z + 1)/2
Let a(n) be the second derivative of -n**8/15680 - n**7/2940 - n**6/1680 - 2*n**4 + 10*n. Let p(t) be the third derivative of a(t). Let p(r) = 0. What is r?
-1, 0
Let o(q) be the third derivative of -q**7/315 - 7*q**6/180 + 17*q**5/90 - q**4/4 - q**2 + 29*q. Factor o(z).
-2*z*(z - 1)**2*(z + 9)/3
Let u(z) be the third derivative of z**8/168 + z**7/35 + z**6/30 - 16*z**2. Determine m so that u(m) = 0.
-2, -1, 0
Suppose 14*d - 320 = 9*d. Let k be d/112*(-7)/(-18). Suppose -16/9*o**2 + 4/9 + k*o + 10/9*o**3 = 0. What is o?
-2/5, 1
Let a be 3*(-7)/63*0. What is b in 2/11*b**3 + 2/11*b**2 + 0 + a*b = 0?
-1, 0
Suppose 4*v + l = 15, 12 = 4*v + 5*l - l. Determine t, given that -6*t + 4*t**4 - 9*t**2 + 4*t - t**v - 4*t = 0.
-1, 0, 2
Let y(i) = 19*i**4 - 101*i**3 + 324*i**2 - 331*i + 7. Let x(c) = -6*c**4 + 34*c**3 - 108*c**2 + 110*c - 2. Let f(k) = 7*x(k) + 2*y(k). Factor f(h).
-4*h*(h - 3)**3
Let f(j) = -119*j**2 - 450*j - 405. Let r(i) = -1665*i**2 - 6300*i - 5670. Suppose -7*t = -8*t - 85. Let c(k) = t*f(k) + 6*r(k). Factor c(n).
5*(5*n + 9)**2
Let r(u) be the third derivative of u**6/840 + 11*u**5/420 - u**4/12 - 4*u**3/7 + 875*u**2. Factor r(m).
(m - 2)*(m + 1)*(m + 12)/7
Let u(d) = -16*d**5 - 23*d**4 - 5*d**3 + 11*d**2. Let h(p) = 9*p**5 + 12*p**4 + 3*p**3 - 6*p**2. Let l(k) = -11*h(k) - 6*u(k). Factor l(y).
-3*y**3*(y - 1)**2
Let x(r) be the second derivative of r**5/120 - r**4/24 + r**3/18 + 11*r - 3. Factor x(i).
i*(i - 2)*(i - 1)/6
Solve 6/5*f**3 + 144/5 - 3/5*f**4 + 111/5*f**2 + 246/5*f = 0 for f.
-3, -2, -1, 8
Let q be 4/(-5) - 12*5/(-75). Let u(n) be the second derivative of q - 3*n - 1/2*n**3 - 1/24*n**4 - 9/4*n**2. Suppose u(k) = 0. Calculate k.
-3
Let z(g) be the second derivative of 5*g**7/84 - 19*g**6/6 + 279*g**5/4 - 810*g**4 + 20655*g**3/4 - 32805*g**2/2 - 42*g. Factor z(o).
5*(o - 9)**4*(o - 2)/2
Let x(u) = 2*u**3 + 33*u**2 - 20*u - 21. Let l be x(-17). Let y be l/(-12)*-4*(-2)/(-10). Determine f so that 5/2*f**y + 3/2 + 1/2*f**3 + 7/2*f = 0.
-3, -1
Let l(b) be the first derivative of b**4/2 + 28*b**3/3 - b**2 - 28*b - 154. Factor l(d).
2*(d - 1)*(d + 1)*(d + 14)
Let q be (-190)/3230 + 12414/357. Factor q + 54/7*t + 3/7*t**2.
3*(t + 9)**2/7
Suppose 4*o - 69 = -9. Suppose -4*r - 3*h = -0*h - 23, 0 = -3*h + o. Let 1/4*y**2 + 4 + r*y = 0. Calculate y.
-4
Determine o so that 0*o + 3/7*o**5 + 33/7*o**3 + 0 + 18/7*o**4 + 18/7*o**2 = 0.
-3, -2, -1, 0
Let k = 3149 + -3149. Factor -4/5*p**2 + k + 0*p.
-4*p**2/5
Let m(o) = -10*o**5 - 5*o**4 + 55*o**3 + 85*o**2 + 35*o. Let s(t) = -15*t**5 - 7*t**4 + 83*t**3 + 127*t**2 + 52*t. Let l(q) = 7*m(q) - 5*s(q). Factor l(b).
5*b*(b - 3)*(b + 1)**3
Suppose 1/4*w**3 + 4 - 4*w**2 - 1/4*w = 0. Calculate w.
