third derivative of u**5/120 - 55*u**4/24 + 3025*u**3/12 + 18*u**2 - 2. Factor h(d).
(d - 55)**2/2
Suppose 0 = -2*o + 3*i - 11, 4*o - 23 = -3*i. Factor -3*w - 121 + 131 - 2*w**o - 5*w.
-2*(w - 1)*(w + 5)
Let r be (6 + 648/(-21))*7. Let d = r + 174. Factor 4/19*o**3 - 2/19*o - 2/19*o**5 + 0 + d*o**4 + 0*o**2.
-2*o*(o - 1)**2*(o + 1)**2/19
Suppose 0 + 0*i - 2/9*i**4 + 10/9*i**3 - 8/9*i**2 = 0. Calculate i.
0, 1, 4
Let j(k) be the second derivative of k**6/80 + 7*k**5/240 - k**4/24 + 7*k**3/2 + 13*k. Let o(i) be the second derivative of j(i). Suppose o(h) = 0. What is h?
-1, 2/9
Let v(d) be the second derivative of 1/60*d**4 + 0*d**2 - 1/10*d**3 + 0 - 7*d. Determine r, given that v(r) = 0.
0, 3
Let v(o) = 10*o**3 - 55*o**2 - 41*o + 24. Let f(y) = 10*y**3 - 55*y**2 - 40*y + 25. Let z(x) = 6*f(x) - 5*v(x). Factor z(i).
5*(i - 6)*(i + 1)*(2*i - 1)
Let f(w) = -3*w**5 - 4*w**4 + 2*w**3 - 5*w**2 - 5*w - 5. Let q(o) = -2*o**4 + o**3 - o**2 - o - 1. Let c(i) = f(i) - 5*q(i). Factor c(x).
-3*x**3*(x - 1)**2
Let j(g) = -3*g**2 - 2*g + 1. Let w be j(1). Let i be -3*(-160)/525 + w/(-14). Factor 2/5*y**4 - 4/5 - 2*y + 2/5*y**3 - i*y**2.
2*(y - 2)*(y + 1)**3/5
Let i = 39 - 60. Let t be (-3)/((i/4)/7). Factor -13*f**3 + 5*f**3 - 8*f**3 - 20*f**2 - 8*f - 4*f**t.
-4*f*(f + 1)**2*(f + 2)
What is a in -6*a - 4*a**4 + 3*a**4 - 2*a + 20*a**3 + a**2 - 16*a**3 + 4*a = 0?
-1, 0, 1, 4
Let u(i) be the second derivative of i**8/10080 - i**7/756 + i**6/135 - i**5/45 + 2*i**4/3 - 3*i. Let r(t) be the third derivative of u(t). Factor r(l).
2*(l - 2)**2*(l - 1)/3
Let v(w) be the first derivative of 4*w**3/21 + 332*w**2/7 + 27556*w/7 - 38. Factor v(j).
4*(j + 83)**2/7
Factor 36/7*r**2 - 48/7*r + 4/7*r**3 - 80/7.
4*(r - 2)*(r + 1)*(r + 10)/7
Suppose t + 5 = -0*t. Let p(j) = -8*j**3 + 8*j**2 + 11*j + 5. Let v(h) = 4*h**3 - 4*h**2 - 6*h - 2. Let a(i) = t*v(i) - 2*p(i). Solve a(r) = 0 for r.
-1, 0, 2
Let o(c) be the second derivative of 8*c + 1/15*c**5 + 1/6*c**4 - 4/3*c**2 - 4/9*c**3 + 0 - 1/45*c**6. Suppose o(p) = 0. What is p?
-1, 2
Let y(m) be the second derivative of m**8/504 - m**6/45 + 27*m**2 + 20*m. Let q(w) be the first derivative of y(w). Solve q(p) = 0 for p.
-2, 0, 2
Let k = 18 - 13. Suppose k*x**4 - 7*x**2 + 27*x**3 - 3*x**2 - 32*x**3 = 0. Calculate x.
-1, 0, 2
Let c(i) be the third derivative of -i**8/112 - 46*i**7/315 - i**6/18 - 5*i**2 + 2*i. Let c(p) = 0. What is p?
-10, -2/9, 0
Suppose 3*d - 2 = 2*d. Suppose 0 = t - 0*x + 4*x - 6, 0 = t - 4*x + d. Factor 5*s + 0*s - t*s**2 - 2*s + 4 - 5*s.
-2*(s - 1)*(s + 2)
Suppose -2*i + 4*z + 26 = 0, -13 - 1 = -2*i + z. Let 13*n**3 + i + 15*n - 5 - 12*n**2 - 16*n**3 = 0. What is n?
-5, 0, 1
Factor 2/17*n**3 + 0*n**2 - 8/17*n + 0.
