3*r**4/14 - 10366*r**3/21 - 5041*r**2/7 - 121. Factor a(y).
-2*y*(y + 1)*(y + 71)**2/7
Let g(a) be the second derivative of 3*a**5/40 - 511*a**4/8 + 64507*a**3/4 + 594441*a**2/4 - 6895*a. What is o in g(o) = 0?
-3, 257
Suppose 330 = 4*n + 2*z, 2*n + 2*n = -4*z + 336. Suppose -n = 6*q - 93. Find l, given that -l**4 + 0 - 1/2*l + 0*l**q + 3/2*l**3 = 0.
-1/2, 0, 1
Let q(c) be the third derivative of c**5/150 - 108*c**4/5 + 139968*c**3/5 + 1160*c**2. Suppose q(w) = 0. What is w?
648
Suppose -3*j + 589 = -2*u - 278, 0 = 5*j - 5*u - 1440. Let s = j + -289. Suppose -2/3*w**4 + 3/2*w**3 + 0 - 1/3*w**s + 0*w = 0. Calculate w.
0, 1/4, 2
Let s = -652 + 620. Let m be 1 + (2/s)/((-5)/(-70)). Factor -m*z**2 + 1/8*z + 3/4.
-(z - 3)*(z + 2)/8
Let q = -15385/2 + 7887. Let f = 196 - q. Solve -6*h - f*h**2 - 6 = 0 for h.
-2
Let l(s) be the first derivative of s**5/15 + 145*s**4/3 + 385*s**3/3 - 290*s**2/3 - 1156*s/3 - 662. Find f such that l(f) = 0.
-578, -2, -1, 1
Let p be (-6504)/1122*(-1 - 2)/57. Let l = 2/187 + p. Factor 8/19*s - l - 2/19*s**2.
-2*(s - 3)*(s - 1)/19
Let w(d) be the second derivative of -9/110*d**5 - 1/231*d**7 + 16*d + 2 + 0*d**2 + 1/33*d**6 + 7/66*d**4 - 2/33*d**3. Find y, given that w(y) = 0.
0, 1, 2
Let -3/5*v + 7/5*v**5 - 4/5*v**3 - 12/5*v**4 - 2/5 + 14/5*v**2 = 0. Calculate v.
-1, -2/7, 1
Let n(a) be the third derivative of a**7/350 + a**6/2 + 9*a**5 + 11*a**2 - 199. Factor n(p).
3*p**2*(p + 10)*(p + 90)/5
Let r be 506/1804*41 - -29. Let -3/4*p**2 - 2187/4 + r*p = 0. What is p?
27
Let m(y) be the second derivative of -y**7/189 - 11*y**6/135 - 43*y**5/90 - 23*y**4/18 - 4*y**3/3 - 2*y + 123. Solve m(i) = 0.
-4, -3, -1, 0
Let b(g) be the second derivative of -11/9*g**3 + 0 + 7/2*g**2 + 139*g + 1/36*g**4. Factor b(x).
(x - 21)*(x - 1)/3
Let i(z) = -2*z**4 + 2*z**3 + z**2 + 1. Let a(y) = -31*y**4 + 18*y**3 - 1111*y**2 + 8232*y + 345760. Let h(t) = -5*a(t) + 80*i(t). Solve h(v) = 0 for v.
-21, 28
Find c, given that -151 + 34*c**2 - 329 - 36*c**2 + 482*c = 0.
1, 240
Let j(f) be the third derivative of 4*f**7/45 + 29*f**6/180 - f**5/20 - 13*f**4/72 - f**3/9 - 2692*f**2. Suppose j(c) = 0. What is c?
-1, -2/7, -1/4, 1/2
Let b = 87910/1791 - -446/1791. Solve b*i - 2/3*i**5 + 18*i**3 + 16 + 154/3*i**2 - 2/3*i**4 = 0.
-4, -1, 6
Suppose 0 = 2*i + 2*v + 26, 259*i - 256*i = v + 21. Factor -1/6*f**4 - 150 + 310*f - 1021/6*f**i + 31/3*f**3.
-(f - 30)**2*(f - 1)**2/6
Let q(g) be the third derivative of -g**6/60 - 7*g**5/5 - 27*g**4/4 - 40*g**3/3 - 3*g**2 + 14*g. Factor q(y).
-2*(y + 1)**2*(y + 40)
Let c(p) be the third derivative of -p**5/105 + 17*p**4/42 - 44*p**3/7 - 2360*p**2. Determine g, given that c(g) = 0.
6, 11
What is x in 9/4*x**3 - 3/2*x**4 - 1/4*x**5 + 29/2*x**2 - 18 + 3*x = 0?
