1
Let c(b) be the third derivative of -11/80*b**5 - 1/20*b**7 + 1/96*b**4 + 0*b - 3*b**2 + 1/8*b**3 - 1/168*b**8 + 12 - 13/96*b**6. Let c(h) = 0. Calculate h.
-3, -1, -1/2, 1/4
Let b(k) be the second derivative of -5*k**4/12 - 55*k**3 - 2065*k**2/2 + 3765*k. Factor b(r).
-5*(r + 7)*(r + 59)
Let t(n) be the second derivative of 225*n + 3/7*n**4 - 5/98*n**7 + 0 + 8/7*n**3 + 0*n**2 - 6/5*n**5 + 33/70*n**6. Determine r, given that t(r) = 0.
-2/5, 0, 1, 2, 4
Suppose 25*n + 125 = 20*n. Let k(y) = -15*y**2 - 345*y - 640. Let l(g) = 2*g**2 + 43*g + 80. Let i(h) = n*l(h) - 3*k(h). Solve i(s) = 0 for s.
-4
Suppose -36248*j = -36195*j - 106. Solve 1/2*b**3 - 19/2*b - 2*b**j - 7 = 0.
-2, -1, 7
Let t = -370 - -373. Find b such that 5 - 6*b**4 - 3*b + 4*b**3 + 4*b**2 + 2*b**5 - t*b + 1 - 2 - 2 = 0.
-1, 1
Let s(h) = -55*h**3 + 80*h**2 + 335*h + 20. Let r(j) = -j**4 + j**3 + j**2 - j - 4. Let f(y) = 5*r(y) + s(y). Factor f(m).
-5*m*(m - 3)*(m + 2)*(m + 11)
Let b(y) be the first derivative of -y**4/6 + 58*y**3/3 + 59*y**2 + 178*y/3 + 29. Factor b(x).
-2*(x - 89)*(x + 1)**2/3
What is h in -52/9*h**2 + 4 + 2*h + 16/9*h**4 - 2/9*h**5 - 16/9*h**3 = 0?
-1, 1, 3, 6
Let x(u) be the third derivative of 9*u**5/20 + u**4/2 - 986*u**2. Factor x(h).
3*h*(9*h + 4)
Let q(d) be the first derivative of 10000*d**3 + 2/5*d**5 + 12500000*d - 500000*d**2 + 16 - 100*d**4. Solve q(i) = 0.
50
Let u(k) = 2*k**4 - 21*k**3 - 91*k**2 - 121*k - 48. Let r(f) = 2*f**4 - 22*f**3 - 92*f**2 - 122*f - 48. Let g(a) = -5*r(a) + 6*u(a). Factor g(t).
2*(t - 12)*(t + 1)**2*(t + 2)
Suppose 962 = 17*v + 724. Let z(y) be the second derivative of 0 - 7/15*y**3 - 6/5*y**2 + 0*y**4 + v*y + 1/50*y**5. Factor z(k).
2*(k - 3)*(k + 1)*(k + 2)/5
Let w(d) be the third derivative of d**5/30 - d**4/6 + d**3/3 - 5*d**2 - 17. Let h be w(2). Factor 0 + 2/3*j**4 - 8/3*j + 2*j**3 + 0*j**h.
2*j*(j - 1)*(j + 2)**2/3
Let s be (-4)/2*(-63)/42. Suppose u + 11 = 3*h, -5 = 3*h + 4*u - 21. Factor 2*m**h + 2*m**s - 6*m**3 + 7*m - 2 - 3*m.
2*(m - 1)**3*(m + 1)
Let o(c) be the first derivative of -7*c**5/5 - 124*c**4/3 + 24*c**3 + 222*c + 153. Let r(z) be the first derivative of o(z). Solve r(l) = 0.
-18, 0, 2/7
Factor 214/13*d - 2/13*d**2 - 48.
-2*(d - 104)*(d - 3)/13
Let h(m) be the first derivative of -m**6/6 - m**4/4 - m + 141. Let a(s) = -s**5 + 3*s**4 - 2. Let b(j) = 3*a(j) - 6*h(j). Find k, given that b(k) = 0.
-2, -1, 0
Let f(y) be the third derivative of 0*y + 105*y**2 + 1/5*y**6 + 0 - 1/84*y**8 + 0*y**4 - 2/21*y**7 + 0*y**5 + 0*y**3. Let f(o) = 0. Calculate o.
-6, 0, 1
Let z(a) be the first derivative of 5*a**6/6 - 35*a**5 - 635*a**4/2 + 1610*a**3/3 + 1265*a**2/2 - 1435*a + 4724. Determine m so that z(m) = 0.
