7
Suppose 0 = 19*i + i + 70*i - 180. Let s(q) be the first derivative of 15/2*q**i + 0*q - 55/3*q**3 - 6 - 5*q**4. Factor s(d).
-5*d*(d + 3)*(4*d - 1)
Let b be 87/21 - 2/14. Factor -6*y**3 - 4*y**2 + 119*y**4 - 123*y**b - y**5 + 0*y - y.
-y*(y + 1)**4
Let i(r) = -r**2 - 17*r + 24. Let z be i(-19). Let f be 276/84 + 4/z. What is k in -5*k**f - k**2 - k**4 - k**3 + 4*k**3 = 0?
-1, 0
Let y = 17419/40 + -3471/8. Find t, given that y*t**2 + 1/5 - 9/5*t = 0.
1/8, 1
Let a = -2/4441 + 4447/13323. Find h such that -1/6*h**2 - a*h + 1/2 = 0.
-3, 1
Let p be ((-4)/6)/(-1*12/(-54)). Let g be 1/p*(-387)/301. Factor 0 - 6/7*j + 3/7*j**3 + g*j**2.
3*j*(j - 1)*(j + 2)/7
Let c(u) be the third derivative of -u**5/4 - u**4/24 + 3*u**2 + 41. Determine h so that c(h) = 0.
-1/15, 0
Let s(d) be the first derivative of 3*d**5/5 + 93*d**4/4 + 249*d**3 + 135*d**2/2 - 4050*d - 1069. Factor s(t).
3*(t - 2)*(t + 3)*(t + 15)**2
Let g(f) = -5*f**3 + 173*f**2 + 72*f - 70. Let v be g(35). Let i(z) be the first derivative of 5*z**2 + v*z + 3 + 2/3*z**3. Suppose i(y) = 0. Calculate y.
-5, 0
Suppose -2296/9*p - 658952/9 - 2/9*p**2 = 0. What is p?
-574
Suppose -334 = -134*v + 427 - 91. Let a(b) be the first derivative of -10/7*b**2 - 7 - 8/21*b**3 - 8/7*b + 2/21*b**6 + 4/7*b**4 + 16/35*b**v. Factor a(n).
4*(n - 1)*(n + 1)**3*(n + 2)/7
Let m(f) be the third derivative of -7*f**7/240 - 91*f**6/960 + 81*f**5/160 + 81*f**4/64 + 9*f**3/8 + 3*f**2 + 28*f + 7. Let m(l) = 0. Calculate l.
-3, -3/7, 2
Factor -615*d + 2*d**2 + 618*d + 1163*d.
2*d*(d + 583)
Factor -7*s + 77*s + 43*s - 13*s + 71*s + 3*s**2 + 330.
3*(s + 2)*(s + 55)
Let z(c) be the first derivative of -3*c**4/4 - 13*c**3 + 30*c**2 + 252*c - 3562. What is f in z(f) = 0?
-14, -2, 3
Let j(b) = 15*b + 10. Let n be j(-5). Let i be 26/n - (-17)/5. Factor 30*v**3 - 74*v**i - 2*v**2 + 34*v**3.
-2*v**2*(5*v + 1)
Let o(p) be the third derivative of -p**7/210 + 19*p**6/120 - 17*p**5/20 + 49*p**4/24 - 8*p**3/3 - 701*p**2. Factor o(x).
-(x - 16)*(x - 1)**3
Let w = -1 - -7. Suppose 72 - w = 6*l. Factor t**5 + l*t - 10*t - t**3 - t**4 - t**3 - 1 + 2*t**2.
(t - 1)**3*(t + 1)**2
Let k(v) be the second derivative of -85/6*v**3 - 5*v**4 + 3/4*v**5 + 23*v + 0 - 15*v**2 + 2/3*v**6. Find u such that k(u) = 0.
-1, -3/4, 2
Let q(f) = -2*f + 2. Let u be q(-3). Suppose -3*z + 53 = u. Let -4*k**3 + 7*k**2 + 12 + 5*k**3 - 34*k + 2*k**4 + 27*k**2 - z*k**3 = 0. Calculate k.
1, 2, 3
Suppose 5*a = 0, -20*t + 3*a - 957 = -23*t. What is b in 54*b**3 - t*b - 266*b + 2*b**4 + 336*b**2 + 193*b = 0?
-14, 0, 1
Let t(n) be the second derivative of n**6/1440 + n**5/48 + n**4/6 - 91*n**3/3 + n + 32. Let k(y) be the second derivative of t(y). Factor k(p).
(p + 2)*(p + 8)/4
Suppose 144937 - 4*y**3 - 144937 - 124*y**2 + 264*y = 0. What is y?
