1. Let q(j) = 3*a(j) - 3*w(j). Solve q(b) = 0 for b.
-2, -1, 0, 1
Let v(p) be the third derivative of -p**7/3360 + p**6/480 + 3*p**5/160 - 3*p**4/8 - 14*p**2. Let i(s) be the second derivative of v(s). Factor i(c).
-3*(c - 3)*(c + 1)/4
Let g(k) be the first derivative of 5*k**7/42 - 2*k**6/3 + k**5 + 14*k - 18. Let o(f) be the first derivative of g(f). Factor o(d).
5*d**3*(d - 2)**2
Let a(m) = -10*m**2 + 4*m + 6. Suppose p - 2*p - 2*x = 1, 5*p = -4*x + 1. Let c(b) = -b**2 + b + 1. Let z(f) = p*a(f) - 6*c(f). Factor z(n).
-2*n*(2*n + 1)
Let k(r) = -122*r + 979. Let m be k(8). Determine f, given that -1/5 - f**m - 7/5*f - 11/5*f**2 = 0.
-1, -1/5
Let n(a) be the first derivative of a**4/18 - 2*a**3/9 - 2*a**2 + 172. Factor n(u).
2*u*(u - 6)*(u + 3)/9
Let w(i) be the first derivative of -8*i**6/3 - 216*i**5/5 - 745*i**4/4 - 303*i**3 - 164*i**2 - 36*i + 37. Let w(b) = 0. What is b?
-9, -2, -1/4
Let c = 38528 - 269632/7. Solve -36/7*h + 8/7 - 8*h**3 + c*h**2 - 4/7*h**5 + 24/7*h**4 = 0 for h.
1, 2
Let j(d) be the first derivative of -4*d**3/21 + 46*d**2/7 - 88*d/7 + 47. Suppose j(n) = 0. What is n?
1, 22
Let x(g) = -g. Let z(v) be the first derivative of -7/3*v**3 + 7*v**2 - 4*v + 1. Let r(c) = 6*x(c) - 3*z(c). Suppose r(u) = 0. Calculate u.
2/7, 2
Let h(x) be the third derivative of -x**7/420 - 11*x**6/120 - 31*x**5/40 - 35*x**4/12 - 17*x**3/3 - 11*x**2 + 1. Solve h(n) = 0.
-17, -2, -1
Let b = 401/294 - -20/147. Suppose -b - 2*h - 1/2*h**2 = 0. Calculate h.
-3, -1
Let j = 1936 - 1935. Solve 3/2*u - 1/2*u**2 - j = 0.
1, 2
Suppose 5*p + 1 = 26. Solve -2*j**p - 32*j**4 - 20*j**2 - 6*j + 35*j**4 - 24*j**3 - 15*j**4 = 0 for j.
-3, -1, 0
Determine t, given that 1/3*t**3 + 7*t + 6 + 8/3*t**2 = 0.
-3, -2
Let a(v) = 41*v**4 + 39*v**3 + 3*v**2 + 5*v - 5. Let w(l) = -102*l**4 - 98*l**3 - 8*l**2 - 12*l + 12. Let d(q) = 12*a(q) + 5*w(q). Factor d(n).
-2*n**2*(n + 1)*(9*n + 2)
Let o(m) be the second derivative of m**4/4 - 37*m**3/2 + 54*m**2 - m + 124. Find q such that o(q) = 0.
1, 36
Suppose 7*l - l - 24 = 0. Factor -6*w**2 + 4 + 5*w**l - 10*w**3 - 4 + 11*w**2.
5*w**2*(w - 1)**2
Let v(h) be the first derivative of -16*h**5/15 + 7*h**4/3 + 88*h**3/9 - 38*h**2/3 - 8*h - 104. Solve v(u) = 0 for u.
-2, -1/4, 1, 3
Factor -59/4*k**3 - 1/4*k**4 + 0 + 225*k - 210*k**2.
-k*(k - 1)*(k + 30)**2/4
Let c(b) be the third derivative of b**8/336 + b**7/30 + b**6/12 + 15*b**2 + 2*b. Factor c(q).
q**3*(q + 2)*(q + 5)
Let n(q) be the first derivative of q**5/15 - 11*q**4/3 + 242*q**3/3 - q**2/2 - 7*q - 34. Let c(j) be the second derivative of n(j). Solve c(p) = 0 for p.
11
Let s(z) = 5*z**4 + 32*z**3 - 8*z**2 - 29*z + 3. Let n(o) = 5*o**4 + 33*o**3 - 7*o**2 - 31*o + 2. Let w(c) = 3*n(c) - 2*s(c). Factor w(a).