-7, -1, 1, 41
Let l be 29 + (-596)/24 - (21/18)/7. Let p(i) be the third derivative of -3/32*i**l - 5*i**2 + 0*i**3 - 1/160*i**5 + 0*i + 0. Factor p(u).
-3*u*(u + 6)/8
Factor 1940*j + 1378125 + 5*j**2 + 3752*j - 442*j.
5*(j + 525)**2
Let 8/5 - 16/5*z**2 - 2/3*z - 14/15*z**3 = 0. What is z?
-3, -1, 4/7
Let s(o) be the first derivative of -o**5/5 - o**4 + 29*o**3/3 - 12*o**2 - 1566. Factor s(j).
-j*(j - 3)*(j - 1)*(j + 8)
Suppose 3*j - 9 = 0, -32*x + 37*x = -4*j + 22. Factor 5 + 3*d**x + 5*d**2 - 7*d**2 - 9*d - 14 + d.
(d - 9)*(d + 1)
Let n(c) = 1025*c**2 - 6146*c - 22. Let r be n(6). Determine p, given that 0 + 3*p - 1/2*p**r - 1/2*p**3 = 0.
-3, 0, 2
Let x be ((-865)/670)/(110/16 + 0). Let n = -2/335 - x. Determine g so that 18/11*g + 14/11*g**3 + 0 - n*g**4 - 30/11*g**2 = 0.
0, 1, 3
Solve -97*a**4 + 22 + 159*a - 102*a**2 + 3*a**5 - 18*a**3 + 224*a**4 - 106*a**4 - 85 = 0 for a.
-7, -3, 1
Let s be (-13)/((-910)/(-49))*(12 - 14 - 36/(-21)). Factor -s*f**2 - 7 - 36/5*f.
-(f + 1)*(f + 35)/5
Find j, given that 56/9*j**2 + 364/3 + 2/9*j**3 - 1150/9*j = 0.
-42, 1, 13
Let w be (427924/126)/(-62) - -55. Let -w*o**2 - 8*o - 72 = 0. What is o?
-18
Let a = 1097/4868 - -30/1217. Suppose -a*v**2 + v - 3/4 = 0. Calculate v.
1, 3
Let l = 2176 + -13051/6. Let u(v) be the third derivative of -l*v**4 + 0 + 0*v - 10*v**2 - 5/2*v**3 - 1/12*v**5. Factor u(a).
-5*(a + 1)*(a + 3)
Let r(w) = -7803*w**2 + 618*w - 18. Let z(x) = 5*x + 31. Let p be z(-5). Let q(h) = -7803*h**2 + 617*h - 17. Let a(i) = p*q(i) - 5*r(i). Factor a(f).
-3*(51*f - 2)**2
Factor -4964/3*h - 2488/3*h**2 - 4/3*h**3 - 2480/3.
-4*(h + 1)**2*(h + 620)/3
Let n = -18 - -49. Suppose -1 + 14 = m - 5*h, -5*h - n = -2*m. Determine k so that 14*k**4 + 20*k**3 + 3 - 10*k**2 - 2*k**3 - m*k - 7 = 0.
-1, -2/7, 1
Let y = 2077/24060 - 6/2005. Let m(v) be the first derivative of -2/3*v**2 - 1/9*v**3 + y*v**4 - 4 + 4/3*v. Factor m(q).
(q - 2)*(q - 1)*(q + 2)/3
Let k be 6*(-6)/(-36) + (-948)/16. Let m = k + 59. Factor m*z**3 - 15/4*z**2 - 3/4*z + 15/4.
3*(z - 5)*(z - 1)*(z + 1)/4
Let i = 476 + -460. Find u such that -i*u**2 - 11*u + 89 - 83*u**2 - 4*u - 33*u**3 + 61 - 3*u**4 = 0.
-5, -2, 1
Let x be 11*(-2)/4*(-15 + 13). Suppose 14*l + 4 + x*l**2 - 42*l**4 + 4*l**3 - 2*l**5 + 5*l**2 + 38*l**4 = 0. What is l?
-1, 2
Suppose -3*g - 19 = u - 1, -5*g = 3*u + 30. Let z(f) be the third derivative of 19*f**2 + 0 - 1/4*f**5 + 55/24*f**4 + 10/3*f**3 + u*f. Factor z(s).
-5*(s - 4)*(3*s + 1)
Let j(h) be the first derivative of -h**6/120 - 9*h**5/40 - h**4 + 41*h**3 - 83. Let v(k) be the third derivative of j(k). Factor v(p).
-3*(p + 1)*(p + 8)
Suppose -3*j = 3*t + 21, 6742 = -t + 4*j + 6780. Factor 25/3*n + 11/3*n**3 + 1/3*n**4 + 0 + 35/3*n**t.
n*(n + 1)*(n + 5)**2/3
Let z(y) be the first derivative of 50/3*y**3 + 25 + 44*y**2 + 3/2*y**4 + 24*y. Solve z(h) = 0 for h.
