o) be the third derivative of o**10/50400 - o**9/7560 + o**8/2880 - o**7/2520 + o**5/20 - 3*o**2. Let m(h) be the third derivative of n(h). Factor m(p).
p*(p - 1)**2*(3*p - 2)
Let g(y) be the third derivative of y**8/1120 - y**7/560 - 2*y**3/3 - 3*y**2. Let n(t) be the first derivative of g(t). Let n(w) = 0. Calculate w.
0, 1
Let h(n) be the second derivative of -9*n + 1/210*n**6 - 1/294*n**7 + 0*n**3 - 1/84*n**4 + 1/140*n**5 + 0 + 0*n**2. Factor h(s).
-s**2*(s - 1)**2*(s + 1)/7
Factor -25*z**4 - 5/2*z**5 - 200*z**2 - 100*z**3 - 200*z - 80.
-5*(z + 2)**5/2
Let u(d) be the third derivative of d**7/350 + 7*d**2. Solve u(y) = 0 for y.
0
Let q(v) be the third derivative of 0*v + 1/21*v**3 - 3/28*v**4 + 0 + 4/35*v**5 + v**2 - 4/105*v**6. Factor q(j).
-2*(j - 1)*(4*j - 1)**2/7
Factor 3/7*s**2 - 4/7 + 4/7*s.
(s + 2)*(3*s - 2)/7
Factor 8/3*x**3 - 2/3*x**4 + 4/3*x - 10/3*x**2 + 0.
-2*x*(x - 2)*(x - 1)**2/3
Let k(u) be the first derivative of -1/12*u**3 - u - 1/2*u**2 + 2. Factor k(q).
-(q + 2)**2/4
Let b = -58 - -64. Let h(z) be the third derivative of z**2 + 0*z**3 - 1/210*z**7 - 1/120*z**b + 0 + 1/60*z**5 + 1/24*z**4 + 0*z. Factor h(f).
-f*(f - 1)*(f + 1)**2
Let o(g) be the third derivative of g**7/210 - 3*g**6/280 - g**5/84 + 3*g**4/56 - g**3/21 + 30*g**2. Let o(y) = 0. Calculate y.
-1, 2/7, 1
Let i(j) be the first derivative of j**6/1260 + j**5/70 + 3*j**4/28 + 8*j**3/3 + 2. Let v(n) be the third derivative of i(n). Suppose v(y) = 0. Calculate y.
-3
Let y(f) be the second derivative of f**5/120 - f**4/24 + f**3/12 + f**2/2 - f. Let t(c) be the first derivative of y(c). Factor t(j).
(j - 1)**2/2
Suppose 4*c + 2 = 6. Let p be c + (28/(-8))/7. What is d in -3*d**2 - 3/2*d**5 - p + 7/2*d**4 - d**3 + 5/2*d = 0?
-1, 1/3, 1
Let z = -14 + 14. Let v(j) be the third derivative of 1/168*j**7 + 3/80*j**5 - 1/40*j**6 + 0*j**3 - 1/48*j**4 + z + j**2 + 0*j. Determine x so that v(x) = 0.
0, 2/5, 1
Suppose 3 = -4*p - 5*a, -4*a + 0 = 2*p + 6. Suppose 0 = -4*j - 3*k - 1, -j + 8 = -4*k - 6. What is l in 8 + 4*l**2 + 3*l + l**2 - p*l**j + 5*l = 0?
-2
Let k(s) be the first derivative of -2*s**3/3 - 2*s**2 - 2*s + 2. Let p(o) = -8*o - 2*o**2 - 4 + 0*o**2 - 2*o**2. Let v(u) = 5*k(u) - 2*p(u). Factor v(b).
-2*(b + 1)**2
Suppose -7 = -3*m + 8. Suppose -5*r + 38 = -2*w, m*r - 10 = -6*w + w. Factor 6*b**5 - 10*b**4 + 2*b**2 + r*b**3 - 5*b**3 - 2*b**3 + 3*b**3.
2*b**2*(b - 1)**2*(3*b + 1)
Let t = 16 + -6. Suppose 5*p - 25 = 5*g, -3*p - t = -4*g - 5*p. Suppose g*q + 0*q + q**3 = 0. What is q?
0
Suppose -20*w = -19*w - 2. What is s in -2/9*s + 8/9*s**w - 4/9 + 2/3*s**3 = 0?
-1, 2/3
Factor -2*z**3 - 6*z**2 + 4*z**3 + 2*z**2 + 0*z**3.
2*z**2*(z - 2)
Let o be (8/6)/((-6)/(-18)). Let a be 0 - ((o - 3) + -5). Determine d so that 40/9*d + 2/9*d**4 + 16/9 + 14/9*d**3 + a*d**2 = 0.
