or 152*d**2 + 7*d**5 - 16*d**4 - 5*d**5 + 10*d**2 - 512 - 2*d**2 - 128*d + 8*d**3.
2*(d - 4)**3*(d + 2)**2
Let w(p) be the first derivative of -p**6/240 + p**5/10 - p**4 + 7*p**3/3 + 8. Let v(l) be the third derivative of w(l). Factor v(b).
-3*(b - 4)**2/2
Suppose 24 + 2 = q + 3*u, 2*u + 78 = 3*q. Suppose 18 = 11*s - q. Determine w so that 2/3*w**3 + 0*w**2 - 1/3*w + 0*w**s + 0 - 1/3*w**5 = 0.
-1, 0, 1
Let w(r) be the first derivative of 49*r**5/150 - 7*r**4/15 + 4*r**3/15 + 33*r**2/2 - 6. Let o(v) be the second derivative of w(v). What is z in o(z) = 0?
2/7
Factor 129 - 5*q**2 + 22 + 35*q - 1.
-5*(q - 10)*(q + 3)
Find y such that 36 + 0*y**5 - 23*y**2 - 10*y**3 - y**5 + 24*y - 27*y**4 + 18*y**4 - 17*y**3 = 0.
-3, -2, 1
Let k(v) = -5*v**5 - 55*v**3 + 45*v**2. Let m(o) = 2*o**4 - o**2. Let t(z) = -k(z) - 15*m(z). Factor t(i).
5*i**2*(i - 3)*(i - 2)*(i - 1)
Let j(h) be the third derivative of h**9/3024 - h**7/504 + h**4/24 + 15*h**2. Let l(s) be the second derivative of j(s). What is z in l(z) = 0?
-1, 0, 1
Let v(d) be the third derivative of 5*d**2 + 1/480*d**6 + 1/12*d**3 - 1/120*d**5 - 1/96*d**4 + 0*d + 0. Factor v(m).
(m - 2)*(m - 1)*(m + 1)/4
Let r(k) = -7*k**2 + 1252*k - 137384. Let d(y) = -8*y**2 + 1244*y - 137383. Let x(f) = 4*d(f) - 5*r(f). What is l in x(l) = 0?
214
Let g(b) be the second derivative of -b**6/6 - 205*b**5 - 210125*b**4/2 - 86151250*b**3/3 - 8830503125*b**2/2 - b - 316. Factor g(q).
-5*(q + 205)**4
Find p, given that -5*p**2 + 10*p - 1 + 26 + 15 + 0 = 0.
-2, 4
Let b(y) be the first derivative of -y**5/60 - y**4/36 + 5*y**3/9 - 4*y**2/3 + 19*y + 5. Let k(d) be the first derivative of b(d). Factor k(m).
-(m - 2)*(m - 1)*(m + 4)/3
Let o(k) be the third derivative of -1/40*k**4 - 1/300*k**5 + 0*k + 0*k**3 + 0 - 15*k**2. What is v in o(v) = 0?
-3, 0
Let q = -1127/34 + 606/17. Factor -7*z**2 + 0 - 9*z**4 + 12*z**3 + 3/2*z + q*z**5.
z*(z - 1)**3*(5*z - 3)/2
Let x(a) be the second derivative of -a**5 + 2285*a**4/12 - 10925*a**3 + 16245*a**2/2 + 80*a + 2. Factor x(l).
-5*(l - 57)**2*(4*l - 1)
Let t(q) = 2*q**3 + 5*q**3 + 6*q + 261*q**2 + 6 - 253*q**2. Let i(x) = -x**3 - x**2 - x - 1. Let n(u) = 6*i(u) + t(u). Factor n(j).
j**2*(j + 2)
Suppose -4*q = 4*q + 24. Let g(n) = 5*n**2 + 10*n - 11. Let y(i) = -5*i**2 - 10*i + 12. Let x(c) = q*g(c) - 4*y(c). Factor x(v).
5*(v - 1)*(v + 3)
Suppose 5*a + 2*w - 2 = 0, 2*a + 0*a - 4*w = -4. Solve 1/2*x**4 - 1/2*x + a + 3/2*x**2 - 3/2*x**3 = 0.
0, 1
Let c(f) be the second derivative of f**7/168 - 2*f**6/15 + 23*f**5/40 + 3*f**4 + 27*f**3/8 + 3*f. Factor c(v).
v*(v - 9)**2*(v + 1)**2/4
Let q(b) be the first derivative of b**5/30 + 9*b**2/2 + 2. Let x(s) be the second derivative of q(s). Let x(g) = 0. What is g?
0
Let f(k) = 20*k**2 + 14*k. Let b be -4 + 1/(-2) + (-6)/4. Let n(h) = 21*h**2 + 15*h. Let r(y) = b*f(y) + 5*n(y). Factor r(v).
