 l(o) = 5*o**2 - 2*o. Let x be l(1). Factor 0*k**2 + k**u + x*k**2.
4*k**2
Let f(c) be the second derivative of 2*c**7/105 + 4*c**6/75 - c**5/25 - 2*c**4/15 + 6*c. Determine s so that f(s) = 0.
-2, -1, 0, 1
Let u(f) be the third derivative of f**5/12 + 5*f**4/4 + 15*f**3/2 + 113*f**2 - 1. Find d, given that u(d) = 0.
-3
Find x such that 122*x - 51 + 29 + 2*x**3 - 38 - 64*x**2 = 0.
1, 30
Let u(n) be the third derivative of -2*n**7/105 - 7*n**6/30 - n**5 - 13*n**4/6 - 8*n**3/3 - 6*n**2 - 2. Suppose u(y) = 0. Calculate y.
-4, -1
Let g(o) be the third derivative of o**5/15 + o**4/2 - 8*o**3/3 + 2*o**2 + 60. Determine h, given that g(h) = 0.
-4, 1
Let i(s) be the third derivative of -s**6/8 - 5*s**5/12 + 55*s**4/24 - 5*s**3/2 - 42*s**2. Suppose i(w) = 0. Calculate w.
-3, 1/3, 1
Let x(t) = 5*t**2 + 18*t + 17. Let y(m) = -m**2. Let k(j) = x(j) + 4*y(j). Factor k(q).
(q + 1)*(q + 17)
Suppose -s + 19 = 15. Factor 4*n**5 - 8*n**5 - 10*n**s + 8*n**2 + 2*n**4 + 4*n.
-4*n*(n - 1)*(n + 1)**3
Let t(l) be the third derivative of -l**7/140 + 47*l**6/80 + 147*l**5/40 + 149*l**4/16 + 25*l**3/2 - 31*l**2 + 2. Let t(g) = 0. Calculate g.
-1, 50
Let l(s) be the first derivative of s**6/3 + 32*s**5/5 - 2*s**4 - 128*s**3/3 - 272. Determine u, given that l(u) = 0.
-16, -2, 0, 2
Suppose -2*x = -3*x - 2*v - 2, -9 = 3*v. What is a in 361*a**x - 337*a**4 - 4*a**2 - 14*a**5 + 0*a**2 - 6*a**3 = 0?
-2/7, 0, 1
Let f(m) be the first derivative of -9 + 0*m**2 - 15/4*m**4 - 2*m**3 - 12/5*m**5 - 1/2*m**6 + 0*m. Factor f(q).
-3*q**2*(q + 1)**2*(q + 2)
Suppose -2*a - 4 = 0, -7*o - a = -2*o - 13. Solve 44*f**o + 2*f**2 - 39*f**3 + 4*f**4 + 0*f**2 + f**5 = 0.
-2, -1, 0
Let b(p) = 10*p**4 - 3*p**3 + 19*p**2 - 18*p - 8. Let z(k) = 6*k**4 - 2*k**3 + 10*k**2 - 10*k - 4. Let u(t) = 4*b(t) - 7*z(t). Let u(d) = 0. What is d?
-1, 1, 2
Let v(f) = -f**2 + 2324*f + 264500. Let b(k) = -2*k**2 + 6968*k + 793500. Let s(m) = -6*b(m) + 17*v(m). Let s(u) = 0. What is u?
-230
Let j be 4/6 + ((-133)/42 - -3). Let r(y) be the second derivative of 0 - 1/4*y**4 + 1/20*y**5 - j*y**2 + 1/2*y**3 + 2*y. Find d, given that r(d) = 0.
1
Let i = -6401 + 25605/4. Suppose -2*c + i*c**2 + 4 = 0. What is c?
4
Let u(i) be the first derivative of i**6/10 - 3*i**5/5 + 3*i**4/4 + 19*i - 15. Let d(v) be the first derivative of u(v). Solve d(m) = 0.
0, 1, 3
Let m(d) = -d + 1. Let b(l) = l**2 - 15*l + 15. Let a be b(14). Let h(j) = 3*j**2 + 18*j + 54. Let x(i) = a*h(i) - 6*m(i). Factor x(z).
3*(z + 4)**2
Determine b so that -50/13*b**3 - 36/13 + 42/13*b**2 - 6/13*b**4 + 50/13*b = 0.
-9, -1, 2/3, 1
Let b be (-2 + 2 + 3)*-7. Let d = -18 - b. Factor 2*r**5 - 8*r**4 + 12*r**d + 18*r**2 - 3*r + 5*r - 26*r**2.
2*r*(r - 1)**4
Suppose 3*o - 139 = 188. Let r = 553/5 - o. Factor 2*x**2 - 2/5*x**3 + r - 16/5*x.
