 2, 27
Let c(r) be the first derivative of -r**3 - 46 + 3/5*r**5 + 0*r**2 - 1/2*r**6 + 0*r + 3/4*r**4. Determine u, given that c(u) = 0.
-1, 0, 1
Let r = -2181 - -297. Let o be r/(-156) - 1 - 10. Let -6/13*f**5 - 16/13*f - 24/13*f**2 + 12/13*f**3 + o*f**4 + 0 = 0. What is f?
-1, -2/3, 0, 2
Suppose -38 - 1/9*r**2 + 13*r = 0. Calculate r.
3, 114
Let b = 7196 + -7196. Let q(f) be the third derivative of -9/4*f**4 - 1/60*f**6 + 3/10*f**5 - 6*f**2 + 9*f**3 + 0 + b*f. Determine g so that q(g) = 0.
3
Let y(x) be the first derivative of x**5/5 - x**4/2 - 64*x**3/3 + 145*x**2 - 225*x + 555. Suppose y(l) = 0. What is l?
-9, 1, 5
Let h(i) be the third derivative of 7/9*i**3 + 1/180*i**5 + 27*i**2 + 0 - 1/8*i**4 + 0*i. Determine r so that h(r) = 0.
2, 7
Let h = -1/1090291 - -14306798513/11993201. Let 2/11*p**5 + 7290/11*p + 900/11*p**3 - h + 4860/11*p**2 + 70/11*p**4 = 0. What is p?
-9, 1
Let d(f) be the second derivative of -f**4/102 - 131*f**3/17 - 392*f**2/17 + 69*f + 5. Suppose d(w) = 0. What is w?
-392, -1
Let j(t) = t**2 + 4*t + 5. Let w = -24 + -27. Suppose 0 = -0*c + c + 6. Let i(v) = -9*v**2 - 33*v - 41. Let m(l) = c*i(l) + w*j(l). Factor m(p).
3*(p - 3)*(p + 1)
Let w(b) be the first derivative of b**8/168 + 4*b**7/105 - 11*b**6/60 + b**5/5 - b**2/2 + 33*b - 39. Let q(o) be the second derivative of w(o). Factor q(c).
2*c**2*(c - 1)**2*(c + 6)
Let n(p) be the first derivative of -p**4/12 - p**3 - 4*p**2 - 106*p + 233. Let v(d) be the first derivative of n(d). Suppose v(f) = 0. Calculate f.
-4, -2
Let v = -337 - -339. Let w be v + 9 + 6 + 4 + -16. Solve -2/9*x**3 + 1 - 14/9*x**2 - 1/9*x**w + 1/3*x + 5/9*x**4 = 0.
-1, 1, 3
Let p be (1 - 4)*(2 + -3). Let z be 75/3 + (2 - p - -1). Factor z*g**2 + 3*g + 22*g**2 - 48*g**2.
-g*(g - 3)
Let u = 46997 - 46988. Let 3/2*p**5 + 6*p**2 - u*p**3 + 12*p + 0 - 3/2*p**4 = 0. Calculate p.
-2, -1, 0, 2
Factor 5/6*s**3 - 1625/6 - 545/2*s**2 + 1085/2*s.
5*(s - 325)*(s - 1)**2/6
Let p(d) = -6*d**3 + 81*d**2 - 316*d - 405. Let z = 68 + -67. Let b(v) = -v**3 - 4*v**2 - v. Let a(r) = z*b(r) - p(r). Factor a(q).
5*(q - 9)**2*(q + 1)
Let y = -963 - -967. Find l, given that 453*l**4 + l**4 - 4*l - 983*l**3 + 255*l**3 - 110*l**2 - 62*l**y = 0.
-1/14, 0, 2
Let p(r) = -r**2 - 35*r + 40. Let q be p(-36). Suppose 0 = q*d + 4 - 12. Find j, given that 2/15*j**4 + 8/15*j**3 + 0 + 2/3*j**d + 4/15*j = 0.
-2, -1, 0
Suppose -180*g + 2 + 154 = -204. Suppose -1/3*u**g - 1/3*u + 1/3*u**4 + 0 + 1/3*u**3 = 0. What is u?
-1, 0, 1
Let u be 4/(-436) + (-74385)/(-88290). Determine o so that -2/3 + 1/6*o**3 + 4/3*o - u*o**2 = 0.
1, 2
Suppose 208/5*t**2 - 46/5*t**4 + 164/5*t**3 - 2/5*t**5 + 0 + 0*t = 0. What is t?
-26, -1, 0, 4
Let d(u) be the second derivative of -2*u**7/7 + 14*u**6/15 - 4*u**4/3 + 1649*u. Solve d(m) = 0 for m.