-33, 0, 2
Let r(x) be the third derivative of -1/24*x**6 + 1/210*x**7 + 5/24*x**4 - x + 1/20*x**5 + 37*x**2 - 2/3*x**3 + 0. Let r(h) = 0. What is h?
-1, 1, 4
Let w(b) be the first derivative of 2*b**3/15 + 906*b**2/5 + 410418*b/5 + 883. Suppose w(l) = 0. What is l?
-453
Suppose 4*b - 2*m = -168, 3*b = -m - 130 - 1. Let y = b + 145/3. Factor y*h**2 + 4*h - 4/3.
4*(h + 1)*(4*h - 1)/3
Factor -40*a**3 - 6900*a**2 + 57*a**3 - 726738*a - 22*a**3 - 1653762*a.
-5*a*(a + 690)**2
Let v = -18 - -20. Suppose 0*j - 4 = -v*j. Find x such that 12*x**2 + j*x**3 + x**3 + 12*x + 149 - 149 = 0.
-2, 0
Suppose 4*l = 6*l - 4*d - 190, -295 = -3*l + d. Suppose -25*z + l - 24 = 0. Suppose 0 - 8/3*s**2 + 2/9*s**z + 8*s = 0. What is s?
0, 6
Let u be (15/30)/(-2 + 1383/690). Let v be 138/u*(-30)/(-8). Determine w so that -v*w**2 - 3/2*w + 3 = 0.
-1, 2/3
Let j(u) = 3*u + 42. Let l be j(16). Let v be (-3 + (-32)/(-12))/((-20)/l). Factor -81/2 - 27/2*x**2 + 81/2*x + v*x**3.
3*(x - 3)**3/2
Let g(n) be the second derivative of n**6/10 + 81*n**5/20 - 39*n**4 + 64*n**3 - n - 41. Find w such that g(w) = 0.
-32, 0, 1, 4
Let y(q) be the first derivative of -5/6*q**2 + 1/9*q**3 - 18 + 4/3*q. What is m in y(m) = 0?
1, 4
Let o(l) be the first derivative of -2/9*l**3 - 70 - 8/9*l - 7/9*l**2. Factor o(k).
-2*(k + 1)*(3*k + 4)/9
Let r(k) = 2*k - 10 + 4*k + 4 + 3. Let o be r(1). Factor -53 + 47 - 9*v - v**2 + 2*v**3 + 4*v**2 + 7*v**3 + o*v**4.
3*(v - 1)*(v + 1)**2*(v + 2)
Suppose 4*u - 7 = 13*r, -2919*r - 4*u + 19 = -2920*r. Find v such that -1/3*v**2 + r + 2/3*v = 0.
-1, 3
Let v(p) = 47*p**2 + 4*p - 12. Let h be v(-2). Factor 9*q**4 - 4*q**4 + h*q - 3*q**4 - 10*q**3 - 14*q**3 + 38*q**2 + 6*q**2 + 98.
2*(q - 7)**2*(q + 1)**2
Let n = 2552 + -2552. Let s(v) be the first derivative of 0*v + n*v**2 + 7 + 5/12*v**4 - 2/9*v**3 + 2/15*v**5 - 5/18*v**6. Let s(q) = 0. Calculate q.
-1, 0, 2/5, 1
Let y(s) be the third derivative of 1/20*s**4 + 0 - s + 1/840*s**8 - 1/75*s**6 + 17*s**2 + 0*s**3 - 2/525*s**7 + 1/75*s**5. Determine r so that y(r) = 0.
-1, 0, 1, 3
Suppose 846 = -2*n - 3*o, -2*n + 7*n - 5*o = -2090. Let j be 10/(2000/n)*10/(-4). Find z such that -3/2*z - j*z**2 + 3*z**3 + 0 = 0.
-1/4, 0, 2
Let u(t) be the first derivative of 38*t**5/55 - 39*t**4/11 - 2*t**3/3 + 78*t**2/11 - 16*t/11 + 452. Let u(w) = 0. Calculate w.
-1, 2/19, 1, 4
Let t(n) = -n - 5. Let h(o) = 2*o**3 + 7*o**2 + 6*o + 4. Let s be h(-3). Let z be t(s). Factor z + 9/7*q + 3/7*q**2.
3*q*(q + 3)/7
Let h(y) = -11*y**2 - 13*y - 23. Let x = -29 + 34. Suppose -x = -u - 19. Let f(i) = 5*i**2 + 7*i + 11. Let k(m) = u*f(m) - 6*h(m). Suppose k(z) = 0. What is z?
-4, -1
Let -8/5*d - 2/5*d**2 + 42/5 = 0. Calculate d.
-7, 3
Let t(v) be the second derivative of 101*v**5/230 - 201*v**4/46 + 297*v**3/23 + 27*v**2/23 - 3086*v. Factor t(n).