-2*(x - 2)**2*(x - 1)/5
Let d = 252 + -173. Suppose 78*c = d*c - 4. Factor -1/7*h**3 + 1/7*h**5 + 1/7*h**c - 1/7*h**2 + 0 + 0*h.
h**2*(h - 1)*(h + 1)**2/7
What is a in 16*a**3 + 240/7*a**2 + 18/7*a**4 + 192/7*a + 32/7 = 0?
-2, -2/9
Find g such that 1/8*g**2 + 0 + 15*g = 0.
-120, 0
Factor -43*d**2 + 240 - 38*d**2 + 10*d - 45*d**2 + 166*d**2 - 45*d**2.
-5*(d - 8)*(d + 6)
Let m(o) be the first derivative of 5*o**3/3 - 90*o**2 + 163. Factor m(p).
5*p*(p - 36)
Let i = 1579/3910 + -3/782. Factor -i*u**4 + 0*u**2 + 0 + 0*u - 2/5*u**3.
-2*u**3*(u + 1)/5
Let r(v) be the first derivative of -16*v - 20/3*v**3 - 32*v**2 - 42 + 7*v**4. Find w, given that r(w) = 0.
-1, -2/7, 2
Suppose 0 = -9*l + 4*l + 25. Factor 5*p**2 - 3*p**2 + 2*p**2 - 2*p + 38*p**4 - 42*p**4 + 2*p**l.
2*p*(p - 1)**3*(p + 1)
Let u(z) be the second derivative of 7*z**6/60 - 3*z**5/10 + z**4/6 - 27*z**2/2 + 2*z. Let b(q) be the first derivative of u(q). Let b(s) = 0. Calculate s.
0, 2/7, 1
Factor 2*x - 5*x**2 + 25 + 0*x**2 - 11*x - 11*x.
-5*(x - 1)*(x + 5)
Factor -2/3*g + 0*g**3 + g**2 + 0 - 1/3*g**4.
-g*(g - 1)**2*(g + 2)/3
Let p be ((-58)/(-4))/(26/260). Let d = p + -142. Suppose 0*q - 2/9*q**5 - 2/9*q**2 + 0 + 2/9*q**4 + 2/9*q**d = 0. Calculate q.
-1, 0, 1
Let u(k) = -k + 6. Let c be u(3). Let v be (-72)/27*c/(-2). Factor -v + 8*g**3 - 4*g**2 + 8*g**4 + 0*g + 3*g - 13*g + 2*g**5.
2*(g - 1)*(g + 1)**3*(g + 2)
Suppose -6*v = -52*v + 92. Determine o so that 8/17 + 2/17*o**v + 10/17*o = 0.
-4, -1
Let c = -53 + 56. Suppose 0 = -p - c*u + 14, 4*u = -2*p + p + 17. Suppose 0 + 7/6*k**2 - 7/6*k**4 + 1/2*k**3 - 5/6*k**p + 1/3*k = 0. Calculate k.
-1, -2/5, 0, 1
Let t(o) be the second derivative of 0 + 0*o**2 + 1/12*o**4 - 36*o + 0*o**3. Factor t(u).
u**2
Suppose -9/2*s - 3/4*s**2 + 0 + 3/4*s**3 = 0. Calculate s.
-2, 0, 3
Let m be (36/(-7))/(117/26*4/(-9)). Factor m + 33/7*p + 18/7*p**2 + 3/7*p**3.
3*(p + 1)*(p + 2)*(p + 3)/7
Let w be 2/(40/58) - (-1)/10. Let j(o) be the second derivative of 1/6*o**w + 0*o**2 + 0 + 1/12*o**4 - 7*o. Suppose j(s) = 0. Calculate s.
-1, 0
Suppose -14 - 8 = -3*i - 2*j, j = 5. Let u(d) be the first derivative of -3*d**i - 16/5*d**5 - d**6 - 5 + 0*d + d**2 + 0*d**3. Suppose u(v) = 0. What is v?
-1, 0, 1/3
Let 1/7*h**4 + 0 + 0*h - 2/7*h**3 - 8/7*h**2 = 0. Calculate h.
-2, 0, 4
Let n(k) be the second derivative of -1/126*k**7 - 1/30*k**6 + 0*k**5 - 16 + 0*k**4 + 0*k**2 + 0*k**3 + 2*k. Factor n(h).
-h**4*(h + 3)/3
Let x be 2/3*(5*7/(-105))/(-1). Factor 0*s - x*s**3 + 1/9*s**2 + 0 + 1/9*s**4.
s**2*(s - 1)**2/9
Factor 0*p - 5/2*p**2 + 0 + 3/2*p**4 + 1/4*p**5 + 3/4*p**3.
p**2*(p - 1)*(p + 2)*(p + 5)/4
Let m(n) be the second derivative of 0 + 2/3*n**6 + 4/3*n**3 + 2/3*n**7 + 0*n**2 + 13*n - 5/3*n**4 - 9/5*n**5. Suppose m(s) = 0. What is s?
