2 - 2*m**3 + 8*m**5 = 0?
-1, -1/4, 0, 1
Let d be (46/(-20) + 2)/((-36)/5). Let g(u) be the third derivative of 0*u + 1/240*u**5 + 0*u**4 - d*u**3 - 2*u**2 + 0. Let g(c) = 0. Calculate c.
-1, 1
Let q(k) be the second derivative of k**7/630 + k**6/180 - k**5/60 - 2*k**2 + 5*k. Let l(f) be the first derivative of q(f). Determine i, given that l(i) = 0.
-3, 0, 1
Let m(s) be the first derivative of s**6/8 + 3*s**5/10 - s**3/2 - 3*s**2/8 - 15. Factor m(i).
3*i*(i - 1)*(i + 1)**3/4
Let r(z) be the second derivative of -9/55*z**6 + 15/22*z**4 + 27/110*z**5 + 4*z + 0 + 17/33*z**3 + 2/11*z**2. Solve r(k) = 0.
-1/3, 2
Let l be ((-1136)/132)/(-4) + (-2)/(-11). Suppose -11/3*f + 2/3 - l*f**3 + 16/3*f**2 = 0. Calculate f.
2/7, 1
Suppose -51*h - 15*h**3 + 17*h**3 - 69*h**2 - 6 + 124*h**3 = 0. What is h?
-2/7, -1/6, 1
Let y(p) be the second derivative of 3*p**5/4 + 85*p**4/6 + 70*p**3 - 180*p**2 - 4*p. Factor y(m).
5*(m + 6)**2*(3*m - 2)
Let a be 1825/455 - 2/13. Let d = a + -33/14. Factor 3/2*u**2 + d*u - 3.
3*(u - 1)*(u + 2)/2
Let x(y) = y**2 - 3*y. Let b be x(2). Let d = b - -2. Factor -1/5*o**4 + 1/5*o**2 + d - 1/5*o + 1/5*o**3.
-o*(o - 1)**2*(o + 1)/5
Let a(g) be the first derivative of -1/18*g**6 + 0*g + 0*g**2 + 4 + 0*g**4 + 0*g**3 - 1/15*g**5. Solve a(k) = 0.
-1, 0
Let s(k) be the second derivative of 0*k**3 + 0*k**2 + 1/80*k**5 + 0 + 1/48*k**4 - 2*k. Factor s(o).
o**2*(o + 1)/4
Suppose -4*k - 2*o = -5*o - 38, -5*k = -3*o - 46. Factor -2*s**3 - k*s**2 + 3*s**3 + 7*s**2.
s**2*(s - 1)
Let d(z) = -z**4 + z**3 + 17*z**2 - 5*z. Let j(s) = 8*s**2 + 4*s**2 + 2*s**2 - 5*s**2 - 3*s. Let u(n) = 3*d(n) - 5*j(n). Factor u(h).
-3*h**2*(h - 2)*(h + 1)
Let w(n) be the second derivative of -n**7/14 + 11*n**6/30 - 37*n**5/60 + 5*n**4/12 - n**3/9 - 16*n. Suppose w(f) = 0. What is f?
0, 1/3, 1, 2
Suppose -51 = -2*t + 3. Let a = 27 - t. Find r such that 2/11*r - 2/11*r**3 + a - 2/11*r**4 + 2/11*r**2 = 0.
-1, 0, 1
Let i(x) be the third derivative of -x**7/105 + 11*x**6/120 - 11*x**5/60 - 5*x**4/8 + 3*x**3/2 - 10*x**2. Factor i(s).
-(s - 3)**2*(s + 1)*(2*s - 1)
Suppose 25 = 3*o + 2*o. Suppose -5*t + 15 = o. Factor -v**3 + 2*v**2 - 4 + v + 0*v**t + 2.
-(v - 2)*(v - 1)*(v + 1)
Let k = 8 - 5. Let u be 2*5/(-60) - 2/(-12). Let 0*j - 2/9*j**k + u - 2/9*j**2 = 0. What is j?
-1, 0
Suppose -2*o = j + 3, -11 = 3*o - 3*j - 2. Let l = 0 - o. Determine r, given that 8/9*r**4 + 8/9*r**l + 2/9*r + 0 + 2/9*r**5 + 4/3*r**3 = 0.
-1, 0
Let d(a) be the third derivative of -a**7/12600 + a**6/3600 + a**5/300 + 5*a**4/24 + 2*a**2. Let s(l) be the second derivative of d(l). Factor s(f).
-(f - 2)*(f + 1)/5
Let w(a) = -14*a**2 - 9. Let n be w(-7). Let y = n - -6263/9. Factor -y + 2/3*o**2 - 2/9*o**3 + 0*o.