-2/3, 0, 1, 2
Factor 403*m + 7025*m - 2660 + 717*m**3 + 1652*m**2 - 705*m**3.
4*(m + 5)*(m + 133)*(3*m - 1)
Let u be (-3)/(-4 + 1)*3. Suppose -4*w = -2*o - 16, -2*w + u + 1 = o. Factor x**w + 6*x - 36 - 3*x**3 + 32.
-2*(x - 1)**2*(x + 2)
Let u = -26 + 96. Determine f, given that -14 - 26*f - 242*f**2 + 8*f - u*f + 6 = 0.
-2/11
Let i(y) be the first derivative of y**5/30 + 2*y**4/9 - y**3/9 - 4*y**2/3 + 20*y - 32. Let t(b) be the first derivative of i(b). Factor t(k).
2*(k - 1)*(k + 1)*(k + 4)/3
Suppose -5*w - 2*o = 1 + 7, -4 = w + o. Suppose 85*c - 694 + 2014 = 525*c. Suppose 11/2*n**2 + w - 3*n - 3/2*n**c = 0. What is n?
0, 2/3, 3
Let a(q) be the third derivative of 1/24*q**4 + 0*q**3 + 0*q - 1/1680*q**7 - 1/480*q**6 - 4 + 1/120*q**5 - 17*q**2. Factor a(v).
-v*(v - 2)*(v + 2)**2/8
Suppose -7 = r + 2*b, -6*b + 2*b = -r + 17. Let k be (1/(-3) + r)*(-45)/(-10). Factor 6*f + 9*f**2 - 2*f - 12*f**k + 3*f**4 - 4*f.
3*f**2*(f - 3)*(f - 1)
Let d be -1 + -2 + (-1 - 0). Let j be 0 - (0 + (d - -1)). Suppose -23*y**4 + 4*y**j + y**3 + 28*y**4 = 0. Calculate y.
-1, 0
Let j = -84 + 69. Let w be (18/j)/((-10)/25). Factor 4*d - 15*d**2 - 15*d**w - 7*d + d - 5*d**4 - 3*d.
-5*d*(d + 1)**3
Let k(l) be the first derivative of 4/3*l**3 - 4*l - 22 + 0*l**2. Determine v, given that k(v) = 0.
-1, 1
Let z(s) be the first derivative of -1/10*s**5 - 122 + 5/6*s**3 - 5/8*s**4 - 2*s + 1/12*s**6 + s**2. Solve z(p) = 0 for p.
-2, -1, 1, 2
Factor -48/7*v + 0 + 2*v**2.
2*v*(7*v - 24)/7
Let m(b) be the first derivative of 3*b**4/8 - 84*b**3 - 1017*b**2/4 - 255*b - 1137. Let m(s) = 0. Calculate s.
-1, 170
Suppose -104*q + 755 = -8*q + 6*q + 49*q. Factor 200 + 4/5*p**q - 180*p - 56*p**2 + 128/5*p**3 + 48/5*p**4.
4*(p - 2)*(p - 1)*(p + 5)**3/5
Let a(u) be the first derivative of 7/20*u**4 - 33/10*u**3 - 3*u**2 + 26 + 7*u. Let s(o) be the first derivative of a(o). Find k, given that s(k) = 0.
-2/7, 5
Suppose 0 = 19*q + 6*q - 150. Factor q*b + 0*b - 9*b + 18 - b**2 - 2*b**2.
-3*(b - 2)*(b + 3)
Let m(b) be the first derivative of -1/360*b**5 + 7*b**2 + 0*b + 0*b**4 + 24 + 1/9*b**3. Let x(a) be the second derivative of m(a). Factor x(w).
-(w - 2)*(w + 2)/6
Let p(s) be the third derivative of s**5/270 + 13*s**4/54 - s**3 - 42*s**2 - 6*s - 4. Let p(c) = 0. What is c?
-27, 1
Let m(d) be the first derivative of -51064811*d**4/4 + 275282*d**3 - 2226*d**2 + 8*d - 821. Factor m(i).
-(371*i - 2)**3
Let g = 1267 + -1262. Let f be ((-2)/(-7))/(g/35). Determine h so that 2*h**3 + 4/3*h + 3*h**f + 0 + 1/3*h**4 = 0.
-4, -1, 0
Let y(u) be the second derivative of -u**7/210 + u**6/30 + u**5/15 - 2*u**4/3 - 109*u**2/2 - 110*u. Let v(n) be the first derivative of y(n). Solve v(z) = 0.