-1, 1, 16
Let c(z) = -44*z**2 - 428*z + 424. Let h(v) = 6*v**2. Let o(n) = c(n) + 8*h(n). Factor o(x).
4*(x - 106)*(x - 1)
Let m(g) = 10166*g**3 - 526*g**2 - 111*g + 1. Let t(r) = 101661*r**3 - 5259*r**2 - 1110*r + 12. Let j(w) = 21*m(w) - 2*t(w). Solve j(p) = 0.
-1/22, 1/7
Let i = -74 + -6. Let v = 402/5 + i. Solve -2/5*a + 2/5*a**4 - 2/5*a**5 - 4/5*a**2 + 4/5*a**3 + v = 0 for a.
-1, 1
Let g(b) = -22*b**2 - 35*b + 21. Let u(c) = -11*c**2 - 18*c + 10. Let s(a) = -4*g(a) + 7*u(a). Let h(k) = k**2 + k - 1. Let w(y) = 2*h(y) - s(y). Factor w(t).
-3*(t + 2)*(3*t - 2)
Let f(b) be the third derivative of 0*b + 1/180*b**5 + b**2 - 1/18*b**3 - 1/90*b**6 + 0 + 1/18*b**4. Let f(o) = 0. What is o?
-1, 1/4, 1
Suppose -5*r - q = -2*r + 13, 5*r + 3 = 3*q. Let h = r - -5. Factor -4*f + 3*f**4 - f + 9*f**h - 9*f**3 + 2*f.
3*f*(f - 1)**3
Factor -96*n**2 - 75/2 + 120*n.
-3*(8*n - 5)**2/2
Let a(t) = 3*t**2 + 2. Let z(l) = l**3 - l**2 - 40*l + 20. Let u(p) = 4*a(p) + z(p). Factor u(o).
(o - 2)*(o - 1)*(o + 14)
Let s be 1/(-3) - (-14)/6. Suppose 5*d = 5*a + 5, 6*d - 5*d = -5*a + 13. Determine k so that k + 3*k**3 + d*k**s + k**4 + k + 0*k**2 - k = 0.
-1, 0
Let h(s) be the second derivative of -s**5/20 + 19*s**4/12 + 10*s**3/3 - 25*s. Determine o so that h(o) = 0.
-1, 0, 20
Let q(n) be the first derivative of n**3/6 - 9*n**2 + 30. Factor q(r).
r*(r - 36)/2
Let g(j) be the third derivative of j**10/120960 - j**9/60480 - j**8/13440 + j**4/4 - 5*j**2 + j. Let x(y) be the second derivative of g(y). Factor x(v).
v**3*(v - 2)*(v + 1)/4
Let d(q) be the third derivative of -q**6/160 + 9*q**5/80 - 13*q**2 + q. Let d(w) = 0. Calculate w.
0, 9
Suppose 0 = -4*c + 6 + 2. Factor -4*s**5 + 3*s**4 - 9*s**4 + 4*s - 2*s**4 + 8*s**c.
-4*s*(s - 1)*(s + 1)**3
Let q(f) be the first derivative of -f**6/540 - 4*f**5/135 - 4*f**4/27 - 7*f**2 + 34. Let j(d) be the second derivative of q(d). Suppose j(w) = 0. What is w?
-4, 0
Let y(s) = s**3 - s**2 + s - 1. Let h(u) = -22*u**4 + 7*u**3 - 3*u**2 + 3*u - 3. Let f(c) = -h(c) + 3*y(c). Factor f(l).
2*l**3*(11*l - 2)
Let r = 12 + -10. Factor 3 + 1 + 4*m**r - 8*m**2.
-4*(m - 1)*(m + 1)
Let r(g) be the first derivative of g**5/15 - 2*g**4 + 24*g**3 - 19*g**2/2 - 21. Let d(p) be the second derivative of r(p). Determine v so that d(v) = 0.
6
Let u be (-3 + 3)*2/12. Let c(p) be the second derivative of p**4 + u*p**2 - 6*p + 0 - 11/20*p**5 - 2/3*p**3 + 1/10*p**6. Let c(g) = 0. Calculate g.
0, 2/3, 1, 2
Let d(j) be the second derivative of -5*j**4/12 - 40*j**3/3 - 160*j**2 + 2*j + 38. Factor d(m).
-5*(m + 8)**2
Let s = 50641/7915 + 3/1583. Let -64/5 - 4/5*o**2 - s*o = 0. Calculate o.
-4
Suppose 3*v - 38 + 2 = 0. Let j be 5/(-30) + v/8. Suppose 11/3*r**2 + 0 + j*r**4 + 13/3*r**3 + 2/3*r = 0. Calculate r.
