 0. Calculate q.
-2, 20
Suppose 2*l = -a + 8, -l + 0*l + 2 = a. Let g be 2 + (-276)/210 + l/(-21). Find q, given that -g*q**5 - 24/5*q**2 + 0 - 26/5*q**3 - 8/5*q - 12/5*q**4 = 0.
-2, -1, 0
Let x = -632/3 + 9482/45. Let z(c) be the third derivative of 0*c + x*c**3 - 5*c**2 + 1/450*c**5 + 1/60*c**4 + 0. Factor z(u).
2*(u + 1)*(u + 2)/15
Let i = -5183 + 36289/7. Let g(u) be the first derivative of 16/7*u**2 + i*u 