2*(n - 3)**2*(101*n + 3)/23
Suppose 4*d + y - 28 = 5*y, 0 = -5*d - 2*y. Let s be (-1 + 1 - 1) + 8 - d. Find n such that -100*n + 105*n - s*n**3 - 18*n**2 + 20 - n**2 - n**2 = 0.
-4, -1, 1
Let x = 89 + -73. Let w = x + -14. Factor -4*n**3 + w - n - 2*n**5 - 7*n**2 - 6*n**4 + 11*n**2 + 2*n + 5*n.
-2*(n - 1)*(n + 1)**4
Let y(l) be the third derivative of -l**6/540 + 16*l**5/135 + 67*l**4/108 + 34*l**3/27 - 24*l**2 - 4*l. Determine u so that y(u) = 0.
-1, 34
Suppose 1 = -s - 1, -4*k - 5*s = 122. Let x be (-12)/15 - -1*k/(-10). Find f such that 1/2*f**x + 0 + 1/2*f**3 - f = 0.
-2, 0, 1
Let t(x) be the first derivative of -8*x**6/9 + 2*x**5/5 + 73*x**4/6 + 34*x**3/3 - 65*x**2/3 - 36*x - 4908. Solve t(k) = 0 for k.
-2, -1, 1, 27/8
Suppose 5*y + 4*p = -7 + 3, -2*y = -2*p - 2. Suppose y = f + g - 2 - 0, -g = 5*f - 14. Factor 5*w**f - 730*w - 10*w**2 + 746*w - 8 - 3*w**3.
2*(w - 2)**2*(w - 1)
Let z(x) be the second derivative of -x**5/70 - 17*x**4/84 + 2*x**3/7 - 111*x**2/2 + 67*x. Let o(f) be the first derivative of z(f). Factor o(j).
-2*(j + 6)*(3*j - 1)/7
Let a(g) be the third derivative of 1/45*g**5 + 0 + 0*g**3 + 0*g**6 + 3*g**2 - 4*g + 1/504*g**8 - 1/36*g**4 - 2/315*g**7. Factor a(h).
2*h*(h - 1)**3*(h + 1)/3
Suppose 47*h = 72*h - 125. Suppose -30*x**2 - 1 - 2 + 10*x**3 - 55*x - 15*x**3 - h - 22 = 0. What is x?
-3, -2, -1
Let g = 27381 - 27378. Let b(c) be the second derivative of 1/5*c**5 + 0*c**2 + 10*c - 1/15*c**6 - 2/3*c**g + 0 + 1/6*c**4. Factor b(z).
-2*z*(z - 2)*(z - 1)*(z + 1)
Suppose 3*r - 4 = 5. Suppose 5*o - 30 = 5*w, r*o - w = -0*w + 14. Solve 37*c**4 - o*c**3 - 6*c**3 - 2*c**4 = 0 for c.
0, 2/7
Let c(m) = -m + 36. Let i be c(16). Suppose 5*s = -l + 42, 4*s = -2*l + 40 + i. Factor 20 + 4*j**3 + 44*j + 5*j**2 + j**2 + l*j**2.
4*(j + 1)**2*(j + 5)
Let z be ((-3036)/230 + -8)*1/(-2) + -10. Let r be 3/(-5)*(-8)/6. Factor r*i - 1/5 - z*i**2.
-(i - 1)*(3*i - 1)/5
Let u(y) be the first derivative of -3*y**4/4 - 57*y**3 - 396*y**2 - 624*y - 12674. Find d, given that u(d) = 0.
-52, -4, -1
Let j be 6/(-48)*-1 + (-46)/(-16)*(126 + -125). Factor 5*o**3 + 0 - j*o**2 + 1/3*o**5 - 7/3*o**4 + 0*o.
o**2*(o - 3)**2*(o - 1)/3
Suppose -v - 14*v - 75 = 0. Let h(t) = 14*t**3 - 31*t**2 + 55*t - 23. Let w(g) = -2*g**3 - g**2 + g - 1. Let r(c) = v*w(c) - h(c). Factor r(k).
-4*(k - 7)*(k - 1)**2
Let b(k) be the second derivative of 160*k**4/3 - 2545*k**3/6 - 30*k**2 - 5717*k. Determine c so that b(c) = 0.
-3/128, 4
Suppose -5*l = -2*l - 6. Determine a, given that 5*a + l*a - 9*a + 2*a**2 - 3*a + 6*a - 3*a**3 = 0.
-1/3, 0, 1
Let s(u) = 14 + 6 - 34 + 2*u**2 - 2*u + 15. Let i(j) = 5*j**3 + 68*j**2 - 163*j + 84. L