
Let k(u) be the first derivative of u**3/4 - 903*u**2/8 - 453*u/2 - 621. Factor k(r).
3*(r - 302)*(r + 1)/4
Let m = -194883/47 - -4146. Let k = 570/329 + m. Determine a so that 0 + a**3 - k*a**2 + 2/7*a = 0.
0, 2/7, 1
Suppose 0 = -5*g - 2*y - 11, -4*g + 4*y + 3 + 5 = 0. Let q be (-2)/(-5) + g/(-5)*88. Factor 6*a**2 + 4 + 480*a**3 + q*a - 488*a**3 + 0*a**2.
-2*(a - 2)*(a + 1)*(4*a + 1)
Let o be (-137 + 3 + 7)/(-1). Suppose o = 12*h + 91. Factor -1/3*i**h - 7/3*i + 1 + 5/3*i**2.
-(i - 3)*(i - 1)**2/3
Factor 0 - 20/7*m + 18/7*m**3 - 26/7*m**2.
2*m*(m - 2)*(9*m + 5)/7
Let g(w) = w**2 + 9*w + 6. Let a be g(-8). Let z be ((-1 - 0)*a)/(8/16). Factor -6*p**4 + 28*p - 24*p**3 + 2*p**z + 4*p**5 + 4*p + 16*p**2.
4*p*(p - 2)**2*(p + 1)*(p + 2)
Let d(l) be the first derivative of l**4 + 4*l - 4/3*l**3 - 2*l**2 - 126. Factor d(k).
4*(k - 1)**2*(k + 1)
Suppose 9*a = 8 + 19. Suppose 11*m**a - 380*m**2 + 48*m + m**3 + 18*m**4 + 6 - 2*m**5 + 762 + 1482 + 102*m = 0. What is m?
-3, 5
Let f(l) be the first derivative of -39 + 7*l**2 + 4/3*l**3 - 14*l. Let m(b) = -4*b**2 - 13*b + 15. Let y(d) = 5*f(d) + 4*m(d). Solve y(q) = 0 for q.
-5, 1/2
Let y(s) be the third derivative of s**6/540 - s**5/270 + 140*s**3/3 - 165*s**2. Let d(t) be the first derivative of y(t). Let d(k) = 0. What is k?
0, 2/3
Let g = 2170167 + -2170165. Let c = -109/12 - -39/4. Factor 0*u - 4/9*u**g - 2/9*u**4 + 0 - c*u**3.
-2*u**2*(u + 1)*(u + 2)/9
Let b(w) = -2*w**2 + 149*w - 1005. Let o be b(67). Let f(a) be the second derivative of -9*a + 9/7*a**2 + 2/7*a**3 + 1/42*a**4 + o. Factor f(m).
2*(m + 3)**2/7
Let j(c) = 3*c**2 + 38*c - 195. Let q(p) = -p**2 + 2*p + 7. Let b(k) = -j(k) - 5*q(k). Factor b(l).
2*(l - 20)*(l - 4)
Let x(b) = 159*b - 2513. Let i be x(16). Suppose 4*k = -4*v - 4, 2*v = -v - 5*k - 9. Determine r, given that i*r + 9*r**4 + 31*r - 9*r**2 - v*r**3 - 60*r = 0.
-1, 0, 2/9, 1
Let z(h) be the third derivative of -h**5/120 + h**4/12 + 5*h**3 + 4780*h**2 - h. Solve z(p) = 0.
-6, 10
Let f be 18800/(-5875)*(-10)/16. Solve -4/9*n**f + 0 - 8/3*n = 0.
-6, 0
Let s = -555 + 629. Suppose -s - 5*a - 59*a - 52*a**2 + 131 - 69 = 0. Calculate a.
-1, -3/13
Let b = 244837/9 + -27204. Let g(j) be the second derivative of 0*j**2 + b*j**3 - 34*j - 19/36*j**4 + 17/60*j**5 + 0. Find k, given that g(k) = 0.
0, 2/17, 1
Let x(r) = -r**3 - 11*r**2 - 35*r - 21. Let f be x(-5). Suppose 3*t - f*d - 14 = 0, 0 = -4*t - 2*d + 6*d + 16. Factor -8/3*i + 7/3 + 1/3*i**t.
(i - 7)*(i - 1)/3
Let l(n) be the third derivative of n**8/504 - 4*n**7/315 - 2*n**6/45 + n**5/9 + 23*n**4/36 + 10*n**3/9 - 1045*n**2 + 1. Factor l(a).
2*(a - 5)*(a - 2)*(a + 1)**3/3
Let j be 424/52 - -3*(-4)/78. Factor j*p**3 - 3*p**3 + 5*p**2 - 5*p**5 - 5*p**4 + 0*p**3.
