ive of m**7/5040 + m**6/480 + m**5/120 - 7*m**4/4 - 20*m. Let h(b) be the third derivative of d(b). Factor h(w).
(w + 1)*(w + 2)/2
Let b(a) be the third derivative of -a**5/20 - 3*a**4/8 - 4*a**2 - 7*a. Factor b(k).
-3*k*(k + 3)
Find q, given that -8/13*q**2 + 14/13*q - 2/13*q**3 + 20/13 = 0.
-5, -1, 2
Let x(r) be the second derivative of 3*r**5/28 + 3*r**4/7 - 118*r**3/7 - 144*r**2/7 - r + 13. Find w, given that x(w) = 0.
-8, -2/5, 6
Let y = 209 - 211. Let u be 28/(-140)*y*1/2. Determine r so that 0*r - u*r**3 + 1/5*r**5 + 0 + 1/5*r**4 - 1/5*r**2 = 0.
-1, 0, 1
Let b be 70/22 + 10/(-55). What is z in 0*z**2 - 140*z**5 + 143*z**5 + 4*z**2 - b*z**4 - z**2 - 3*z**3 = 0?
-1, 0, 1
Let m(g) = -51*g**3 - 39*g**2 - 21. Let z = -7 + 7. Let f(h) = 5 + z + 4*h**2 + 5*h**3 - 3. Let v(d) = 21*f(d) + 2*m(d). Factor v(p).
3*p**2*(p + 2)
Suppose -15 = -5*f + 4*k, 0*f + 6 = 2*f + 3*k. Factor 4*d**3 - 2*d**2 - 7*d**2 - 16*d - f*d**2.
4*d*(d - 4)*(d + 1)
Let g(k) = 12*k**3 - 21*k**2 + 8*k + 5. Let i be (-10)/(-15) - 58/6. Let v(f) = 48*f**3 - 84*f**2 + 33*f + 21. Let w(u) = i*g(u) + 2*v(u). Factor w(q).
-3*(q - 1)**2*(4*q + 1)
Suppose 43267*z = 43245*z + 22. Solve 4/3*m + z + 1/3*m**2 = 0 for m.
-3, -1
Let p = -2675 - -2678. Factor 1/5*q + 0*q**2 + 0 - 1/5*q**p.
-q*(q - 1)*(q + 1)/5
Suppose -12*l = -13*l + 3. Let -2 - 4*w**2 - w**2 + 5*w**l + 2 = 0. What is w?
0, 1
Let l = -9 + 9. Suppose -5*b - 4*s + 18 = 0, l = -b - 3*b - 5*s + 18. Factor 1 + 6*y**2 + 0*y**3 - 3*y + 0*y**2 - y**3 - 3*y**b.
-(y - 1)**3
Suppose 13*t + 32 - 32 = 0. Let p(b) be the second derivative of t - 7/39*b**3 - 3/13*b**2 - 5/78*b**4 - 1/130*b**5 + 3*b. Factor p(l).
-2*(l + 1)**2*(l + 3)/13
Let o(l) be the third derivative of -l**5/210 + 55*l**4/42 - 3025*l**3/21 - 98*l**2. Factor o(t).
-2*(t - 55)**2/7
Let i(u) = 2*u**3 - u + 2*u**2 + 0*u**2 + 9*u. Suppose y + 6 + 1 = 0. Let z(l) = -3*l**3 - 3*l**2 - 15*l. Let o(b) = y*i(b) - 4*z(b). Factor o(f).
-2*f*(f - 1)*(f + 2)
Let c be (53/1855)/(16/14). Let p(x) be the third derivative of 0*x + 0*x**4 + c*x**6 - 1/210*x**7 + 0*x**3 + 0 + 11*x**2 - 1/30*x**5. Factor p(j).
-j**2*(j - 2)*(j - 1)
Let t(j) = 7*j**2 - 7. Let w = 1 - -19. Let m(y) = -48*y**2 + 48. Let l(o) = w*t(o) + 3*m(o). Find b such that l(b) = 0.
-1, 1
Suppose 2*u - 4*t = -5*t - 4, -u - 2*t = 8. Suppose 4*j + u*j - 12 = 0. Factor 3 + n**2 + 7*n**j + 5*n**3 - 4*n**2 - 12*n.
3*(n - 1)*(n + 1)*(4*n - 1)
Factor -58/13*s + 56/13*s**2 + 0 + 2/13*s**3.
2*s*(s - 1)*(s + 29)/13
Suppose 4*x = 4*g - 4, 0*g + 2*g + 4 = 5*x. Let j = 13/9 - -29/36. Factor m**5 - 1/4*m**2 - j*m**4 + 3/2*m**g + 0 + 0*m.
m**2*(m - 1)**2*(4*m - 1)/4
Let z = 28 - -7. Suppose -5*a + z = -0*a. Factor -x - x**2 + a*x**3 + 3 - 6*x**3 - 2.
