p(g) = 2*a(g) - 18*i(g). What is d in p(d) = 0?
-1/3, 0, 2
Let m(q) be the first derivative of q**9/22680 - q**7/2100 + q**6/1350 - 7*q**3/3 - 3. Let o(a) be the third derivative of m(a). Factor o(d).
2*d**2*(d - 1)**2*(d + 2)/15
Let p(q) = 48*q**2 + 27. Let v(c) = 7*c**2 + 4. Let g(f) = -4*p(f) + 27*v(f). Suppose g(w) = 0. What is w?
0
Let b(g) be the second derivative of g**9/68040 + g**8/10080 + g**7/3780 + g**6/3240 - 2*g**4/3 - 6*g. Let k(v) be the third derivative of b(v). Factor k(d).
2*d*(d + 1)**3/9
Let g(b) = -b**3 + 3*b**2 + 3*b + 3. Let z(i) = i**3 - 3*i**2 - 2*i - 2. Let x(p) = -2*g(p) - 3*z(p). Factor x(q).
-q**2*(q - 3)
Suppose -i + 9*i = 24. Let k(y) be the third derivative of 2/9*y**i + 1/30*y**5 + 0 - 5/36*y**4 + 1/180*y**6 - 1/315*y**7 + 0*y - y**2. Factor k(j).
-2*(j - 1)**3*(j + 2)/3
Let y(o) be the first derivative of -o**5/5 - o**4/4 + o**3 + o**2/2 - 2*o - 4. Solve y(n) = 0 for n.
-2, -1, 1
Let d(z) be the first derivative of 1/3*z**2 + 0*z - 1/6*z**4 - 2/15*z**5 - 7 + 2/9*z**3. What is s in d(s) = 0?
-1, 0, 1
Suppose 3*v + 2*z - 4 = v, -10 = -5*v + 5*z. Suppose v*u + 0 = -2*h + 16, -12 = -3*u + h. Factor 0*i**u + 6*i**4 + 0*i**5 + 4*i**3 - 4*i**2 + 2*i**5 - 2 - 6*i.
2*(i - 1)*(i + 1)**4
What is n in -8/13*n + 2/13*n**2 + 0 = 0?
0, 4
Factor -3 - 29*s**3 - 15*s - 30*s**2 - s**3 + 4*s**4 - 19*s**4 - 3*s**5.
-3*(s + 1)**5
Let j(u) be the third derivative of 5*u**7/504 - u**6/72 + u**5/120 - 3*u**4/8 + 3*u**2. Let b(c) be the second derivative of j(c). Factor b(n).
(5*n - 1)**2
Let x(s) be the third derivative of s**8/2016 - s**7/420 + s**6/720 + s**5/120 - s**4/72 + 25*s**2. Determine y so that x(y) = 0.
-1, 0, 1, 2
Let g = 679/6 - 113. Factor -1/2*c**2 - 1/6*c**4 + g*c + 0 + 1/2*c**3.
-c*(c - 1)**3/6
Suppose 0 = 2*t + 2*t + 20. Let n = t - -8. Suppose -5*s + 6*s**3 - 4*s**n + 3*s = 0. Calculate s.
-1, 0, 1
Let w(q) be the first derivative of q**6/720 - q**5/240 - q**4/24 - q**3 - 1. Let s(l) be the third derivative of w(l). Factor s(k).
(k - 2)*(k + 1)/2
Suppose -o - h + 7 + 8 = 0, 3*o + h - 35 = 0. Let p be (-19)/(-5) - 8/o. Let 8/9*b**p + 4/3*b + 2/9 + 2*b**2 = 0. Calculate b.
-1, -1/4
Let v be (-9)/(-21) + (-1788)/(-42). Let u = -41 + v. What is y in 4/3*y**u - 4/3*y**4 + 14/3*y**5 + 0 - 14/3*y**3 + 0*y = 0?
-1, 0, 2/7, 1
Let h be (-23)/7 + 2 + 3. Factor 2/7*z**2 + 18/7 - h*z.
2*(z - 3)**2/7
Suppose 3*m = 5*v + 1, 5 = 5*m - 5*v - 0. Factor -64/11*n - 32/11 - 2/11*n**4 - 48/11*n**m - 16/11*n**3.