-2, -1, -1/4, 0
Let p(i) be the third derivative of -i**5/60 - 5*i**4/3 - 200*i**3/3 + 18*i**2. Factor p(b).
-(b + 20)**2
Let w(x) = 5*x**2 - x - 2. Let q be w(-1). Find t such that -q*t**3 + 2*t**3 - 18*t**3 - 10*t**2 + 5*t**3 = 0.
-2/3, 0
Let 0 + 3/7*n**3 + 27/7*n + 18/7*n**2 = 0. Calculate n.
-3, 0
Let b(i) be the second derivative of i**7/21 - i**6/5 + 61*i + 1. Factor b(r).
2*r**4*(r - 3)
Let q(w) = 7*w**3 + 71*w**2 - 128*w - 759. Let n(k) = 2*k**3 + 18*k**2 - 32*k - 190. Let l(m) = -9*n(m) + 2*q(m). Factor l(y).
-4*(y - 3)*(y + 4)**2
Suppose -73062*k = -73063*k. Solve k - 35/4*q**3 + 5/4*q**4 + 10*q**2 + 20*q = 0.
-1, 0, 4
Let y(h) be the first derivative of -2*h**5/15 + 3*h**4/2 - 40*h**3/9 + 4*h**2 + 632. Factor y(m).
-2*m*(m - 6)*(m - 2)*(m - 1)/3
Let z(g) be the first derivative of 16/5*g**5 + 4/3*g**3 - g**6 - 19 + 0*g**2 + 0*g - 7/2*g**4. Factor z(c).
-2*c**2*(c - 1)**2*(3*c - 2)
Let f(h) be the second derivative of -h**4/6 + 8*h**3/3 - 39*h. Let f(m) = 0. What is m?
0, 8
Let p(g) = g**2 + 20*g + 6. Let l be p(-14). Let o be (20/(-6))/(52/l). Suppose 3/2*w**o - 21/2*w - 12*w**2 - 3 - 3*w**3 + 3*w**4 = 0. Calculate w.
-1, 2
Let x(l) = 11*l**2 - 184*l + 131. Let j be x(16). Let -6*u**2 - 4/3*u + 0 - 2*u**5 - 10*u**j - 22/3*u**4 = 0. Calculate u.
-1, -2/3, 0
Suppose 2*q - 19 = t, -2*t + 6*q - q - 37 = 0. Let r be -2 + (-4 - 150/t). Suppose -2/7*v**2 - r - 8/7*v = 0. What is v?
-2
Let c(k) = -k**4 + k**3 - k + 1. Let q(p) be the second derivative of 2*p**5 + 25*p**4/4 + 10*p**3 + 25*p**2/2 - 3*p. Let f(r) = 5*c(r) - q(r). Factor f(v).
-5*(v + 1)**3*(v + 4)
Find q, given that -2*q**2 - 4/3*q + 0 = 0.
-2/3, 0
Let f(p) be the second derivative of -p**5/330 + p**4/66 - p**3/33 + 7*p**2 + 13*p. Let i(t) be the first derivative of f(t). Factor i(w).
-2*(w - 1)**2/11
Determine o, given that -1/2*o**2 + 7/2 - 3*o = 0.
-7, 1
Suppose 11 = -15*n + 56. Let l(z) be the second derivative of 1/14*z**7 + 0*z**4 + 0*z**n + 0*z**2 + 1/10*z**6 + 0 - z + 0*z**5. Find f such that l(f) = 0.
-1, 0
Suppose 5*c = -57 - 48. Let f be (-28)/(-8)*(-18)/c. Find i such that 7*i**3 - 112 + 144*i - 16 - 64 - 36*i**2 - 4*i**f = 0.
4
Let n be ((-8)/(-4))/(118/2*-1). Let s = 250/413 + n. Factor -4/7*k - 2/7*k**4 + 2/7 + s*k**3 + 0*k**2.
-2*(k - 1)**3*(k + 1)/7
Suppose 9*k = 42*k - 132. Let u(j) be the first derivative of j**6 + 8/5*j**5 + 0*j**3 + 1/2*j**k + 0*j + 4 + 0*j**2. Find v such that u(v) = 0.
-1, -1/3, 0
Let r(j) = j**2 + 11*j + 3. Let x(y) = y**2 + 12*y + 4. Let g(f) = 4*r(f) - 3*x(f). Find k such that g(k) = 0.
-8, 0
Let o = -59 - -56. Let q(k) = 6*k**4 - 6*k**3 - 3*k**2. Let u(m) = 17*m**4 - 17*m**3 - 9*m**2 + m. Let f(c) = o*u(c) + 8*q(c). Factor f(d).
-3*d*(d - 1)**2*(d + 1)
Let a(u) = u**3 + u. Suppose 5*h = 2 +