(x - 1)**2*(x + 1)
Let q be 3 - (4 - 2)*(-13)/(-2). Let j be (-4 - q/2)/(3/6). Determine o, given that -4/5 - 4/5*o**j - 8/5*o = 0.
-1
Let h(l) = 27*l**2 + 71*l + 2. Let m(g) = -9*g**2 - 22*g - 1. Let k(c) = -2*h(c) - 7*m(c). Factor k(y).
3*(y + 1)*(3*y + 1)
Let b = -2 + 5. Suppose 12*i - b = 11*i. Factor -7*d**i - 8*d + 3 - 6*d**2 + 1 - 8*d**2 - 5*d**2.
-(d + 1)*(d + 2)*(7*d - 2)
Let q(k) = -24*k**3 - 105*k**2 + 162*k - 33. Let d(g) = -g**3 - 2*g**2 + 2*g + 1. Let z(j) = 3*d(j) - q(j). Factor z(l).
3*(l - 1)*(l + 6)*(7*l - 2)
Determine w, given that -4*w - 4/9*w**2 - 32/9 = 0.
-8, -1
Let q(n) be the third derivative of -3*n**7/280 - n**6/12 - n**5/40 + 3*n**4/4 - n**3/3 + 5*n**2. Let m(d) be the first derivative of q(d). Factor m(t).
-3*(t + 1)*(t + 3)*(3*t - 2)
Let x(n) = n**5 - 13*n**4 + 22*n**3 - 19*n**2 + 5*n + 1. Let m(h) = h**5 + h**4 + 2*h**3 - h**2 + h - 1. Let y(i) = m(i) + x(i). Factor y(o).
2*o*(o - 3)*(o - 1)**3
Let p(v) = -v**2 + 11*v + 13. Let m be p(10). Suppose 6*c - m + 11 = 0. Find x such that 1/3 - 1/2*x + 1/6*x**c = 0.
1, 2
Let c(z) = -10*z**2 - 5. Let a(h) = h**3 + 10*h**2 + 6. Let f(w) = -5*a(w) - 6*c(w). Factor f(p).
-5*p**2*(p - 2)
Let b(l) be the third derivative of -5/2*l**4 + 2*l**2 + 0 - 30*l**3 - 1/12*l**5 + 0*l. Factor b(g).
-5*(g + 6)**2
Let a(b) be the second derivative of 5*b**4/12 + 140*b**3/3 + 1960*b**2 - 34*b + 7. Suppose a(n) = 0. Calculate n.
-28
Let u(q) be the third derivative of q**8/504 + q**7/45 + q**6/20 - 7*q**5/90 - 5*q**4/18 + 76*q**2 + 1. Solve u(t) = 0.
-5, -2, -1, 0, 1
Suppose -2*j + 55 = 49. Let u(r) be the first derivative of -4/3*r**3 + r**4 - 2 + 6/5*r**5 - 2*r + 1/3*r**6 - j*r**2. Let u(l) = 0. Calculate l.
-1, 1
Let d(t) be the second derivative of 0*t**2 - 7/6*t**3 + 1/15*t**5 + 2*t + 0 + 1/3*t**4 + 1/180*t**6. Let f(v) be the second derivative of d(v). Factor f(y).
2*(y + 2)**2
Factor -51/5*l**2 - 1/5*l**3 - 867/5*l - 4913/5.
-(l + 17)**3/5
Let q be 1 + -3 + 10 + -6. Suppose -5*i + 31 = 2*f, q = -4*f + 2*i + 4. Find o such that -56*o**2 - 15*o**3 + 8 - 11*o**3 + 6*o**f - 28*o = 0.
-2, -1, 1/5
Let p(g) be the third derivative of g**7/350 - 17*g**6/200 + 93*g**5/100 - 207*g**4/40 + 81*g**3/5 + 57*g**2 + g. What is z in p(z) = 0?
2, 3, 9
Let r = -57 - -57. Let h(y) be the second derivative of 1/12*y**4 - 2*y + r*y**2 + 1/3*y**3 + 0. Determine z so that h(z) = 0.
-2, 0
Let g be ((-7596)/396 + 19)/((-2)/22*4). Find h, given that -g*h**2 + 2/3*h**3 + 0*h - 1/6*h**4 + 0 = 0.
0, 1, 3
Let x(u) be the third derivative of -u**8/13440 - u**7/1680 + u**4/2 + 26*u**2. Let r(j) be the second derivative of x(j). Factor r(n).
-n**2*(n + 3)/2
Factor 3*b - 3/4*b**2 + 0.