-2, -1
Let m be (-93)/540 + 5/25. Let a(p) be the second derivative of -1/6*p**2 + 0*p**3 - 2*p + 0 + m*p**4. Solve a(z) = 0.
-1, 1
Let a = -1 + 4. Suppose 4 = 4*x - 4. Find t, given that -2*t - 2*t**2 + 0*t**4 - x*t**a + 2*t**4 + 4*t**3 = 0.
-1, 0, 1
Let o(n) be the third derivative of n**2 + 1/48*n**4 + 0*n**3 + 0 + 0*n - 1/48*n**5. Find b such that o(b) = 0.
0, 2/5
Let a = -3 + 6. What is o in -2*o**3 + 4*o**4 - a*o**4 - 2*o**4 = 0?
-2, 0
Let n(d) be the third derivative of -d**7/2520 - d**6/1080 + d**5/360 + d**4/72 + d**3/2 - 3*d**2. Let m(f) be the first derivative of n(f). Solve m(k) = 0.
-1, 1
Let u be -9 + -1 - (-2 + 0). Let o = 11 + u. Solve 54*d**4 - d + 0*d - 81*d**5 - 12*d**2 + 27*d**o - 3*d = 0 for d.
-1/3, 0, 2/3
Let i = 43382/1925 - 566/25. Let y = i + 1033/308. Solve y*m**3 - 1/4*m + 9/4*m**2 + 5/4*m**4 - 1/2 = 0.
-1, 2/5
Factor -3/7*t**3 + 12/7*t**2 + 6/7 - 15/7*t.
-3*(t - 2)*(t - 1)**2/7
Let x(v) = -v**3 - 9*v**2 - v - 4. Let k be x(-9). Suppose -21 = -k*t + 4*s + 1, 3*t - 2*s - 12 = 0. Factor -2*j**t - 6*j**3 - 2*j**4 + 8*j**3 - 2*j + 4*j**2.
-2*j*(j - 1)**2*(j + 1)
Let l(i) be the first derivative of -2*i**5/75 + 3*i**4/10 - 6*i**3/5 + 9*i**2/5 + 31. Factor l(p).
-2*p*(p - 3)**3/15
Let n = -28 - -28. Let o(j) be the first derivative of n*j + 1/2*j**2 - 1 + 1/6*j**3. Factor o(b).
b*(b + 2)/2
Factor 26 + 50*m - 20 + 32*m**3 + 91*m**2 + 21*m**2.
2*(m + 3)*(4*m + 1)**2
Let b(u) be the first derivative of u**4/18 - 2*u**3/9 + 2*u**2/9 - 3. Suppose b(i) = 0. What is i?
0, 1, 2
Let h(x) be the third derivative of x**7/105 + x**6/30 + x**5/30 - 25*x**2. Factor h(z).
2*z**2*(z + 1)**2
Let o be -1*3*25/(-15). Let a(c) be the third derivative of 0 + 0*c**3 + 1/180*c**o + 0*c**4 - 1/252*c**8 + c**2 + 0*c - 1/90*c**7 - 1/180*c**6. Factor a(p).
-p**2*(p + 1)**2*(4*p - 1)/3
Suppose 2*r = -5*w - 6 + 7, -4*r - 3*w + 9 = 0. Find f such that -2/7*f**r + 2/7 + 2/7*f - 2/7*f**2 = 0.
-1, 1
Let t(n) = -n + 2. Let p be t(-1). Let 0*y**2 - 3 + 9/2*y - 3/2*y**p = 0. Calculate y.
-2, 1
Let z = -2509/3 - -840. Suppose -z*x**2 + 2/3*x + 0 = 0. Calculate x.
0, 2/11
Let z(p) = 12*p**4 - 30*p**2 - 45*p - 7. Let v(c) = -12*c**4 - c**3 + 31*c**2 + 44*c + 8. Let h(d) = -5*v(d) - 4*z(d). Solve h(k) = 0.
-1, -3/4, -2/3, 2
Let l(r) be the third derivative of -r**6/160 - r**5/40 - r**4/32 + 8*r**2. Factor l(s).
-3*s*(s + 1)**2/4
Let m(z) be the first derivative of 3*z + 1/42*z**4 - 2 + 1/21*z**3 + 0*z**2. Let f(y) be the first derivative of m(y). Factor f(o).
2*o*(o + 1)/7
Suppose 15/8*r + 3/4 - 9/8*r**2 = 0. What is r?
-1/3, 2
Suppose -m + x = 0, -3*m + 11 + 1 = x. Suppose 4*h**2 + 2*h + 2*h**2 + 2*h**4 + 5*h**3 + 0*h**2 + h**m = 0. What is h?
-1, 0
Suppose 3*m - 8 = -2. Suppose m*j + 3*j = 0. Factor 0 + 2/5*i + j*i**2 - 8/5*i**3.