-5*p**2*(p - 1)*(p + 1)**2
Let k(v) be the second derivative of 5*v**4/12 - 775*v**3/6 + 3227*v. Factor k(i).
5*i*(i - 155)
Let u(x) be the first derivative of x**3 - 81*x**2 + 600*x + 764. Factor u(c).
3*(c - 50)*(c - 4)
Let h(q) = -3*q**3 - 35*q**2 - 41*q - 29. Let x(j) = 3*j**3 + 33*j**2 + 42*j + 30. Let f = 208 - 202. Let z(u) = f*h(u) + 7*x(u). Factor z(p).
3*(p + 2)**2*(p + 3)
Solve -288*r**2 - 48*r**4 + 188*r**3 + 390 + 0*r**4 - 788 + 398 + 144*r + 4*r**5 = 0 for r.
0, 1, 2, 3, 6
Solve -88/7*a**2 + 0*a + 0 + 2/7*a**3 = 0 for a.
0, 44
Let n = -30665 - -30671. Let c(a) be the second derivative of -7/54*a**4 + 2/45*a**5 + 4/135*a**n - 9*a + 0*a**2 + 2/27*a**3 + 0. Factor c(s).
2*s*(s + 2)*(2*s - 1)**2/9
Suppose 2*a + 3*h - 3 = 0, 3*a + 12 + 6 = 3*h. Let c be ((-4)/(-10))/(a/(-30)). Factor -2*v**2 - 3*v + c*v**2 - 5*v - 10.
2*(v - 5)*(v + 1)
Let r = -654 - -654. Suppose 228*v - 215*v - 31590 = r. Suppose v*g + 1080*g**2 + 160*g**3 + 3645/2 = 0. What is g?
-9/4
Let x(r) be the first derivative of 19/14*r**4 + 16/21*r**3 - 4/7*r**2 + 2/5*r**5 + 0*r + 17. Determine g, given that x(g) = 0.
-2, -1, 0, 2/7
Suppose -2*n = -p + 1288, -2*p = -6*p + 8. Let v = n + 10937/17. Solve -10/17*s**3 + 2/17 - 18/17*s**2 - v*s = 0.
-1, 1/5
What is z in 2*z**4 + 157*z**3 + 1476*z**2 - 1124*z - 804*z**2 + 496 - 37*z**4 - 816*z = 0?
-4, 2/7, 2, 31/5
Let b = 1666/27 - 1648/27. Let -2/9*u**3 + b*u**2 - 8/9 + 0*u = 0. Calculate u.
-1, 2
Let i be ((-18)/10)/((-480)/(-1152)*18/(-5)). Determine z so that 24/5 - 3/5*z**2 - i*z = 0.
-4, 2
Let n = 31184 + -31184. Let y = -72 + 218/3. Solve n*i**3 - 2/3*i**2 + 0 + y*i**4 + 0*i = 0 for i.
-1, 0, 1
Let m(z) be the first derivative of -4*z**3 + 50 + 0*z**2 - 1/2*z**4 + 0*z. Factor m(k).
-2*k**2*(k + 6)
Let 0 - 35/2*m**2 - 1/2*m**4 + 25/2*m + 11/2*m**3 = 0. What is m?
0, 1, 5
Let k(h) = 232*h**2 + 564*h + 72. Let n(i) = -270*i**2 - 658*i - 84. Let t(z) = 15*k(z) + 13*n(z). Factor t(y).
-2*(y + 3)*(15*y + 2)
Let d(q) be the second derivative of 1/3*q**3 + 77*q + 0 - 2*q**2 + 1/6*q**4. Determine w so that d(w) = 0.
-2, 1
Let a(w) be the first derivative of -w**6/3 + 38*w**5/5 + w**4/2 - 38*w**3/3 + 4127. Suppose a(k) = 0. What is k?
-1, 0, 1, 19
Let i be 206/264 + 178/(-178)*(-6)/(-8). Let p(h) be the second derivative of 1/33*h**4 + i*h**3 + 0 - 1/110*h**5 + 16*h - 2/11*h**2. What is w in p(w) = 0?
-1, 1, 2
Suppose 3*a + a = 136. Let f = a - 32. Suppose g - 70*g**f + 69*g**2 + 2 - g**3 - 2 + g**4 = 0. Calculate g.
-1, 0, 1
Factor -265*p - 169*p - 70*p**2 + 48*p - 169*p - 100*p**2 + 5*p**3.
5*p*(p - 37)*(p + 3)
Solve 67/5*f - 133/5*f**2 + 0 + 1/5*f**4 + 13*f**3 = 0 for f.
-67, 0, 1
Let d(m) = -m**3 - 12*m**2 - 21*m + 6. Let b be d(-10). Let t be ((-11)/66)/((-2)/b). Solve 4/3*y**2 + 28/3*y**3 + t*y**5 - 32/3*y + 16/3 - 20/3*y**4 = 0 for y.
