 24
Factor -148/21*u**4 + 3848/7*u**2 + 2426/21*u**3 + 0 + 4056/7*u + 2/21*u**5.
2*u*(u - 39)**2*(u + 2)**2/21
Let s be ((-30)/(-9))/((-20)/30). Let v(w) = w**2 + 336*w - 10. Let p(x) = -168*x + 6. Let y(o) = s*p(o) - 3*v(o). Suppose y(f) = 0. Calculate f.
-56, 0
Let l(q) be the third derivative of q**6/150 + 19*q**5/25 - 121*q**4/30 - 118*q**3/5 - 277*q**2. Let l(k) = 0. Calculate k.
-59, -1, 3
Let t be 5 - (-4 - (159/21 + 2)). Let n = 56/3 - t. What is w in -4/21*w**2 + 2/21*w + n*w**3 + 0 = 0?
0, 1
Let 13/3*j**2 - 106/3*j + 80/3 + 16/3*j**3 - j**4 = 0. Calculate j.
-8/3, 1, 2, 5
Let p = 33 - 32. Suppose 8*o - 10*o + 4 = 0. Solve 8*m + 14*m**2 + o*m**3 - 7 - 16 - p = 0.
-6, -2, 1
Let w(v) = -23*v**2 - 2006*v - 10440. Let s(y) = -15*y**2 - 1330*y - 6960. Let o(z) = 8*s(z) - 5*w(z). Let o(q) = 0. Calculate q.
-116, -6
Let f be 5 - 2 - (-25 + 25). Suppose -49*j**2 - j - 46*j**2 + j**4 + 98*j**2 - 3*j**f = 0. What is j?
0, 1
Let c be -24*1*(-1903)/692. Suppose 0 = 62*s - c*s + 8. Factor -3/10*v + 2/5 - 1/10*v**s.
-(v - 1)*(v + 4)/10
Let i be (-102)/(-68) + (-1)/((-4)/46). Determine g so that 10*g + 5*g**4 + i*g - 5*g**2 + 5*g**5 - 23*g - 5*g**3 = 0.
-1, 0, 1
Suppose 5*d + 3*n + 109 = 157, -32 = 3*d - 2*n. Factor 0 + d*g - 1/2*g**4 - 2/5*g**2 + 4/5*g**3 + 1/10*g**5.
g**2*(g - 2)**2*(g - 1)/10
Let g(h) = 9*h + 555 + 3*h - 241. Let i be g(-26). Factor -2/5*d + 18/5*d**i + 0.
2*d*(9*d - 1)/5
Factor 693*i**2 - 244*i**3 + 4*i**4 + 5616 - 5724*i + 0*i + 1287*i**2.
4*(i - 52)*(i - 3)**3
Suppose -295*d + 322*d - 2 = 106. Suppose 2*l + 142 = 3*r, 4*l = -3*r + 2*l + 158. Determine q, given that 106*q**5 - 57*q**5 - r*q**5 - q**d = 0.
-1, 0
Let x(l) be the third derivative of l**5/30 + 47*l**4/12 + 46*l**3/3 + 830*l**2. Factor x(o).
2*(o + 1)*(o + 46)
Suppose -3*a + 6 = -3*k, 3*a + 94 - 98 = 5*k. Suppose -22/7*m**2 + 0*m + 0 - 2/7*m**4 - 24/7*m**a = 0. What is m?
-11, -1, 0
Let o(a) be the third derivative of -a**6/30 - 14*a**5/5 - 41*a**4/6 - 2639*a**2. Suppose o(x) = 0. What is x?
-41, -1, 0
Let z = 1013699 + -3041093/3. Factor 0 + 10/9*u**3 + z*u**2 + 0*u - 8/9*u**4.
-2*u**2*(u - 2)*(4*u + 3)/9
Suppose -13*q - 4*q = 612. Let y = 75/2 + q. Solve -9/2*f + 3 + y*f**2 = 0 for f.
1, 2
Let s be (2994/(-5489))/(57/(-88)). Suppose -2/19*p**5 + 18/19*p - s*p**3 + 12/19*p**4 - 8/19 - 4/19*p**2 = 0. What is p?
-1, 1, 4
Factor 320 + 2/3*u**2 + 92/3*u.
2*(u + 16)*(u + 30)/3
Let t(u) = -u**3 - 11*u**2 - 11*u - 6. Let k be t(-10). Determine y so that y**2 - 2*y**4 + 5*y**4 - 2*y**k + 2*y**3 + 0*y**2 = 0.
-1, 0
Let z(j) be the third derivative of -2*j**7/735 - 122*j**6/105 - 5042*j**5/35 - 14762*j**4/21 - 29282*j**3/21 - 796*j**2. Factor z(c).