-2, 0, 2, 4
Let p(l) be the second derivative of l**7/3360 + l**6/1440 - l**5/48 + l**4/12 - 53*l**3 + l - 31. Let w(s) be the second derivative of p(s). Factor w(y).
(y - 2)*(y - 1)*(y + 4)/4
Let q(c) be the third derivative of -c**7/42 - c**6/5 - c**5/6 + 2*c**4 - 3*c**3/2 - c**2 - c - 336. Factor q(d).
-(d - 1)*(d + 3)**2*(5*d - 1)
Let l(m) be the second derivative of -2*m**7/63 + 8*m**6/9 - 19*m**5/3 - 20*m**4/9 + 64*m**3/3 + 4314*m - 1. Solve l(h) = 0 for h.
-1, 0, 1, 8, 12
Suppose -7*k + k = 3*k. Let f(w) be the first derivative of -4 + 3/4*w**2 - 3/8*w**4 + k*w**3 + 0*w. What is o in f(o) = 0?
-1, 0, 1
Let n(k) = 3*k**2 - 78*k + 432. Let l(b) be the first derivative of -b**3 + 79*b**2/2 - 432*b + 40. Let g(q) = -6*l(q) - 7*n(q). Factor g(i).
-3*(i - 12)**2
Factor 141/5*v**4 + 9*v**5 + 153/5*v**3 + 63/5*v**2 + 0 + 6/5*v.
3*v*(v + 1)**3*(15*v + 2)/5
Solve 18/7*p - 40/7 - 2/7*p**2 = 0.
4, 5
Factor -1065021/4*w**2 - 267289 + 1033/2*w**3 - 534061*w - 1/4*w**4.
-(w - 1034)**2*(w + 1)**2/4
Determine d so that -187*d**2 + 2*d**3 + 348*d**2 - 195*d**2 - 36*d = 0.
-1, 0, 18
Find h, given that 122/3*h - 34/3*h**2 - 20 = 0.
10/17, 3
Let b be 49/11 - (196/(-77) - -2). Let s(f) be the third derivative of 0*f**3 + 0*f + 1/12*f**4 + 14*f**2 - 1/20*f**b + 0 + 1/120*f**6. Factor s(p).
p*(p - 2)*(p - 1)
Let n(w) be the third derivative of 4/5*w**5 + 0*w**3 + 15/8*w**4 + 1/40*w**6 + 0 - w**2 - 28*w. Suppose n(v) = 0. Calculate v.
-15, -1, 0
Suppose 2*z + 2*v = 6*z - 20, -4*z + 16 = -v. What is m in z*m**3 - 29*m**2 + 253*m**5 + 6*m - 248*m**5 + 42*m**3 - 27*m**4 = 0?
0, 2/5, 1, 3
Factor 2*y - 334 - 14*y**2 - 270 - 2*y**3 + 618.
-2*(y - 1)*(y + 1)*(y + 7)
Let x(b) be the third derivative of b**8/560 - 121*b**7/1050 + 721*b**6/300 - 1069*b**5/75 + 3*b**4 + 432*b**3/5 - 52*b**2 + 16. Find g such that x(g) = 0.
-2/3, 1, 4, 18
Factor -3354044/7*b**2 - 3343698/7 - 2/7*b**4 + 6692568/7*b + 5176/7*b**3.
-2*(b - 1293)**2*(b - 1)**2/7
Let q(u) be the second derivative of u**6/150 + 13*u**5/50 - u**4/20 - 38*u**3/15 + 26*u**2/5 + 2*u + 116. Factor q(j).
(j - 1)**2*(j + 2)*(j + 26)/5
Let i be 4/3*((-17)/(-5) - (-1180)/1475). Find m, given that -68/5*m + 68/5*m**2 - i*m**3 + 24/5 + 4/5*m**4 = 0.
1, 2, 3
Let b(n) = -20*n**3 - 65*n**2 - 135*n - 60. Let v(i) = 17*i**3 + 66*i**2 + 133*i + 60. Let m(k) = 4*b(k) + 5*v(k). Factor m(z).
5*(z + 1)**2*(z + 12)
Let h = 34588 - 34586. Let w(v) be the second derivative of -1/60*v**6 + 8/3*v**3 + 0 - 4*v**h + 22*v + 1/5*v**5 - v**4. Factor w(p).
-(p - 2)**4/2
Let v(s) be the first derivative of 2*s**6/3 + 16*s**5 + 116*s**4 + 568*s**3/3 - 234*s**2 - 648*s + 1729. Let v(a) = 0. What is a?
-9, -2, -1, 1
Let z = 1594 - 2409. Let r = z - -818. Factor -1/2*o**r + 2 - 1/2*o**2 + 2*o.
-(o -