-2*i*(2*i - 1)*(2*i + 1)/5
Let j(s) = 4*s**4 - 5*s**2 - 8*s + 7. Suppose 25 = -3*k + t, k + k = -2*t - 6. Let x(a) = 2*a**4 - 2*a**2 - 4*a + 4. Let n(y) = k*x(y) + 4*j(y). Factor n(v).
2*v*(v - 2)*(v + 1)**2
Let q(j) = j**2 - 11*j. Let v be q(11). Let k(z) be the first derivative of v*z + 42/5*z**5 + 28/5*z**3 - 207/20*z**4 + 3 - 5/2*z**6 - 6/5*z**2. Factor k(h).
-3*h*(h - 1)**2*(5*h - 2)**2/5
Factor -2/7 + 0*d + 0*d**3 + 4/7*d**2 - 2/7*d**4.
-2*(d - 1)**2*(d + 1)**2/7
Let j be 12/66 - 62/(-22). Suppose j*k - 5*k + 4 = 0. Factor 5/6*b**k + 1/3 + 7/6*b.
(b + 1)*(5*b + 2)/6
Let d(g) = g**3 - 2*g**2 + 4*g. Suppose 9 = -4*m - 43. Let v = -5 - m. Let j(h) = 3*h**3 - 6*h**2 + 11*h. Let q(b) = v*d(b) - 3*j(b). Factor q(p).
-p*(p - 1)**2
Solve -60*r**2 + 15*r**5 + 10*r + 225/2*r**3 - 145/2*r**4 + 0 = 0.
0, 1/3, 1/2, 2
Let x(l) be the first derivative of l**3/3 - 5*l**2 + 11*l + 2. Let f be x(9). Solve -f*s**2 + 3*s**2 + 6*s**3 + 5*s**2 + 2*s**4 + 2*s = 0.
-1, 0
Let t(i) = -i**3 - 25*i**2 + 33*i - 17. Let z(p) = 12*p**2 - 16*p + 8. Let x(g) = 2*t(g) + 5*z(g). Factor x(f).
-2*(f - 3)*(f - 1)**2
Let g(j) be the second derivative of j**6/180 + j**5/20 + j**4/6 - j**3/3 + 6*j. Let w(m) be the second derivative of g(m). Factor w(f).
2*(f + 1)*(f + 2)
Let s(b) be the second derivative of 4*b**7/105 + 13*b**6/60 + 11*b**5/30 + b**4/6 + b**2/2 - 2*b. Let n(g) be the first derivative of s(g). Factor n(c).
2*c*(c + 1)*(c + 2)*(4*c + 1)
Let g(d) = -12*d + 38. Let o be g(3). Determine t, given that 0*t**o + 3/2*t - 3/2*t**3 + 0 = 0.
-1, 0, 1
Let c(m) be the third derivative of -5*m**8/336 - m**7/42 + m**6/24 + m**5/12 + 2*m**2 + 15*m. Factor c(t).
-5*t**2*(t - 1)*(t + 1)**2
Let q(b) be the second derivative of 0 + 0*b**6 + 1/21*b**3 + 1/147*b**7 + 0*b**2 + 0*b**4 - 3*b - 1/35*b**5. Let q(o) = 0. Calculate o.
-1, 0, 1
Let y(u) be the third derivative of 4*u**2 + 1/84*u**4 + 1/105*u**5 + 0*u**3 - 2/735*u**7 + 0 - 1/1176*u**8 + 0*u**6 + 0*u. Factor y(b).
-2*b*(b - 1)*(b + 1)**3/7
Suppose -3*g + 5*v = -5 - 19, 2*g + v = 3. Factor 0 - 2/17*p**4 - 6/17*p**2 + 2/17*p + 6/17*p**g.
-2*p*(p - 1)**3/17
Determine f, given that -2/15*f**3 + 2/5*f - 4/15 + 0*f**2 = 0.
-2, 1
Let d = 283/4 - 2539/36. What is m in 2/9*m**2 - 2/9*m - 2/9 + d*m**3 = 0?
-1, 1
Suppose i - 3*i - 5*t - 36 = 0, 28 = -5*i + 3*t. Let x(b) = -b - 8. Let u be x(i). Solve 1/5*z**2 - 2/5*z**3 + 1/5*z**4 + u*z + 0 = 0 for z.
0, 1
Suppose 0 = -3*g, 1 = 3*x - 4*g - 32. Factor x*a**3 + a**2 + 18*a**3 - 30*a**3 - a**4 + a.
-a*(a - 1)*(a + 1)**2
Let q(o) be the second derivative of o**4/9 - 4*o**3/9 - 4*o. Let q(z) = 0. What is z?
0, 2
Factor -y + 4*y + 26*y**2 - 27*