-1, 1, 2
Let p = 50 + -24. Let g(s) = s**2 + 5*s + 2. Let r be g(-5). Factor 55*w**r - 34*w**2 - p*w**2 - 5*w**3.
-5*w**2*(w + 1)
Let n(o) = 11*o**2 + 17*o - 88. Suppose 192 = 16*l - 64. Let t(s) = -58*s**2 - 86*s + 440. Let v(b) = l*n(b) + 3*t(b). Find r such that v(r) = 0.
-11, 4
Let j be (52/12 - 3) + -3*1/3. Let c(q) be the first derivative of 1/20*q**4 + 14 + 3/5*q + 7/10*q**2 + j*q**3. Find b such that c(b) = 0.
-3, -1
Let g(s) be the second derivative of -s**6/30 - 91*s**5/100 + s**4/30 + 182*s**3/15 + 36*s**2/5 + 526*s. What is l in g(l) = 0?
-18, -2, -1/5, 2
Suppose 14*i = 23*i - 225. Suppose -8 = -27*z + i*z. Factor 3 - 10 - 6*d**3 + 6*d - 3*d**z + 10.
-3*(d - 1)*(d + 1)**3
Let i(r) = 3*r**3 - 178*r**2 + 13*r - 7975. Let f be i(60). Find a such that -27/4*a**4 - 75/2*a - 3/8*a**f + 0 + 135/2*a**2 - 183/8*a**3 = 0.
-10, 0, 1
Let o be (-119)/(-56) + (-27)/(-216). Let d(q) be the second derivative of -1/20*q**5 + 1/12*q**4 + 5/8*q**3 - o*q**2 + 0 + 4*q. Let d(s) = 0. Calculate s.
-2, 3/2
Let v(s) = 22*s**2 + 2. Let l(j) = -527*j**2 - 365*j + 18. Let w(h) = l(h) + 6*v(h). Let w(m) = 0. What is m?
-1, 6/79
Let 3*d**5 + 1662*d**2 + 837 + 60*d**4 + 0*d**5 - 15396*d**3 + 15855*d**3 + 2820*d + 963 = 0. Calculate d.
-6, -5, -2
Let k(h) = -564*h**2 - 1191*h - 177. Let p(v) = 89*v**2 + 188*v + 28. Let b(t) = 8*k(t) + 51*p(t). Solve b(z) = 0 for z.
-2, -2/9
Let k(j) = -j**5 - j**4 - j. Let d(m) = -18*m**5 + 879*m**4 - 9009*m**3 - 2646*m**2 + 3*m. Let u(t) = d(t) + 3*k(t). Solve u(r) = 0.
-2/7, 0, 21
Let o(a) be the first derivative of -a**4/22 - 2*a**3/33 + 10*a**2/11 - 16*a/11 + 494. Factor o(d).
-2*(d - 2)*(d - 1)*(d + 4)/11
Suppose -4*j**2 + 638*j - 162*j - 244*j - 660 = 0. Calculate j.
3, 55
Factor -1/3*b**2 - 22/3*b + 45.
-(b - 5)*(b + 27)/3
Find a such that 0 - 14/9*a**4 + 0*a + 0*a**2 - 4/3*a**3 - 2/9*a**5 = 0.
-6, -1, 0
Solve 1092 - 4/3*o**2 + 3272/3*o = 0.
-1, 819
Let z(a) be the second derivative of -23*a**5/100 + 58*a**4/15 - 2*a**3/3 + 3991*a. Factor z(h).
-h*(h - 10)*(23*h - 2)/5
Let p(z) be the first derivative of 50 - 2*z**4 + 2/3*z**6 + 2*z**2 + 16/3*z**3 - 8*z - 8/5*z**5. Solve p(v) = 0 for v.
-1, 1, 2
Let k = -4873 + 4875. Let v(h) be the first derivative of 1/7*h**3 - 6/7*h**k + 0*h + 5. Factor v(p).
3*p*(p - 4)/7
Let a(t) be the first derivative of 4*t**3/21 + 52*t**2/7 - 108*t/7 - 114. Solve a(y) = 0.
-27, 1
Let r(u) be the third derivative of -u**7/420 + 3*u**6/80 - u**5/15 - 5*u**4/4 - 413*u**2. Factor r(k).
-k*(k - 6)*(k - 5)*(k + 2)/2
Let h(g) = -9*g**4 + g**3 - g**2 + 2*g - 2. Let o(l) = -17*l**4 + 22*l**3 + 30*l**2 - 25*l - 1. Let x(v) = 5*h(v) + 5*o(v). What is z in x(z) = 0?
-1, -3/26, 1
Let r(t) = 2*