-4*(c + 1)**2*(c + 121)**2/7
Let o(y) = 8*y - 7 + y**2 + 0 + 0. Let n be o(-9). Let -10*j**5 - n*j**5 + 2*j**2 + 3*j + 18*j**3 + 22*j**2 - 9*j**5 - 24*j**4 = 0. What is j?
-1, -1/7, 0, 1
Let d(s) = 3*s**2 - 523*s + 156. Let c(j) = -22*j**2 + 4182*j - 1251. Let u(p) = 6*c(p) + 51*d(p). Factor u(m).
3*(m - 75)*(7*m - 2)
Let u(s) be the second derivative of 5/6*s**2 + 10*s + 23/36*s**4 - 1/90*s**6 + 7 + 1/8*s**5 + 13/12*s**3. Suppose u(y) = 0. What is y?
-1, -1/2, 10
Let k = 1088259/4 - 272028. Factor 21/4*v**2 + 343/4 + 1/4*v**3 + k*v.
(v + 7)**3/4
Let m(y) be the third derivative of -y**6/80 - 86*y**2 - 12*y. Suppose m(a) = 0. Calculate a.
0
Let s(f) = f**4 - 2*f**2 + 2*f - 2. Let i(x) = 18*x**4 - 2*x**3 - 254*x**2 + 34*x + 188. Let h(t) = i(t) - 16*s(t). Determine r so that h(r) = 0.
-10, -1, 1, 11
Let p = -177814 + 177828. Let 56/5*s - 8/5 + 22/5*s**3 - p*s**2 = 0. What is s?
2/11, 1, 2
Suppose 114/5 + 63/5*h - 3/5*h**3 - 54/5*h**2 = 0. What is h?
-19, -1, 2
Let u = 1936 - 1933. Let j(p) be the first derivative of p**u + 9/2*p**2 - 12 + 6*p. Factor j(w).
3*(w + 1)*(w + 2)
Let 186*g - 432/5 + 1/5*g**4 - 563/5*g**2 + 64/5*g**3 = 0. What is g?
-72, 1, 6
Let t(h) = 8*h - 142. Let u be t(18). Factor -4*a**2 + 5*a + 4*a**2 - 3*a**u + 5 - 5*a**3 - 2*a**2.
-5*(a - 1)*(a + 1)**2
Determine b so that 64*b**2 + 1131*b**4 - 32 + 6*b**5 + 2*b - 24*b**3 - 1145*b**4 - 2*b = 0.
-2, -2/3, 1, 2
Suppose -177*r = -142*r - 70. Let -8/3 - 1/3*u**2 + r*u = 0. What is u?
2, 4
Suppose 49/2*t + 3*t**2 - 1/2*t**3 + 33 = 0. Calculate t.
-3, -2, 11
Let g(n) be the third derivative of -2*n**2 + 32/3*n**3 + 0*n - 4/15*n**6 + 8/5*n**5 - 24 - 16/3*n**4 + 2/105*n**7. Solve g(i) = 0 for i.
2
Let k(j) be the first derivative of -192 - 52/7*j + 4/21*j**3 - 24/7*j**2. Let k(m) = 0. Calculate m.
-1, 13
Factor 3312*x + 4/3*x**2 + 2056752.
4*(x + 1242)**2/3
Let j(w) be the second derivative of w**4/30 + 17*w**3/15 - 22*w**2 - 390*w. Determine m so that j(m) = 0.
-22, 5
Suppose -y - 5*u = 93, 1602*u + 57 = 1599*u. Factor 210870/7*l**2 + 2978/7*l**3 - 1431644/7 + 4950262/7*l + y*l**4.
2*(l + 71)**3*(7*l - 2)/7
Let y(j) = j**2 - 2. Let v(g) = -4*g**2 - 3*g + 3. Let m(d) = -v(d) - 3*y(d). Let i be m(0). Find p, given that 56*p - 15*p**2 - 34*p - i*p**3 - 34*p = 0.
-4, -1, 0
Factor 29*v - 71*v**2 - 20*v**3 - 85*v**2 + 61*v**2 - 60*v**2 + 11*v.
-5*v*(v + 8)*(4*v - 1)
Let v be (-32)/(-14) + 4/(-14) - 3. Let o be (8/2 + -7)*v. Factor -6*t**4 - 8*t - 16*t**o + 2*t**4 - 13*t**2 - 7*t**2.
-4*t*(t + 1)**2*(t + 2)
Let q be 5*(-12)/(-56)*7*(-2)/(-10). Let b(p) be the first derivative of -1/2*p**3 + 0*p - 4 + q*p**2. Let b(n) = 0. What is n?
0, 2
Suppose 0 = 5*a - 5*c, 0*a = -4*a - 3*c + 28. Suppose -a*j + 20 = 5*u, -4*u = j - 4*j - 47. Find h, given that -4*h**3 - u*h - 12*h**2 + 7*h + h = 0.