-3*b*(b - 4)/4
Let y(k) be the second derivative of -k**6/50 + k**5/50 + 4*k**4/15 + 7*k**3/15 + 3*k**2/10 - 18*k. Let y(h) = 0. Calculate h.
-1, -1/3, 3
Suppose 4*k - 30 = k + 3*n, 1 = -2*k - n. Solve 0*o**k + 2/5*o**4 + 0*o - 2/5*o**2 + 0 = 0 for o.
-1, 0, 1
Let z = 26 - 166. Let w = 142 + z. Suppose -1 - 1/3*p**w - 4/3*p = 0. What is p?
-3, -1
Let a(i) be the first derivative of -i**4/12 - 26*i**3/9 + 58*i**2/3 - 40*i - 871. What is y in a(y) = 0?
-30, 2
Let o(z) be the second derivative of 1/90*z**5 + 0 + 0*z**2 + 0*z**3 + 5/54*z**4 - 44*z. Suppose o(h) = 0. What is h?
-5, 0
Let k(d) be the first derivative of d**4/22 + 2*d**3/33 - 9*d**2/11 - 18*d/11 + 9. What is z in k(z) = 0?
-3, -1, 3
Let v(k) be the first derivative of -k**5/300 + k**4/30 - 2*k**3/15 + 8*k**2 - 7. Let z(w) be the second derivative of v(w). Factor z(t).
-(t - 2)**2/5
Suppose 4*q = -5*z - 97, 78 = 2*q - 5*q - 2*z. Let g be 7/q - 26/(-8). Factor -4*a**3 + 7*a**g - a**3 + 16*a**2 + 16*a + 2*a**3.
4*a*(a + 2)**2
Let b = 65881/120 - 549. Let s(t) be the third derivative of 0 + 0*t + 4/3*t**3 + b*t**5 + 4*t**2 - 1/6*t**4. Solve s(k) = 0.
4
Let n = 10113 - 10113. Solve 4/9*f**4 - 2/9*f**5 + n*f - 4/9*f**2 + 0 + 2/9*f**3 = 0 for f.
-1, 0, 1, 2
Suppose 300*t**5 - 5174 + 415*t**4 - 283*t + 5134 - 1650*t**2 - 1075*t**3 - 217*t = 0. Calculate t.
-2, -1, -1/4, -2/15, 2
Suppose -21*a - 40 = -17*a. Let q be (a/(-2) - 2) + 1. What is x in 0 - 5/3*x**q - 7/3*x**3 + 0*x - 2/3*x**2 = 0?
-1, -2/5, 0
Let n(v) be the third derivative of -2*v**7/21 - 13*v**6/15 - 7*v**5/3 - v**4 + 24*v**2 + 11*v. Suppose n(c) = 0. Calculate c.
-3, -2, -1/5, 0
Suppose 0 = -89*j + 41*j + 15*j + 66. Factor -4/9*t**j + 4/3*t + 0.
-4*t*(t - 3)/9
Let i(p) be the second derivative of p**4/108 - 5*p**3/18 + 2*p**2 - 2*p - 86. Factor i(x).
(x - 12)*(x - 3)/9
Factor 369*j**2 - 739*j**2 - 80*j + 374*j**2.
4*j*(j - 20)
Suppose -4 - 44 = -12*k. Let o(n) be the third derivative of 0 + 0*n - 1/20*n**5 + 6*n**2 - 1/9*n**3 - 11/72*n**k. Factor o(w).
-(w + 1)*(9*w + 2)/3
Let h = 67 - 64. Let p be 2/8 + (-108)/(-16). Suppose -3*d**h - 9*d + 6 + 2*d**2 + 4 - 7 + p*d**2 = 0. Calculate d.
1
Let t(f) be the first derivative of -1/10*f**5 - 1/2*f**2 + 0*f**3 - 9 + 1/2*f + 1/4*f**4. Factor t(h).
-(h - 1)**3*(h + 1)/2
Let v(i) be the first derivative of i**3/4 - 9*i**2/8 - 27*i/2 + 121. Determine w, given that v(w) = 0.
-3, 6
Let j(a) = -a**2 - 5*a - 2. Let t be j(-3). Suppose -t*y + 1 + 1 = 3*x, -3*y - 3*x = 0. Solve -9*l + 3*l**3 - 2*l**2 - 6 + 0 + 2*l**y = 0 for l.
-1, 2
Let o(p) be the second derivative of 1/12*p**3 + 3*p + 1/24*p**4 + 0*p**2 + 0. Factor o(t).
t*(t + 1)/2
Let z(u) = -10*u**2 - 28*u + 274. Let h be z(4). Determine t, given that 0 - 3/4*t**h - 1/8*t**3 - 9/8*t = 0.
-3, 0
Let d(f) be the first derivative of 7*f**2 - f + 23 + 21*f**4 - 36/5*f**5 - 61/3