2*n*(n - 2)*(n + 2)/17
Suppose -3*u - 2*t + 2 = 8, -6 = -2*u + 2*t. Let f(n) be the first derivative of 5 + u*n + 0*n**2 + 1/12*n**3 + 0*n**4 - 1/20*n**5. Factor f(g).
-g**2*(g - 1)*(g + 1)/4
Let z be ((-3)/4 + 2)*(104 + -103). Factor 0 + 1/2*v**2 - z*v**3 + 3/4*v**4 + 0*v.
v**2*(v - 1)*(3*v - 2)/4
Let p(u) be the third derivative of -2/3*u**3 + 5*u**2 - 1/40*u**5 + 0*u - 1/12*u**4 + 1/180*u**6 + 0. Let a(v) be the first derivative of p(v). Factor a(i).
(i - 2)*(2*i + 1)
Let k be -1*((-1305)/75 + 16). Factor 12/5*x**2 + k*x**3 - 4/5*x + 0.
x*(x + 2)*(7*x - 2)/5
Suppose 2*i + 3*c - 8*c - 15 = 0, -5*i + c + 95 = 0. Let n be 2/(-4) + (126/i)/3. Find p such that 2/5*p**3 + 6/5*p + 0 + n*p**2 = 0.
-3, -1, 0
Let u(q) be the second derivative of 0*q**2 + 0 + 64/21*q**3 + 42*q - 8/21*q**4 + 1/70*q**5. Factor u(h).
2*h*(h - 8)**2/7
Let l(h) be the first derivative of -5*h**3/3 + 60*h**2 - 720*h - 67. Determine v, given that l(v) = 0.
12
Factor -a**3 - 33*a + 30*a**2 + a**2 - 78 + 4*a**3 - 6*a**3 + 11*a**2.
-3*(a - 13)*(a - 2)*(a + 1)
Suppose x + 14 = -x. Let j be (x/((-28)/(-8)))/(-1). Let -4*r**2 - r - 2 - j - 7*r = 0. What is r?
-1
Suppose 18*d + 48 = 30*d. Let s(j) be the second derivative of 0*j**3 + 1/60*j**d + 3/100*j**5 + 1/75*j**6 + 4*j + 0*j**2 + 0. Factor s(f).
f**2*(f + 1)*(2*f + 1)/5
Let h(d) = -d**4 - 1. Let k = 50 + -51. Let v(o) = 4*o**4 + 12*o**3 + 12*o**2 - 28*o - 16. Let j(p) = k*v(p) - 8*h(p). Let j(l) = 0. Calculate l.
-1, 2, 3
Find g such that 237/4*g**3 + 3/8*g**5 + 156*g**2 + 243/4 + 1323/8*g + 33/4*g**4 = 0.
-9, -2, -1
Let c(v) = -47*v**3 + 1203*v**2 - 9307*v + 2257. Let i(n) = 23*n**3 - 602*n**2 + 4653*n - 1128. Let h(d) = 3*c(d) + 7*i(d). Solve h(x) = 0.
1/4, 15
Suppose -3*i - 5 = 4*t, 4*i + i - 2*t = -17. Let b(g) = -g**2 + 1. Let m(s) = -2*s**2 + 2. Let k(c) = i*b(c) + 3*m(c). What is o in k(o) = 0?
-1, 1
Let s(m) be the third derivative of -m**5/12 + 5*m**4/24 + 85*m**2. Factor s(q).
-5*q*(q - 1)
Let t(h) be the first derivative of h**4/10 - 22*h**3/5 + 24*h**2 - 232*h/5 + 550. Factor t(f).
2*(f - 29)*(f - 2)**2/5
Let r(d) be the third derivative of 1/24*d**4 - 10*d**2 + 0*d - 1/20*d**5 + 1/40*d**6 + 0*d**3 + 0 - 1/210*d**7. Solve r(k) = 0 for k.
0, 1
Let p = 33 + -31. Factor 15*b - 3*b**p + 5*b**2 - 19*b.
2*b*(b - 2)
Let b(c) = -c**3 - c**2 + 10*c - 7. Let n be b(5). Let a = 109 + n. Find w, given that -119/4*w**4 + 67/4*w**3 - 1 + 23/4*w**a + 49/4*w**5 - 4*w = 0.
-2/7, 1
Let k(x) be the first derivative of 6*x**5/5 + 2*x**4 - 28*x**3/3 + 4*x**2 + 6*x + 94. Solve k(y) = 0 for y.
-3, -1/3, 1
Let c(k) be the third derivative of -2*k**7/105 + k**6/15 - k**4/3 + 2*k**3/3 - 46*k**2. Factor c(j).
-4*(j - 1)**3*(j + 1)
Let u(f) be the third derivative of 5*f**8/336 - 41*f**7/42 + 5*f**6/3 - 380*f**2. Solve u(x) = 0.
