e the third derivative of -g**7/1050 + g**6/300 - g**5/300 - 5*g**2. Let a(f) = 0. Calculate f.
0, 1
Let q(p) be the first derivative of 1/15*p**3 - 2 - 1/5*p**2 + 1/30*p**4 - 2*p - 1/50*p**5. Let m(o) be the first derivative of q(o). Factor m(s).
-2*(s - 1)**2*(s + 1)/5
Let d(m) = -m**4 - 33*m**3 + 19*m**2 - 5*m + 5. Let i(x) = -32*x**3 + 20*x**2 - 4*x + 4. Let f(r) = 4*d(r) - 5*i(r). Factor f(v).
-4*v**2*(v - 6)*(v - 1)
Let i(w) = -w**2 + 30*w + 27. Let p be i(30). Factor -4/3*g - p*g**3 + 12*g**2 + 0.
-g*(9*g - 2)**2/3
Let i(x) be the second derivative of x**7/168 - x**6/24 + 9*x**5/80 - 7*x**4/48 + x**3/12 - 4*x. Find k, given that i(k) = 0.
0, 1, 2
Let f = 25 + -13. Suppose 2*d + d = f. Factor 0*i**3 + 3*i**2 + 1 - 3*i + 3*i**3 - d*i**3.
-(i - 1)**3
Let v(w) be the third derivative of w**5/3 - 35*w**4/24 + 5*w**3/2 - 12*w**2 + 2. Determine r so that v(r) = 0.
3/4, 1
Let u(q) = -q**4 + q**3 + q**2 + 1. Let z(x) = x**4 - 7*x**3 - 8*x**2 + 4*x + 6. Let i(s) = 2*u(s) + z(s). Factor i(c).
-(c - 1)*(c + 2)**3
Suppose 0*f + 0 + 2/7*f**3 + 2/7*f**2 = 0. Calculate f.
-1, 0
Let d be ((-477)/24)/((-3)/(-2)). Let c = 14 + d. Factor -c*p**3 - 1/4*p + 0 + 3/4*p**2 + 1/4*p**4.
p*(p - 1)**3/4
Solve -49*m**2 + 14*m**2 + 16*m**2 + 20*m + 23*m**2 = 0 for m.
-5, 0
Let z(h) be the third derivative of h**6/600 - h**4/40 + h**3/15 - h**2. Determine s so that z(s) = 0.
-2, 1
Let n(y) = y**2 + 4*y - 4. Let k be n(-5). Let p be -1*12/(-4) + k. Factor 0*c**3 + 0*c - 1/6*c**p + 0*c**2 + 0.
-c**4/6
Let y = 59/2 - 29. Find h, given that 1/2*h**3 - 1/2*h**2 + 0 - y*h + 1/2*h**4 = 0.
-1, 0, 1
Suppose -35 = -2*q - 5*m, 2*q - 6*m - 15 = -7*m. Let u(c) be the first derivative of 0*c + 0*c**2 + 0*c**3 + 2/9*c**6 + 2 + 1/12*c**4 + 1/3*c**q. Factor u(i).
i**3*(i + 1)*(4*i + 1)/3
Suppose 2*z - 12*s = -9*s, -2*s = 5*z. Determine j so that 1/3*j**3 + z - 1/3*j + 0*j**2 = 0.
-1, 0, 1
Let g(w) = 2*w**4 + 12*w**3 + 10*w**2 - 3*w - 3. Let t(n) = 15*n**4 + 85*n**3 + 70*n**2 - 20*n - 20. Let a(q) = 20*g(q) - 3*t(q). Factor a(m).
-5*m**2*(m + 1)*(m + 2)
Let r(n) = n**3 + 3. Let u be r(0). Suppose -4 = u*b - 10. Factor 5*y**b - 3*y**3 + 0*y**3 + 2*y + 0 + 0.
-y*(y - 2)*(3*y + 1)
Let t be ((-2)/(-5))/((-3)/(-15)). Let c(l) be the first derivative of 0*l - 2/3*l**3 + 1/4*l**4 + 0*l**2 - t. Factor c(u).
u**2*(u - 2)
Suppose 0 = -0*s - 4*s + 768. Let k = s + -1342/7. Factor -k*q**5 + 2/7*q + 0*q**3 - 4/7*q**2 + 4/7*q**4 + 0.
-2*q*(q - 1)**3*(q + 1)/7
Let m be (-3)/(-5 + 1 + 3). Let h(j) be the third derivative of -1/660*j**6 - 2*j**2 - 1/33*j**4 + 0 + 0*j - 2/165*j**5 + 0*j**m. Factor h(n).
-2*n*(n + 2)**2/11
Let o(m) be the third derivative of m**8/112 - m**7/70 - m**6/20 - 5*m**2. Solve o(n) = 0 for n.