-2*(o - 2)**2*(o + 1)/9
Let t = -1 - -3. Suppose t*h = 2 + 2. Suppose 4*z**2 + 5*z**4 + z**3 - z - 6*z**4 - 3*z**h = 0. What is z?
-1, 0, 1
Let k(y) be the first derivative of y**7/840 + y**6/180 + y**5/120 - 2*y**3 + 8. Let d(i) be the third derivative of k(i). Factor d(v).
v*(v + 1)**2
Let q = -24 + 28. Let c(z) be the second derivative of 0 + 2*z - 1/15*z**6 + 1/4*z**q - 1/6*z**3 - 1/2*z**2 + 1/20*z**5. Factor c(x).
-(x - 1)**2*(x + 1)*(2*x + 1)
Let r(j) be the second derivative of -100*j**4/3 + 40*j**3 - 18*j**2 - 28*j. Determine n, given that r(n) = 0.
3/10
Let b(h) be the third derivative of -h**9/20160 + h**7/1680 + h**5/60 - 6*h**2. Let f(q) be the third derivative of b(q). Factor f(j).
-3*j*(j - 1)*(j + 1)
What is c in 15/4*c**2 + 0 + 3/4*c**4 + 3/2*c + 3*c**3 = 0?
-2, -1, 0
Let b(n) be the third derivative of n**8/192 - n**7/70 - n**6/120 + 7*n**5/120 - n**4/32 - n**3/12 - 10*n**2. Factor b(l).
(l - 1)**3*(l + 1)*(7*l + 2)/4
Let l = -16 - -10. Let z = 9 + l. Factor 0*n**4 + 6*n**4 + 6*n**z + 21*n**4 + 21*n**5.
3*n**3*(n + 1)*(7*n + 2)
Let h(c) be the third derivative of -c**8/36960 + c**6/1320 + c**5/330 - c**4/6 + 4*c**2. Let x(l) be the second derivative of h(l). Factor x(a).
-2*(a - 2)*(a + 1)**2/11
Let m(y) = -y**2 + 13*y + 16. Let f be m(14). Let h(a) be the second derivative of -a - 1/42*a**4 + 0*a**f + 0 + 0*a**5 + 1/105*a**6 + 0*a**3. Factor h(r).
2*r**2*(r - 1)*(r + 1)/7
Let m be ((-1)/9)/((-36)/54). Let o(h) be the second derivative of 0 + 1/4*h**2 - 4*h + m*h**3 + 1/24*h**4. What is y in o(y) = 0?
-1
Let l(k) be the second derivative of -k**8/168 + 2*k**7/105 - k**5/15 + k**4/12 + k**2/2 + 2*k. Let w(p) be the first derivative of l(p). Solve w(q) = 0.
-1, 0, 1
Let u(v) be the first derivative of -2 + 0*v**2 - 1/5*v + 1/15*v**3. Factor u(t).
(t - 1)*(t + 1)/5
Let w(c) be the first derivative of c**4/2 - c**3/2 + 2*c - 1. Let b(p) be the first derivative of w(p). Determine h so that b(h) = 0.
0, 1/2
Let g(i) = -16*i**3 - 7*i**2 + 4*i. Let c(w) = w**4 - 17*w**3 - 7*w**2 + 5*w. Let r(d) = -5*c(d) + 6*g(d). Suppose r(z) = 0. Calculate z.
-1, -1/5, 0
Let i = 86 + -82. Let w(n) be the second derivative of -1/42*n**i + 0 - 4/7*n**2 + 2*n - 4/21*n**3. Let w(s) = 0. What is s?
-2
Suppose 3*p - 8 = -2. Factor q**3 - q**p + 3*q**2 - 2*q**3.
-q**2*(q - 2)
Let y be (2 - 162/75)*(-15 - -10). Factor -6/5*n - 6/5*n**4 + 2/5*n**5 + y*n**2 + 4/5*n**3 + 2/5.
2*(n - 1)**4*(n + 1)/5
Let n(d) = 25*d**4 + 204*d**3 + 479*d**2 + 369*d + 69. Let x(k) = 276*k**4 + 2244*k**3 + 5268*k**2 + 4060*k + 760. Let w(a) = -32*n(a) + 3*x(a). Factor w(h).
4*(h + 1)*(h + 3)**2*(7*h + 2)
Let o(a) be the first derivative of a**3/12 + 3*a**2/4 + 9*a/4 - 7. Factor o(z).
(z + 3)**2/4
Let x(o) be the first derivative of -o**6/39 + 4*o**5/65 - 4*o**3/39 + o**2/13 - 20. Suppose x(i) = 0. Calculate i.