0, 1, 40
Let g(r) be the third derivative of -3/10*r**5 + 0*r - 7/12*r**4 + 0 - 3*r**2 + 2/3*r**3. Find l such that g(l) = 0.
-1, 2/9
Let r(o) be the third derivative of -2/105*o**5 + 0 - 1/42*o**4 + 19*o**2 + 1/588*o**8 + 0*o**6 + 0*o + 0*o**3 + 4/735*o**7. Let r(u) = 0. Calculate u.
-1, 0, 1
Let o(r) = -12*r**3 + 99*r**2 - 24*r + 6. Let f(j) = -24*j**3 + 198*j**2 - 48*j + 13. Let q(y) = -6*f(y) + 13*o(y). Factor q(n).
-3*n*(n - 8)*(4*n - 1)
Let p = -9305 - -37221/4. Factor p*o**5 + 3/2*o**2 + 3/2*o**4 + 11/4*o**3 + 0 + 0*o.
o**2*(o + 1)*(o + 2)*(o + 3)/4
Let x be ((-13)/91)/(2/7)*0. Factor -4/5*f**3 + 2/5*f**2 + 0*f + 2/5*f**4 + x.
2*f**2*(f - 1)**2/5
Find w such that 53*w**2 + 4*w - 11*w**2 - 9*w - 9*w**3 + 4*w - 18 - 38*w = 0.
-1/3, 2, 3
Let p be 2/(-16)*(-1 - 1). Let k = 2/3369 - -3365/6738. Factor k*j + p*j**2 + 0.
j*(j + 2)/4
Let r(k) be the third derivative of -k**5/180 - 59*k**4/72 + 10*k**3/3 + 13*k**2 - k. Suppose r(i) = 0. Calculate i.
-60, 1
Let w be (-1876)/(-220) - 6 - 4/(-10). Let l = 52/11 - w. Let l*g**2 + 1/5 - 6/5*g = 0. Calculate g.
1/3
Let f(z) be the first derivative of -16/3*z**3 + 1 + z**4 + 8*z**2 + 0*z. Find p, given that f(p) = 0.
0, 2
Suppose -2/11*y**2 + 0*y - 2/11*y**3 + 0 = 0. What is y?
-1, 0
Let w(o) = 10*o**2 + 30*o + 35. Let u(j) = -j**2 - 2. Let k(h) = 5*u(h) + w(h). Factor k(q).
5*(q + 1)*(q + 5)
Let h(c) be the second derivative of -10*c**7/231 - 31*c**6/165 + 39*c**5/110 + 5*c**4/33 - 8*c**3/33 - 24*c. Let h(u) = 0. Calculate u.
-4, -1/2, 0, 2/5, 1
Let u(l) = -8*l - 2. Let v(g) = -g**2 - g - 1. Let j = 28 + -29. Let s(z) = j*u(z) + 2*v(z). Let s(d) = 0. What is d?
0, 3
Find p such that 44 - 62*p - 153*p + 423*p - 8*p**4 + 32*p**2 + 28 + 4*p**5 - 40*p**3 - 76*p = 0.
-2, -1, 3
Let g = 76 - 74. Let y(a) be the third derivative of -1/30*a**6 + 1/30*a**5 - 3*a**g + 0*a + 0 + 0*a**3 + 0*a**4. Suppose y(m) = 0. Calculate m.
0, 1/2
Let r = 203 - 811/4. Let d(l) be the second derivative of 1/80*l**5 + 0 - 1/8*l**3 + 0*l**4 + r*l**2 + 2*l. Factor d(h).
(h - 1)**2*(h + 2)/4
Suppose g = -2*g + 6. Let d(r) = r**2 - g - 5*r**3 + 4 + 2*r**3 + 0*r**2. Let p(s) = -7*s**3 + 2*s**2 - s + 5. Let h(n) = -5*d(n) + 2*p(n). Factor h(v).
v*(v - 2)*(v + 1)
Suppose -3*y = -12, -4*m + m - 587 = -5*y. Let z = 191 + m. Factor -88/7*i - 8/7 - 242/7*i**z.
-2*(11*i + 2)**2/7
Let b(y) be the third derivative of 1/40*y**5 + 0 + 1/16*y**4 + 0*y + 1/240*y**6 + 12*y**2 + 1/12*y**3. What is u in b(u) = 0?
-1
Let u(l) be the first derivative of 4/3*l**3 - 1/6*l**6 - 3 - 2/5*l**5 + 0*l - 2*l**2 + 3/4*l**4. Factor u(x).
-x*(x - 1)**2*(x + 2)**2
Let t(y) be the first derivative of y**4/2 + 44*y**3/3 - 23*y**2 + 319. Suppose t(l) = 0. What is l?
-23, 0, 1
Let p(d) be the thi