-3*v*(5*v + 3)
Let j(v) be the third derivative of 0*v + 0*v**4 + 0*v**5 + 2*v**2 + 0 + 0*v**3 - 1/1365*v**7 - 1/390*v**6. Solve j(l) = 0 for l.
-2, 0
Let l(y) be the third derivative of y**6/660 + 2*y**5/165 - 5*y**4/44 - 6*y**3/11 + y**2 + 3. Solve l(m) = 0 for m.
-6, -1, 3
Let p(y) = -y**4 - y**3 + y**2 - y - 2. Suppose 11*r - 10*r = 2. Let m(i) = i**4 + i**3 - i**2 + 2*i + 3. Let v(w) = r*m(w) + 3*p(w). Let v(u) = 0. What is u?
-1, 0, 1
Let k(n) = 6*n**3 - 24*n**2 - 42*n + 138. Let x(q) = -7*q**3 + 25*q**2 + 42*q - 136. Let p(m) = -4*k(m) - 3*x(m). Factor p(d).
-3*(d - 8)*(d - 2)*(d + 3)
Let x = -3 - -8. Let a = -15396 - -76984/5. Suppose 1/5*o**4 - a*o**x - 1/5*o**2 + 4/5*o**3 + 0 + 0*o = 0. What is o?
-1, 0, 1/4, 1
Let o = 980 - 976. Let z(i) be the third derivative of -2/51*i**3 + 0 - 1/510*i**5 + 0*i - 1/68*i**o + 6*i**2. Find s, given that z(s) = 0.
-2, -1
Let x(c) = -c - 1. Let g be x(3). Let m(t) = -5*t - 16. Let h be m(g). Suppose 7/8*j**h + 9/8*j**3 - 1/4 - 9/8*j - 5/8*j**2 = 0. Calculate j.
-1, -2/7, 1
What is n in -2/3*n**4 - 70/9*n**2 + 0 - 112/9*n**3 + 4*n = 0?
-18, -1, 0, 1/3
Let d(z) = 7*z**3 + 19*z**2 - 28*z - 40. Let s(w) = -8*w**3 - 20*w**2 + 28*w + 40. Let h(c) = -4*d(c) - 3*s(c). Factor h(x).
-4*(x - 2)*(x + 1)*(x + 5)
Let o(z) = 3*z**4 - 76*z**2 + 266*z - 295. Let n(f) = 13*f**4 - f**3 - 306*f**2 + 1062*f - 1179. Let w(m) = 2*n(m) - 9*o(m). Suppose w(y) = 0. What is y?
-11, 3
Let t(x) be the second derivative of 0*x**2 + 33*x + 0*x**4 + 2*x**3 + 0 + 1/10*x**6 - 9/20*x**5. Factor t(q).
3*q*(q - 2)**2*(q + 1)
Let p be (42/15)/((-38)/(-95)). Let j(l) be the first derivative of 12*l**2 - 2 + 3/4*l**4 - p*l**3 + 48*l. Factor j(r).
3*(r - 4)**2*(r + 1)
Let a be (-19000)/(-1064) - 51/3. Factor 6/7*r**2 - 6/7*r**4 + 0 - a*r**3 + 6/7*r.
-6*r*(r - 1)*(r + 1)**2/7
Let l(h) = h**4 + 21*h**3 + 8*h**2 - 70*h + 50. Let q(s) = 21*s**3 + 9*s**2 - 72*s + 48. Let y(o) = -6*l(o) + 7*q(o). Determine g so that y(g) = 0.
-2, 1/2, 2, 3
Factor -4 + 30/7*d - 2/7*d**2.
-2*(d - 14)*(d - 1)/7
Let o(k) be the third derivative of 1/192*k**4 + 1/1680*k**7 - 7*k + 1/2688*k**8 + 2*k**2 + 1/48*k**3 - 1/480*k**6 - 1/240*k**5 + 0. Factor o(c).
(c - 1)**2*(c + 1)**3/8
Let f(d) be the first derivative of -3*d**4/4 - 7*d**3 - 45*d**2/2 - 27*d - 146. Factor f(a).
-3*(a + 1)*(a + 3)**2
Suppose 39*r - 3 - 114 = 0. Factor 1/2*o**r - 1/2 + 1/2*o**2 - 1/2*o.
(o - 1)*(o + 1)**2/2
Suppose 88 = -5*s - h, s - 3*s - 34 = h. Let z be (-2)/(-6) + (-30)/s. Factor 240*o - 240*o - o**3 + z*o**2.
-o**2*(o - 2)
Let p be -3*(-19)/(-38) - (-13)/6. Solve -5/3*j**3 + 0 + p*j + j**2 = 0.