-6, -2, -1/3
Let m(r) be the first derivative of -r**6/20 + r**5/40 + r**4/3 + r**3/3 + 10*r - 47. Let d(k) be the first derivative of m(k). Factor d(l).
-l*(l - 2)*(l + 1)*(3*l + 2)/2
Let v be ((-1)/(-6))/(((-2)/(-6))/(6/30)). Let g(s) be the first derivative of 0*s - 16 + 0*s**2 - 1/4*s**4 + 1/6*s**3 + v*s**5. Solve g(l) = 0.
0, 1
Let m(s) be the first derivative of -1/9*s**4 + 44/9*s**2 - 8/3*s + 2/9*s**5 - 70/27*s**3 + 74. What is g in m(g) = 0?
-3, 2/5, 1, 2
Let d(k) be the third derivative of -k**7/735 + k**6/70 - 9*k**4/14 + 27*k**3/7 + 70*k**2 - 5. Let d(t) = 0. What is t?
-3, 3
Suppose -5*k + 3*v + 19 = 0, -66*v = -63*v + 9. Let r(l) be the second derivative of 1/4*l**4 - 5*l + 3*l**k + 3/2*l**3 + 0. Solve r(n) = 0 for n.
-2, -1
Suppose -2*j = -5*b - 9, 4*j + 0 = -2*b + 6. Factor 2*a**2 + 64 + 68*a + 0*a**j + 2*a**2.
4*(a + 1)*(a + 16)
Determine j, given that 0*j - 208/7*j**4 - 120/7*j**2 + 0 - 428/7*j**3 - 12/7*j**5 = 0.
-15, -2, -1/3, 0
Let s(u) be the second derivative of u**3/3 - u**2 + 11*u. Let w be s(2). Factor -4*z + 202*z**4 - 206*z**4 + z - 5*z + 12*z**w.
-4*z*(z - 1)**2*(z + 2)
Let y(i) be the second derivative of i**6/180 + i**5/30 - i**4/9 + 17*i**2 + 61*i. Let k(u) be the first derivative of y(u). Factor k(a).
2*a*(a - 1)*(a + 4)/3
Let c = 11 + -7. Suppose -7*k + 112 = -0*k. Suppose -4*d**3 - 2*d**3 + 5*d**5 + k*d**c + 3*d**5 + 4*d - 10*d**2 = 0. What is d?
-2, -1, 0, 1/2
Let y(m) = -m**2 + 10*m + 27. Let k be y(12). Solve 11*j**4 - 4*j**4 - 20*j + 31*j**3 + 44*j**k - 60*j**2 - 27*j**4 = 0.
-1/4, 0, 2
Let h = -567 - -570. Suppose -6 - 68*s - 9*s**3 - 18 - 22*s**3 - 452*s**4 - 68*s**2 + 448*s**4 + h*s**3 = 0. Calculate s.
-3, -2, -1
Let z(q) be the second derivative of q**5/200 - 2*q**4/15 - 11*q**3/15 + 36*q**2/5 + 614*q + 3. Let z(j) = 0. What is j?
-4, 2, 18
Let b be 12/(-40)*5/(-6) + 2590/7400. Factor b*w**2 - 54/5 + 21/5*w.
3*(w - 2)*(w + 9)/5
Let q(g) be the first derivative of g**5 + 45*g**4/2 - 305*g**3/3 + 105*g**2 - 423. Factor q(t).
5*t*(t - 2)*(t - 1)*(t + 21)
Let k = -8462 + 169241/20. Let m(v) be the first derivative of 1 + k*v**2 - 1/40*v**4 - 1/30*v**3 + 1/10*v. Factor m(w).
-(w - 1)*(w + 1)**2/10
Let b(r) = -r**5 + r. Let c(p) = 2*p**5 - 65*p**4 + 255*p**3 - 315*p**2 + 3*p. Let k(y) = -3*b(y) + c(y). What is m in k(m) = 0?
0, 3, 7
Suppose 4*g - 10*g = -576. Let w = g + -93. Factor 127*i**4 - 132*i**4 - 4*i**2 - i**2 - 10*i**w.
-5*i**2*(i + 1)**2
Factor 994*m**4 + 368*m**4 - 375*m**5 + 384*m**2 - 162*m**4 - 1080*m**3 - 48*m.
-3*m*(m - 2)*(5*m - 2)**3
Suppose 3984 - 566*x + 3254*x**2 - 6867*x + 1289*x - 1820*x + 722*x**2 + 4*x**3 = 0. What is x?
-996, 1
Let w be 153/30 + (3 - 62/20). Factor 20*z