-1, 0, 2
Let u(j) = -j**3 + 8*j**2. Let r be u(8). Let v be 4/(-2 + 16 - r). Find q such that -v*q**2 + 0 - 2/7*q = 0.
-1, 0
Let q = 14 + -1. Suppose 14*z**3 + 138*z + 101*z**2 + 11*z**2 + 36 - 3*z**5 - 50*z**3 - 36*z**4 + q*z**5 = 0. Calculate z.
-1, -2/5, 3
Let a be 12/8 - 1/(-2). Factor 4*x**a + 4 - 4*x**3 - 2*x**3 + 0*x**2 + 14*x.
-2*(x - 2)*(x + 1)*(3*x + 1)
Let a(d) be the second derivative of -d**7/42 + d**5/5 - d**4/6 - d**3/2 + d**2 + 29*d. Factor a(v).
-(v - 1)**3*(v + 1)*(v + 2)
Let q(o) = -o**3 - 10*o**2 + 10*o - 14. Let x be q(-11). Let d be ((-13)/(-4) + x)*2. Factor 1/2*h**3 - 1/4*h**2 - d*h + 1/4.
(h - 1)*(h + 1)*(2*h - 1)/4
Let l be 63/28 + (-2)/8. Factor 0*y**3 - 1/3*y**4 + 1/3*y**l + 0*y + 0.
-y**2*(y - 1)*(y + 1)/3
Let g(n) = -5*n**2 + n + 7. Let x(v) = -24*v**2 + 4*v + 34. Let u(y) = 14*g(y) - 3*x(y). Factor u(d).
2*(d - 1)*(d + 2)
Suppose -36*p + 41*p = 20. Suppose -2*x + 4 + 2 = 0. Suppose -j**2 + 3*j - 8*j**x - 8*j**p + 3*j**4 - j = 0. Calculate j.
-1, 0, 2/5
Let r = 80 + -56. Suppose 228*u + 122*u**3 + 169*u**3 - 74*u**3 + 594*u**2 + r + 26*u**3 = 0. Calculate u.
-2, -2/9
Let d(f) = -f - 5. Let q be d(-7). Let z(n) = 0*n**2 + 1 + 4*n + 1 - q*n**2. Let i(t) = 1. Let v(k) = 4*i(k) - z(k). Solve v(s) = 0 for s.
1
Let w(d) be the second derivative of -d**7/42 - d**6/10 + d**5/20 + 7*d**4/12 - 2*d**2 + 29*d. Find p such that w(p) = 0.
-2, -1, 1
Factor 4*f**3 + 8/5*f**2 - 12/5*f**4 + 0 + 0*f.
-4*f**2*(f - 2)*(3*f + 1)/5
Suppose 5*s + 0*s = -0*s. Let q(i) be the third derivative of 0*i**3 + 0*i**5 - 2*i**2 + 0*i - 1/1050*i**7 + 0*i**4 + s - 1/600*i**6. Factor q(h).
-h**3*(h + 1)/5
Determine m so that 2/7*m**2 - 2/7*m + 0 = 0.
0, 1
Let j(a) be the first derivative of 0*a**2 + 3*a + 2 + 1/36*a**4 + 0*a**3 - 1/60*a**5. Let u(g) be the first derivative of j(g). Factor u(p).
-p**2*(p - 1)/3
Let w(u) be the first derivative of 0*u + 0*u**2 - 2/3*u**3 - 1. Let w(h) = 0. What is h?
0
Factor -2/11*g**2 - 12/11*g - 18/11.
-2*(g + 3)**2/11
Let p(w) be the third derivative of 25*w**7/42 + 5*w**6/6 - 7*w**5/4 - 25*w**4/6 - 10*w**3/3 - 18*w**2. Factor p(o).
5*(o - 1)*(o + 1)*(5*o + 2)**2
Suppose -272 = 15*w - 16*w. Let z = 1366/5 - w. Let -z*v + 3/5*v**2 + 0 = 0. Calculate v.
0, 2
Let h be 3 + (-2884)/18*2. Let m = -317 - h. What is n in -2/9*n**2 - 2/9*n + m = 0?
-2, 1
Let x(k) be the third derivative of -k**5/150 + k**4/60 - 16*k**2. Factor x(y).
-2*y*(y - 1)/5
Let m(q) be the third derivative of -5*q**8/336 - q**7/42 + 5*q**6/24 - q**5/4 + 8*q**2. Solve m(k) = 0 for k.
-3, 0, 1
Let v(d) be the third derivative of 0 + 0*d - 1/36*d**4 - 1/180*d**5 - 2*d**2 - 1/18*d**3. Factor v(t).
-(t + 1)**2/3
Let j(o) be the second derivative of -1/11*o**2 + 1/33*o**3 + 1/66*o**4 - 1/110*o**5 - o + 0. Factor j(a).