5*a*(a - 1)*(a + 1)*(a + 7)
Let i(a) be the second derivative of -a**9/22680 - a**8/5040 - a**7/3780 + 5*a**4/6 - 13*a. Let y(m) be the third derivative of i(m). Factor y(l).
-2*l**2*(l + 1)**2/3
Suppose s - 12 + 4 = 0. Let d(z) = 4*z**3 - 12*z**2 + s + 21*z - 11 - 10. Let w(q) = -q**3 + 3*q**2 - 5*q + 3. Let k(x) = -4*d(x) - 18*w(x). Factor k(l).
2*(l - 1)**3
Suppose -o + 2*u = o + 6, -o = u - 5. Let p(m) be the first derivative of 3*m**4 - 7 + m**5 + 2 + o - m**3 + m**2 + 4*m**3. Factor p(z).
z*(z + 1)**2*(5*z + 2)
Let d(i) be the second derivative of -7/60*i**4 - 19/30*i**3 + 0 + 14*i + 3/5*i**2. Determine l, given that d(l) = 0.
-3, 2/7
Let a(b) = -3*b**2 - 67*b - 269. Let o be a(-17). Factor 3/4*u**2 - 3/2 - 9/4*u + 9/4*u**o + 3/4*u**4.
3*(u - 1)*(u + 1)**2*(u + 2)/4
Let u(h) = h**2 - 8*h - 6. Let z(a) = a**3 - 4*a**2 + 2*a + 1. Let s be z(4). Let v be u(s). Factor -3*m + m + 2*m**4 - 2*m + 4*m**v - 2*m**2 + 0*m**4.
2*m*(m - 1)*(m + 1)*(m + 2)
Let a(w) be the first derivative of -w**4/12 + 17*w**3/9 - 185. Suppose a(b) = 0. What is b?
0, 17
Let v(m) be the second derivative of 0 - 1/48*m**4 - 1/40*m**5 + 0*m**2 + 0*m**3 + 41*m. Factor v(g).
-g**2*(2*g + 1)/4
Suppose -5/2*x + 1/2 + 5*x**2 - 5*x**3 - 1/2*x**5 + 5/2*x**4 = 0. Calculate x.
1
Factor -135/4*w - 3/8*w**2 - 6075/8.
-3*(w + 45)**2/8
Let k(j) be the first derivative of 8*j**5/5 - 33*j**4/2 - 53*j**3/3 - 9*j**2/2 - 236. Solve k(u) = 0 for u.
-1/2, -1/4, 0, 9
Let g be (2 - 3)/(6/(-174)). Suppose 3*z + 2*m - 38 = -z, -3*z - m = -g. Let 16*j + 0*j**3 - z*j**2 + 0*j**3 + 4*j**3 - 6*j**2 = 0. Calculate j.
0, 2
Let y(t) be the second derivative of -t**5/40 + 21*t**4/8 - 341*t**3/4 + 961*t**2/4 + 66*t + 4. Let y(z) = 0. Calculate z.
1, 31
Let d(o) = -3*o**2 - 246*o + 224. Let y(h) = 12*h**2 + 990*h - 897. Let u(i) = -21*d(i) - 5*y(i). Determine q so that u(q) = 0.
-73, 1
Let h(x) be the first derivative of 3/20*x**5 + 1/4*x**4 + 0*x**2 + 0*x**3 - 5 + 3*x. Let a(m) be the first derivative of h(m). Determine z so that a(z) = 0.
-1, 0
Let -10/3*k**2 + 2/3*k**3 - 8/3 + 16/3*k = 0. What is k?
1, 2
Suppose 2296*w**4 - 1800 - 98*w**5 + 1028*w**3 - 11158*w**3 - 904 - 39484*w**2 - 19864*w = 0. Calculate w.
-2, -2/7, 13
Let z(f) be the first derivative of -f**4/42 - f**3/7 - 2*f**2/7 - 27*f + 31. Let x(n) be the first derivative of z(n). Factor x(c).
-2*(c + 1)*(c + 2)/7
Let a(i) be the second derivative of -i**4/6 - 2*i**3 - 5*i**2 + 76*i. Factor a(d).
-2*(d + 1)*(d + 5)
Let u(x) = 2*x**4 + 50*x**3 - 571*x**2 - 1151*x + 40891. Let t(y) = -y**4 - 22*y**3 + 285*y**2 + 575*y - 20446. Let v(r) = -7*t(r) - 3*u(r). Factor v(j).
(j - 11)**2*(j + 13)**2
Suppose 2*s = s - 5*c + 23, c = 2*s - 35. Let k = 25 - s. Factor k*x - 7*x + 2*x**3 - 2*x**5.