-6, -2, 1, 3
Let z(p) be the first derivative of p**4/28 - 4*p**3/21 - p**2/14 + 4*p/7 + 1097. What is f in z(f) = 0?
-1, 1, 4
Suppose -1588*x**2 + 283*x + 4*x**4 + 81 + 5*x**4 - 240*x**3 + 746*x**2 - 43*x + 752*x**2 = 0. What is x?
-1, -1/3, 1, 27
Let q be 3/((6/20)/(13/65)). Factor 2*k**3 + 44*k**q - 2*k**3 - 9*k**4 - 38*k**2 - 3*k**3.
-3*k**2*(k + 1)*(3*k - 2)
Suppose -8*k + 36 = -2*k. Factor -3*c**2 + k*c - 12 - 11*c - 3*c - 4*c.
-3*(c + 2)**2
Let x(g) be the first derivative of g**7/224 - g**6/72 + g**5/96 - 35*g**3/3 + 7. Let n(c) be the third derivative of x(c). Factor n(d).
5*d*(d - 1)*(3*d - 1)/4
Let f = -16315 + 16317. Solve 15/4*n + 1/4*n**f + 0 = 0 for n.
-15, 0
Let b(p) be the third derivative of 0*p + 1/1050*p**7 + 19*p**2 + 0 + 1/30*p**4 - 7/300*p**5 + 0*p**3 + 1/300*p**6. Factor b(f).
f*(f - 1)**2*(f + 4)/5
Let -2/15*o**3 + 8/15*o + 8/3*o**2 - 32/3 = 0. What is o?
-2, 2, 20
Let t(m) = -4*m + 5. Let f be t(-2). Suppose 4*k + 5*b + f = 0, 0 = -k + 3*b + 27 - 9. Let w**k + w**2 + 3 + 6 - 6*w**2 - 15*w + 18*w = 0. Calculate w.
-1, 3
Let q be 6*(28/(-6) + 5). Factor -15 + 52*y - 9 + 92*y**q + 20*y**2.
4*(4*y + 3)*(7*y - 2)
Let r(i) be the second derivative of -247*i + 0 + 45/4*i**4 + 0*i**3 + 33/4*i**5 + 19/18*i**6 + 0*i**2 + 5/126*i**7. Factor r(b).
5*b**2*(b + 1)*(b + 9)**2/3
Let l be (-6392)/32 - (-5 + 2). Let z = l + 197. Suppose 0*m + z*m**5 + 0 - 1/4*m**4 + 1/4*m**2 - 1/4*m**3 = 0. What is m?
-1, 0, 1
Suppose 142*o + 3*o - 310 - 914 = -263*o. Determine b, given that -4/3*b**2 + 7/2*b + 1/6*b**o - 3 = 0.
2, 3
Let j(b) be the first derivative of 4*b**3/3 + 74*b**2 + 144*b + 997. Factor j(i).
4*(i + 1)*(i + 36)
Suppose 7*y - 239 + 218 = 0. Factor -200*v**2 + 3*v**4 - 44*v**3 + 140*v**y + 88*v + 19*v**2 - 7*v**4 + v**2.
-4*v*(v - 22)*(v - 1)**2
Factor -97*r - 347*r**2 - 7*r**4 + 4*r**4 - 155*r - 258*r**3 - 160*r**2.
-3*r*(r + 1)**2*(r + 84)
Let i(u) be the second derivative of u**4/24 - 9*u**3/2 - 28*u**2 + 3*u + 6. Solve i(p) = 0.
-2, 56
Let p(b) be the first derivative of b**5/300 + b**4/60 - b**3/10 - 55*b**2/2 - b + 249. Let c(v) be the second derivative of p(v). Let c(d) = 0. Calculate d.
-3, 1
Let f(a) = -92*a. Let b be f(1). Let w = 492/5 + b. Find g such that 1022/5*g**2 - 272/5*g**4 + 338/5*g**3 + 86*g + 10 + w*g**5 = 0.
-1, -1/4, 5
Factor 12*u**3 - 56*u**2 - 2*u**3 - 93*u**2 - 3*u**3 - 154 - 9*u**3 + 383*u.
-(u - 2)*(u + 77)*(2*u - 1)
Let f(p) = 6*p**3 + 24*p**2 + 39*p + 39. Let x(g) = -3063*g - g**3 + 3061*g + 2*g**3 + 1. Let y(b) = f(b) - 9*x(b). Factor y(j).
-3*(j - 10)*(j + 1)**2
Factor -176293*d**2 - 275*d - 4633*d + 2 - 2 + 176295*d**2.
2*d*(d - 2454)
Let m be (12/(-16))/(4/(-16)). Let b be (18 - 14) + (-16)/4. Factor 500/3*k - 400/3*k**2 - 5/3*k**4 + b - 95/3*k**m.