-1, 0, 2/7, 1
Let z(s) = -s**3 + 6*s**2 + 7*s + 3. Let v be z(7). Let j(l) = -l**2 + 5*l - 4. Let w be j(v). Factor -3*r**4 + w - 4*r**2 - 2*r**4 + 6*r**4 + r**4.
2*(r - 1)**2*(r + 1)**2
Let u(b) = -4*b**3 + b**2 - b - 1. Let c be u(-1). Suppose 8*r + 8*r**2 + 6*r**2 - 13*r**2 + 11 + c = 0. What is r?
-4
Factor 20*n**2 + 20*n + 5/2*n**4 + 10*n**3 + 8 + 1/4*n**5.
(n + 2)**5/4
Let y(c) be the first derivative of c**4/22 - 4*c**3/33 - 8*c**2/11 + 149. Factor y(m).
2*m*(m - 4)*(m + 2)/11
Let a(z) be the first derivative of 5 - 8/21*z**3 - 4/7*z - 9/7*z**2. Solve a(c) = 0 for c.
-2, -1/4
Let o(z) = 6*z**4 + 29*z**3 + z**2. Let b be -4 - (-4 - -6) - 5. Let f(u) = 2*u**4 + 10*u**3. Let a(w) = b*f(w) + 4*o(w). Suppose a(k) = 0. Calculate k.
-2, -1, 0
Let q(s) = -7*s**3 - 26*s**2 - 28*s. Let w(u) = -8*u**3 - 28*u**2 - 29*u. Let o(i) = 5*q(i) - 4*w(i). Factor o(l).
-3*l*(l + 2)*(l + 4)
Let d(l) be the second derivative of -l - 2*l**2 + 4/3*l**3 + 0 + 1/3*l**4 + 1/30*l**5. Let x(k) be the first derivative of d(k). Solve x(m) = 0.
-2
Let d = 5375/2 + -2686. Let 9/2 - 6*j + d*j**2 = 0. What is j?
1, 3
Let l(u) be the third derivative of -u**6/30 - u**5/5 + 27*u**2 - 2*u. Determine f, given that l(f) = 0.
-3, 0
Factor 391/9*w**2 + 0 + 37/9*w**3 + 1/9*w**4 + 289/3*w.
w*(w + 3)*(w + 17)**2/9
Let o(v) = -21*v**2 + 25*v - 21. Let y be o(-13). Let r be (y/(-350))/19 - 4/14. Let 0 - 1/10*f**2 - r*f = 0. Calculate f.
-3, 0
Let o(w) be the first derivative of 2*w**3/57 + 58*w**2/19 + 6*w - 286. Factor o(g).
2*(g + 1)*(g + 57)/19
Let x(r) = -20*r**3 + 11*r**2 + r + 4. Let o(v) = 40*v**3 - 23*v**2 - 3*v - 7. Let s(f) = -4*o(f) - 7*x(f). Let s(c) = 0. What is c?
-1/4, 0, 1
Let k(u) = -13*u**3 - 53*u**2 + 306*u - 250. Let r(c) = 20*c**3 + 80*c**2 - 460*c + 376. Let q(n) = -8*k(n) - 5*r(n). Factor q(i).
4*(i - 3)*(i - 1)*(i + 10)
Let l(o) be the first derivative of 3*o**6/2 - 7*o**5/5 - 5*o**4 - 4*o**3/3 + 186. Determine q, given that l(q) = 0.
-1, -2/9, 0, 2
Let i(s) = 2*s**4 - 33*s**3 + 3*s**2 + 33*s + 5. Let v(f) = 2*f**4 - 32*f**3 + 4*f**2 + 32*f + 6. Let h(m) = 6*i(m) - 5*v(m). Factor h(l).
2*l*(l - 19)*(l - 1)*(l + 1)
Let u(v) be the first derivative of -v**8/504 + v**7/63 - v**6/45 + 41*v**2/2 - 41. Let z(a) be the second derivative of u(a). Factor z(r).
-2*r**3*(r - 4)*(r - 1)/3
Find y, given that 4*y**5 - 108*y**4 - 1442*y - 628*y**2 - 1509*y + 3215*y + 468*y**3 = 0.
0, 1, 3, 22
Let g(r) be the first derivative of 5*r**6/6 - 3*r**5 - 125*r**4/4 - 35*r**3 + 118. Factor g(p).
5*p**2*(p - 7)*(p + 1)*(p + 3)
Let t(p) = 4*p**2 - 10*p + 4. Let a(q) = q - 1. Let f(v) = 4*a(v) + t(v). Let x(m) = -m**3 + 5*m**2 - 7*m. Let w(d) = 3*f(d) - 2*x(d). Fact