-1, 0, 1
Determine m, given that 2*m**5 + 45*m**4 - m**2 + 6*m**2 - 17*m**3 - 22*m**5 - 13*m**3 = 0.
0, 1/4, 1
Let q = -85/4 - -1279/60. Let t(c) be the second derivative of c + 1/25*c**6 + 0 - 1/10*c**4 - q*c**3 + 1/50*c**5 + 0*c**2. Find s, given that t(s) = 0.
-1, -1/3, 0, 1
Let f be (4/8)/(22/(-32) + 1). Find r such that -48/5*r**2 + 82/5*r**3 - 42/5*r**4 + f*r + 0 = 0.
0, 2/7, 2/3, 1
Let m(s) be the third derivative of s**8/1176 - 13*s**7/735 + 29*s**6/210 - 53*s**5/105 + 85*s**4/84 - 25*s**3/21 + 2*s**2. Solve m(b) = 0.
1, 5
Let m(i) be the first derivative of 3 + 0*i**2 - 1/4*i + 1/6*i**3 - 1/20*i**5 + 0*i**4. Factor m(j).
-(j - 1)**2*(j + 1)**2/4
Let g(b) = -b**4 - 11*b**3 - 6*b**2 - 4*b + 6. Let u(m) = -m**3 + 1. Let o(i) = 4*g(i) - 28*u(i). Factor o(c).
-4*(c + 1)**4
Let s(m) = 10*m**2 + 4*m - 30. Let p(l) = -9*l**2 - 4*l + 29. Let u(c) = 6*p(c) + 5*s(c). Factor u(w).
-4*(w - 2)*(w + 3)
Factor 2/3*o**3 - 8/3*o + 0 + 2*o**2.
2*o*(o - 1)*(o + 4)/3
Let v(k) = k**2 - 10*k + 9. Let q be v(7). Let h be q/(-7) - (-2)/7. Suppose -j**5 + 0*j**2 + 0*j**h = 0. Calculate j.
0
Let t(l) = 7*l**3 - 3*l**2 + 6*l - 4. Let k(j) = -20*j**3 + 9*j**2 - 17*j + 11. Let z(i) = -6*k(i) - 17*t(i). Let u be z(3). Factor -u + c**2 + 2.
c**2
Let y(x) = 10*x**2 + 235*x - 350. Let z(s) = s**2 + 26*s - 39. Let l(g) = 4*y(g) - 35*z(g). Factor l(c).
5*(c - 1)*(c + 7)
Let v be 0/(2 + -4) - -9. Suppose g = y - 1, 0 = -v*g + 4*g - y + 19. Factor 10/9*u**4 + 4/9*u + 2/9*u**2 + 0 - 16/9*u**g.
2*u*(u - 1)**2*(5*u + 2)/9
Suppose -3*w + 2 + 13 = 0. Suppose 2*b - 3*n - n = -8, 5*n = -w*b + 10. Factor b + 0*z + 2/5*z**3 + 2/5*z**2.
2*z**2*(z + 1)/5
Let b(o) = -2*o + 1 + 3*o**2 + o**3 - 2*o**2 - 5*o**2 + 2*o**2. Let l be b(3). Factor -5*c + 0*c**2 + 4*c - l*c**2 + 5*c**2.
c*(c - 1)
Let a(z) = -20*z**2 + 96*z - 192. Suppose -5*h + 20 = -20. Let q(i) = -7*i**2 + 32*i - 64. Let w(k) = h*q(k) - 3*a(k). Factor w(p).
4*(p - 4)**2
Suppose 5*p = 0, 3*p = 4*n + 5*p - 52. Determine h, given that -n*h**3 - 13*h**4 - 5*h**4 - 27*h**5 + 3*h + 18*h**2 + 37*h**3 = 0.
-1, -1/3, 0, 1
Let w(j) = -48*j**2 + 321*j - 399. Let s(h) = -3*h**2 + 20*h - 25. Let u(n) = -33*s(n) + 2*w(n). Let u(x) = 0. What is x?
3
Let w be -3 + -1 + 2 - -2. Let v(d) be the first derivative of -2 + 0*d + w*d**2 - 2/3*d**3. Find q such that v(q) = 0.
0
Let z(k) be the third derivative of k**5/420 - 2*k**3/21 - 17*k**2. Let z(o) = 0. What is o?
-2, 2
Let s(x) be the second derivative of x**8/10080 + x**7/3780 - x**6/1080 - x**5/180 + x**4/12 - 4*x. Let c(k) be the third derivative of s(k). Solve c(y) = 0.
-1, 1
Let m(a) be the second derivative of -a**5/4 - 5*a**4/6 - 15*a. Factor m(o).
-5*o**2*(o + 2