-5*k*(k - 1)*(k + 10)**2/3
Suppose -65*g**3 + 68*g**3 + 7*g**2 - 3554*g + 3558*g = 0. Calculate g.
-4/3, -1, 0
Let s = 352/217 - 290/217. Let -s*q**2 - 32/7*q + 0 = 0. Calculate q.
-16, 0
Let u = 615405/2 - 307635. Factor 30 - u*o**2 - 50*o + 25/2*o**3.
5*(o - 6)*(o + 1)*(5*o - 2)/2
Suppose -3*n + 3 = -6*t + 3*t, -2*n - t = -8. Suppose -v + 6*v = 15. Factor -j**v + 13*j - 12*j + 4*j**2 - 9*j + 5*j**n.
4*j*(j - 1)*(j + 2)
Let y(w) = -w**3 + w**2. Suppose 13*i - 2 = -28. Let q(k) = 11*k**3 + 9*k**2 + 22*k - 42. Let g(x) = i*q(x) - 18*y(x). Factor g(c).
-4*(c - 1)*(c + 3)*(c + 7)
Let p(d) = 0 + 1 + 1 + 24*d - 6 - 2*d**2 + 5*d**2. Let o(v) = -v - 2. Let z(t) = 5*o(t) + p(t). Factor z(q).
(q + 7)*(3*q - 2)
Let z(k) be the second derivative of -6*k - 1 - 1/27*k**4 + 14/9*k**2 + 4/9*k**3. Factor z(a).
-4*(a - 7)*(a + 1)/9
Let x be ((-1)/2)/(39/(-234)). Determine i, given that 25 - 3*i**x + 30*i + 5 + 3*i**2 - 6 = 0.
-2, -1, 4
Determine f, given that 10/21*f**5 - 5200/21 - 1156/3*f**2 - 316/21*f**4 - 16760/21*f + 3142/21*f**3 = 0.
-1, -2/5, 10, 13
Let d = -312 + 367. Let d*c**3 + 63*c**3 + 2*c - 35 - 6*c + 120*c**2 - 114*c**3 - 85 = 0. What is c?
-30, -1, 1
Let n(s) be the third derivative of s**8/1680 + s**7/210 + s**6/90 - 13*s**3/6 - 3*s**2 + 3. Let z(f) be the first derivative of n(f). Solve z(r) = 0 for r.
-2, 0
Let 0 - 18/7*d + 46/7*d**2 = 0. What is d?
0, 9/23
Let w = -56 + 51. Let d(c) = 15*c**3 - 143*c**2 + 208*c - 76. Let k(g) = -30*g**3 + 285*g**2 - 415*g + 150. Let i(y) = w*d(y) - 2*k(y). Let i(p) = 0. What is p?
2/3, 1, 8
Solve 108/23*b**4 + 4/23 + 548/23*b**2 + 226/23*b + 434/23*b**3 = 0.
-2, -1, -1/54
Let x(n) be the third derivative of n**6/30 + 19*n**5/15 + 37*n**4/3 + 112*n**3/3 - 12*n**2 + 24. Determine r so that x(r) = 0.
-14, -4, -1
Let w(l) be the second derivative of -l**7/70 + 2*l**6/5 - 291*l**5/100 + 97*l**4/10 - 86*l**3/5 + 84*l**2/5 - 348*l. Determine j, given that w(j) = 0.
1, 2, 14
Suppose -456/7*m - 5*m**3 - 180/7 - 209/7*m**2 - 2/7*m**4 = 0. What is m?
-6, -5, -1/2
Factor 610/3*f**2 + 202 - 2/3*f**3 - 1214/3*f.
-2*(f - 303)*(f - 1)**2/3
Let m(w) be the second derivative of 0 - 3*w**2 - 19/2*w**3 - 22*w + 75/4*w**4. Factor m(v).
3*(3*v - 1)*(25*v + 2)
Let c(r) = 10*r**2 + 10082*r - 9996. Let f(p) = 4*p**2 + 4033*p - 3997. Let x(u) = 5*c(u) - 12*f(u). Factor x(y).
2*(y - 1)*(y + 1008)
Let n(l) be the third derivative of -1/6*l**4 - 22*l - 1/18*l**5 - 1/180*l**6 + 0*l**3 + 0 + 3*l**2. Suppose n(y) = 0. Calculate y.
-3, -2, 0
Let z(a) be the third derivative of a**8/2520 + a**7/525 + a**6/300 + a**5/450 + 4*a**2 + 50*a. Factor z(m).
2*m**2*(m + 1)**3/15
Let w be ((-1131651)/4284)/((-4)/48) - (-3)/(-17). Solve -w - 3/7*v**2 - 516/7*v = 0 for v.
-86
Let u =