-2/5, 0, 1
Let w = -96477/4 - -24120. Let -3/4*m**5 + 0*m + w*m**4 + 0 - 3/4*m**2 + 3/4*m**3 = 0. Calculate m.
-1, 0, 1
Let c(x) be the second derivative of 3*x**8/4480 + x**7/2240 - x**6/480 - 5*x**3/6 + 8*x. Let a(i) be the second derivative of c(i). Factor a(k).
3*k**2*(k + 1)*(3*k - 2)/8
Find f such that -51*f + 17*f**2 - 81*f**3 - 18 + 69*f**3 + 64*f**2 = 0.
-1/4, 1, 6
Let c(y) be the third derivative of y**8/14 - 43*y**7/70 + 71*y**6/40 - 9*y**5/4 + 9*y**4/8 - y**2 - 8*y. Let c(n) = 0. Calculate n.
0, 3/8, 1, 3
Let k(u) be the first derivative of -15/7*u**2 - 24 - 1/7*u**3 - 27/7*u. Factor k(a).
-3*(a + 1)*(a + 9)/7
Let g(x) be the second derivative of 2/45*x**3 + 0*x**2 + 0 - 1/315*x**7 - 1/30*x**4 - 12*x + 1/75*x**6 - 1/150*x**5. Suppose g(c) = 0. Calculate c.
-1, 0, 1, 2
Let p = -171 + 175. Let f(m) be the first derivative of -37*m**4 + 0*m - p + 24*m**5 - 6*m**6 - 8*m**2 + 80/3*m**3. Solve f(r) = 0.
0, 2/3, 1
Let p(q) be the second derivative of 0*q**4 + 1/140*q**5 + 0*q**3 + 0*q**2 + 0 + 1/210*q**6 + 4*q. Suppose p(a) = 0. Calculate a.
-1, 0
Let a(p) = -59*p + 651. Let w be a(11). Factor 8/7*n + 2/7*n**w + 8/7.
2*(n + 2)**2/7
Suppose 48/5*q + 3/5*q**2 + 192/5 = 0. What is q?
-8
Suppose -272*w = -242*w - 120. Let h(l) be the second derivative of -5/6*l**3 + l**2 + 0 + 5*l + 1/4*l**w. Factor h(u).
(u - 1)*(3*u - 2)
Let v(d) be the second derivative of -d**4/12 - 11*d**3/3 - 121*d**2/2 - 74*d. Factor v(m).
-(m + 11)**2
Let k be 1/8*2*1. Let f(m) = -m**3 + 24*m**2 - 22*m - 23. Let g be f(23). Factor -k*u + 1/2*u**2 - 1/4*u**3 + g.
-u*(u - 1)**2/4
Suppose -4*g = -5*a + 60 - 169, -a = -g + 27. Let q = -22 + g. Factor -3*k + k**4 - k - 4*k**q + 12*k**3 - 5*k**4.
-4*k*(k - 1)**2*(2*k + 1)
Let j(x) be the first derivative of 4*x**5/5 + 55*x**4 + 968*x**3 - 1792*x**2 - 6272*x - 157. Solve j(w) = 0.
-28, -1, 2
Let f(z) be the second derivative of -z**4/36 + 25*z**3/18 + 13*z**2/3 - 85*z. Find h such that f(h) = 0.
-1, 26
Let r(c) = -c**3 + 10*c**2 - 10*c + 13. Let o be r(9). Suppose o*g = 14 - 2. Factor 1 - q**4 - q + g*q - 2*q**3 + 0*q.
-(q - 1)*(q + 1)**3
Let u(m) be the first derivative of -m**5/5 - 31*m**4/16 - m**3 + 61*m**2/8 - 7*m/2 - 326. Determine b so that u(b) = 0.
-7, -2, 1/4, 1
Let h(u) be the third derivative of 0 + 1/36*u**4 - 1/90*u**5 + 0*u + 2/3*u**3 - 9*u**2. Factor h(b).
-2*(b - 3)*(b + 2)/3
Let k(w) be the second derivative of w**4/4 - w**3 - 45*w**2/2 - 2*w - 59. Find t, given that k(t) = 0.
-3, 5
Determine h, given that 21*h**2 + 10*h**2 + 35*h + 2*h**3 - h**3 - 22 - 45*h**2 = 0.
1, 2, 11
Let p(i) = -i - 20. Let c be p(6). Let o be 6/(-39) - 108/c. Find y, given that -21*y**2 - 5*y**4 + 27*y**2 + 2*y**o - 3 = 0.
-1, 1
Suppose l - 35 = a + 7, -3*a - 15 = 0. Suppose 12*h + l = 73. Solve 2/3*