-3, 0
Factor -49*u**2 + 25*u**2 + 22*u**2 + u + 224 + 11*u.
-2*(u - 14)*(u + 8)
Let y(t) be the third derivative of t**5/160 + 129*t**4/64 + 8*t**3 + 10*t**2 - 20. Suppose y(g) = 0. What is g?
-128, -1
Let u(m) = -m**2 + 16*m - 69. Let f be u(10). Let z be (f/(-81))/(3/102). Suppose 8/9 + z*p + 8/9*p**2 = 0. Calculate p.
-4, -1/4
Let k(s) be the first derivative of s**6/6 - 2*s**5 + 15*s**4/2 - 40*s**3/3 + 25*s**2/2 - 112*s - 207. Let o(c) be the first derivative of k(c). Factor o(q).
5*(q - 5)*(q - 1)**3
Factor 368*i**2 - 1091*i**2 + 361*i**2 + 367*i**2 + 460*i.
5*i*(i + 92)
Factor t**2 + 181*t - 16*t + 32 - 172 - 194.
(t - 2)*(t + 167)
Let x(v) = 3*v**3 - 66*v**2 - 827*v - 2856. Let z(j) = 5*j**3 - 98*j**2 - 1240*j - 4288. Let a(t) = 8*x(t) - 5*z(t). Determine i, given that a(i) = 0.
-22, -8
Let q = -901 - -7. Let w = q - -4494/5. Find y such that w*y - 13/5*y**2 + 2/5*y**3 - 9/5 = 0.
1/2, 3
Let t(w) be the first derivative of 3*w**5/5 + 48*w**4 + 1336*w**3 + 14976*w**2 + 73008*w + 5846. Factor t(n).
3*(n + 6)**2*(n + 26)**2
Let o(i) be the first derivative of -41*i**3/5 + 62*i**2/5 - i/5 + 1426. Factor o(c).
-(c - 1)*(123*c - 1)/5
Let s(c) be the second derivative of 1/30*c**6 + 1/6*c**3 + 31/36*c**4 - 3*c**2 - 2 - 36*c - 19/60*c**5. Solve s(a) = 0 for a.
-2/3, 1, 3
Let y(w) be the third derivative of 0*w - 1/40*w**5 + 77*w**2 + 1/8*w**4 + 0*w**3 + 0 - 1/28*w**7 - 1/10*w**6. Determine o so that y(o) = 0.
-1, 0, 2/5
Let d(r) be the first derivative of r**7/1785 - r**6/340 - 2*r**5/255 + 45*r**2/2 + 16. Let x(c) be the second derivative of d(c). Solve x(w) = 0.
-1, 0, 4
Suppose 4*o + 4*z - 8179 + 8175 = 0, 4*z = 3*o - 17. What is q in -33/4*q**2 + 3/4*q**4 + 0*q**o - 27/2*q - 6 = 0?
-2, -1, 4
Let t(a) be the third derivative of 17*a**8/840 - 53*a**7/525 - 77*a**6/60 - 103*a**5/30 - 43*a**4/15 + 28*a**3/15 - 3*a**2 - 52*a. Let t(d) = 0. Calculate d.
-2, -1, 2/17, 7
Let r(u) be the first derivative of 4*u**5/15 - 245*u**4/3 + 1497. Solve r(w) = 0 for w.
0, 245
Let x = 11/19 + -9/19. Let w = x + 53/38. What is n in 2 - 1/2*n**2 - w*n = 0?
-4, 1
Let k(c) = c**3 + 7*c**2 + 4*c + 24. Let j be k(-7). Let t be (j - 0)*((-917)/98 + 9). Factor 0 - 8/7*b**4 + 2/7*b**5 + 0*b - 4/7*b**2 + t*b**3.
2*b**2*(b - 2)*(b - 1)**2/7
Let a(v) be the third derivative of -2/25*v**6 + 0*v - 1/10*v**4 + 17/75*v**5 + 0 - 268*v**2 - 4/15*v**3. Suppose a(h) = 0. What is h?
-1/4, 2/3, 1
Let x(w) be the first derivative of 5*w**6/6 - 65*w**4/4 + 80*w**3/3 + 30*w**2 - 80*w - 7322. Find y such that x(y) = 0.
-4, -1, 1, 2
Let t = 177 + -18. Solve -75*l - 3*l**4 - 3*l**3 - t + 39*l**2 + 6*l**3 + 195 = 0.
-4, 1, 3
Suppose 0*u - 1/9*u**5 + 5/3*u**4 + 0 + 49/9*u**2 - 7*u**3 = 0. Calculate u.
0, 1, 7
Let k(p) be the first derivat