-2*x**3*(x - 1)*(x + 1)
Let f(w) = w**5 - w**4 - 2*w**3 + w**2 - w + 1. Let c(t) = 7*t**5 + 9*t**4 - 13*t**3 - 9*t**2 - 6*t + 6. Let o(n) = -c(n) + 6*f(n). Factor o(i).
-i**2*(i - 1)*(i + 1)*(i + 15)
Let v(h) be the second derivative of h**7/21 - 3*h**5/10 - h**4/3 + 91*h. What is d in v(d) = 0?
-1, 0, 2
Let z = -41 + 34. Let q(b) = 11*b**2 - b - 12. Let o(a) = -10*a**2 + 2*a + 12. Let x(i) = z*o(i) - 6*q(i). Find n, given that x(n) = 0.
-1, 3
Let q(p) be the first derivative of -3*p**5/5 - 3*p**4/4 + 65*p**3 + 675*p**2/2 + 649. Factor q(n).
-3*n*(n - 9)*(n + 5)**2
Let t = -25 + 50. Factor -w**2 + t*w - 10*w - 16*w.
-w*(w + 1)
Let x = 1187 - 23731/20. Let c(j) be the second derivative of 3/2*j**2 - x*j**5 - 1/4*j**4 + 3/2*j**3 - 4*j + 0. Factor c(i).
-3*(i - 1)*(i + 1)*(3*i + 1)
Find x such that 55*x**2 - 13 + 7*x**3 - 47*x**3 - 15*x**4 + 140*x + 73 = 0.
-3, -1, -2/3, 2
Let x = 1 - 1. Factor -13*y**2 + x*y + 0*y - 4*y**3 - 11*y**2.
-4*y**2*(y + 6)
Suppose -5*y - 27*h + 25*h = 8, -3*y + 5*h = -20. Let f(p) = -3*p. Let o be f(-1). Factor 2/5*t**o - 4/5*t**2 + y + 2/5*t.
2*t*(t - 1)**2/5
Let l(a) be the third derivative of 0*a + a**2 - 1/20*a**5 + 13/4*a**4 - 169/2*a**3 + 0. Determine f, given that l(f) = 0.
13
Factor 0 - 8/13*j**3 - 30/13*j**2 + 8/13*j.
-2*j*(j + 4)*(4*j - 1)/13
Let k = 42160/3 - 14053. Find w such that -k + 4/3*w**3 - 4/3*w + 1/3*w**2 = 0.
-1, -1/4, 1
Let h be 4/(-14) + (1620/(-63))/(-6). Let j(r) be the second derivative of -r**2 + 0 - 1/20*r**5 + 2*r + 1/2*r**3 + 0*r**h. Let j(c) = 0. Calculate c.
-2, 1
Let u(o) = o**2 + o + 1. Let c be u(0). Let k be c/2 - (-15)/6. Factor r**3 + 14*r**5 - 4*r**4 - k*r**3 - 8*r**5.
2*r**3*(r - 1)*(3*r + 1)
Let z(y) be the first derivative of y**3 + 1/4*y**4 + 0*y**2 + 0*y + 17. Solve z(u) = 0 for u.
-3, 0
Let b(u) = -2*u**4 + 2*u**3. Let p(y) = -5*y**4 + 5*y**3. Let c(j) = 7*b(j) - 2*p(j). Determine h so that c(h) = 0.
0, 1
Let j(p) be the second derivative of -2*p**7/21 - 2*p**6 - 62*p**5/5 - 34*p**4/3 + 42*p**3 + 98*p**2 - 188*p. Determine i, given that j(i) = 0.
-7, -1, 1
Let f be (-9)/(1/(-4)*6). Suppose 3*b = 9, -n = 4*n - 3*b - f. Find k such that -2*k**n + 12*k**2 - 6*k**2 - 6 - 2 = 0.
-1, 2
Let b(q) = -7*q**5 + 22*q**4 - 4*q**3 - 12*q**2 + q. Let c(k) = 2*k**5 - 7*k**4 + k**3 + 4*k**2. Let j(g) = -3*b(g) - 10*c(g). Determine f, given that j(f) = 0.
-3, -1, 0, 1
Let r(d) be the third derivative of -d**7/315 + d**6/144 + d**5/24 - 5*d**4/36 + d**3/9 - 32*d**2. Find b, given that r(b) = 0.
-2, 1/4, 1, 2
Suppose -612*w + 613*w = 0. Factor 0 + w*o + 1/3*o**2 - 1/3*o**4 + 1/3*o**3 - 1/3*o**5.
-o**2*(o - 1)*(o + 1)**2/3
Suppose -9*h = 2*h - 44. Let l(f) be the third derivative of -4*f**2 - 1/360*f**6 - 1/9*f**3 + 0*f + 0 + 1/90*f**5 + 1/72*