-2*(a - 1)**2*(a + 1)/11
Let j(m) be the third derivative of 17/525*m**7 + 2/75*m**5 + 0*m - 4*m**2 + 0 + 1/168*m**8 + 0*m**3 + 4/75*m**6 + 0*m**4. Suppose j(l) = 0. What is l?
-2, -1, -2/5, 0
Suppose -x = -6*x - 325. Let n = x + 115. Factor -64/5 + 544/5*t + 464*t**3 - 260*t**4 + n*t**5 - 1696/5*t**2.
2*(t - 2)**2*(5*t - 2)**3/5
Let q(x) be the second derivative of -1/8*x**3 - 9/80*x**5 + 0*x**2 + 0 - 2*x + 1/40*x**6 + 3/16*x**4. Factor q(g).
3*g*(g - 1)**3/4
Suppose 0 = -5*y - 3*s + 12, -3*s + 3 = 3*y - 3. Let z be (-1)/(y + 8/(-2)). Factor 25/2*v**2 + z + 15/2*v.
(5*v + 1)*(5*v + 2)/2
Factor 13 + 98*v**2 + 24*v**3 + 3*v**4 - 32*v**2 + 72*v + 14.
3*(v + 1)**2*(v + 3)**2
Solve 24/13*h**3 + 28/13*h**2 + 4/13*h**4 - 2/13*h**5 + 10/13*h + 0 = 0.
-1, 0, 5
Factor 0 - 2/13*a**2 - 6/13*a**3 + 6/13*a + 2/13*a**4.
2*a*(a - 3)*(a - 1)*(a + 1)/13
Let j(u) be the third derivative of -u**6/540 - 4*u**5/135 - 13*u**4/108 - 2*u**3/9 + 33*u**2. Factor j(z).
-2*(z + 1)**2*(z + 6)/9
Let m = 401 - 399. Factor 3/2*t**m - 3/4*t**3 - 3/4*t + 0.
-3*t*(t - 1)**2/4
What is b in b**2 + 8*b + 1 - 10*b - 1 = 0?
0, 2
Let l = 221 - 218. Suppose -10/9*g**l - 2*g**2 + 14/9*g**4 + 4/9 + 10/9*g = 0. What is g?
-1, -2/7, 1
Let f(v) be the third derivative of -1/40*v**5 - 1/48*v**4 - 1/420*v**7 + 0*v**3 + 0*v - 1/80*v**6 - 2*v**2 + 0. Factor f(y).
-y*(y + 1)**3/2
Let j = -17 - -22. Suppose 5*m + 4*y - 26 = -0, j*m = -3*y + 22. Factor -6*o**m - 4/3 + 22/3*o.
-2*(o - 1)*(9*o - 2)/3
Let f be 9/(-18)*(-4)/10 + 0. Let b(k) be the second derivative of f*k**2 + 1/100*k**5 + 1/6*k**3 + 3*k + 0 + 1/15*k**4. Let b(d) = 0. What is d?
-2, -1
Let h(p) be the third derivative of -3/2*p**4 + 0 + 0*p + 9/16*p**8 + 3*p**2 - 54/35*p**7 + 33/10*p**5 - 4*p**3 - 1/40*p**6. Let h(v) = 0. Calculate v.
-2/3, -2/7, 2/3, 1
Let w(t) = -t**2 + 10*t + 234. Let f be w(21). Factor 1/4*h**f - 1/8*h + 0*h**4 + 0 - 1/8*h**5 + 0*h**2.
-h*(h - 1)**2*(h + 1)**2/8
Let g = -8 - -11. Factor 6*v**3 - 5*v**g + 3*v + 4*v**3 - 2*v**3 + 6*v**2.
3*v*(v + 1)**2
Let s(j) be the first derivative of 6*j**5/25 - 3*j**4/4 + 4*j**3/5 - 3*j**2/10 - 8. Find a, given that s(a) = 0.
0, 1/2, 1
Let t be (-1282)/(-18) - 6/2. Let s = t - 68. What is z in 0 - 4/9*z + s*z**2 = 0?
0, 2
Let d = 780167/98956 + 111/1903. Let i = -22/13 + d. Factor 1 + i*c**2 + 5*c.
(5*c + 2)**2/4
Determine m, given that 9/8*m + 0 - 3/8*m**2 = 0.
0, 3
Let a(h) = -2*h. Let i(k) = -2*k**2 + 2*k - 16*k + 3*k**2. Suppose 3*v + 13 - 3 = -f, 2 = 5*f + 2*v. Let x(q) = f*i(q) - 14*a(q). Factor x(m).
2*m**2
Let d = -6 + 9. Let 2*z**d + z**4 - 2*z**2 + 6*z**2 - 3*z**2 = 0. Calculate z.
-1, 0
Let j be (-15)/6*8/(-10). Let w be 3 + (1 - 3) + j. Factor -2/5*i**5 - 2/5*i + 2/5*i**4 - 4/5*i**2 + 4/5*i**w + 2/5.
-2*(i