-2*(n + 2)**4/11
Let z be 0/((1/(-5))/((-5)/25)). Let x(b) be the third derivative of 1/30*b**4 - 1/150*b**5 + z*b - b**2 - 1/105*b**7 - 2/75*b**6 + 0*b**3 + 0. Factor x(o).
-2*o*(o + 1)**2*(5*o - 2)/5
Let g(j) = -j**5 - 2*j**4 - 4*j**2 + 4. Let d = 3 + -3. Let w = 4 + d. Let i(f) = -4*f**5 - 6*f**4 - 11*f**2 + 11. Let o(q) = w*i(q) - 11*g(q). Factor o(n).
-n**4*(5*n + 2)
Let f(o) = -2*o + 1. Let w be f(4). Let q(j) = j + 9. Let t be q(w). Find b, given that 1/3*b**3 + 0 - 1/3*b + 0*b**t = 0.
-1, 0, 1
Let l be 1*1/(-1)*5/(-18). Let m(d) be the second derivative of l*d**3 + 11/36*d**4 - 3*d + 1/15*d**5 - 1/3*d**2 + 0. Solve m(r) = 0 for r.
-2, -1, 1/4
Let s be 19/(-60) + 13/39. Let u(g) be the third derivative of 3*g**2 + 0*g**4 + 0 + s*g**6 + 0*g**5 + 0*g + 0*g**3 - 1/105*g**7. Factor u(y).
-2*y**3*(y - 1)
Let m(a) be the second derivative of -1/4*a**5 + a**2 + 0 + 1/30*a**6 - 4*a - 7/6*a**3 + 3/4*a**4. Find k such that m(k) = 0.
1, 2
Let l(s) be the first derivative of -s**3 + 30*s**2 - 300*s + 24. Let l(n) = 0. What is n?
10
Let i(n) be the first derivative of 9*n**5 - 25*n**4 - 115*n**3/3 + 15*n**2 - 7. Factor i(p).
5*p*(p - 3)*(p + 1)*(9*p - 2)
Let a(l) be the second derivative of -l**7/3360 - l**6/720 - l**5/480 + 7*l**3/6 + 3*l. Let t(m) be the second derivative of a(m). Determine r so that t(r) = 0.
-1, 0
Let n(s) be the third derivative of 1/60*s**6 + 2*s**2 + 1/105*s**7 + 0*s**3 + 0 + 0*s**4 - 1/15*s**5 + 0*s. Factor n(q).
2*q**2*(q - 1)*(q + 2)
Suppose 13*l - 8 = 9*l. Let v(d) be the second derivative of 1/18*d**4 - l*d + 1/27*d**3 + 1/135*d**6 + 0 + 0*d**2 + 1/30*d**5. Factor v(a).
2*a*(a + 1)**3/9
Let o = 1 - -2. Suppose -k - 2*k + 15 = o*b, -7 = 4*b - 5*k. Factor -7*n**2 + b*n - n + 6*n**2.
-n*(n - 1)
Suppose s - 4*c - 32 = -4*s, -4*s + c = -30. Suppose 3*q = 1 + s. Determine p, given that -3*p**2 - 3*p**2 - 14*p + 8*p**4 + 16*p**q + 0*p**2 - 4 = 0.
-2, -1/2, 1
Let c(o) = -9*o**2 + 25*o - 13. Let t(v) be the third derivative of v**5/15 - v**4/2 + v**3 - 9*v**2. Let q(w) = 6*c(w) + 13*t(w). Factor q(r).
-2*r*(r + 3)
Let z be (-4)/(-56) + (-2)/28. What is p in 4/13*p - 10/13*p**2 + z = 0?
0, 2/5
Let s(p) be the third derivative of -1/36*p**3 + 0*p**4 + 0 + 0*p - 2*p**2 + 1/360*p**5. Suppose s(c) = 0. What is c?
-1, 1
Let w = 989/1743 - -1/249. Find u such that 2*u**2 + 0 + w*u = 0.
-2/7, 0
Let d be 24/(-16)*(-1 + 4/6). Let s(n) be the second derivative of 1/20*n**5 + d*n**3 + 0 - 1/4*n**4 - 1/2*n**2 + n. Factor s(b).
(b - 1)**3
Let d(o) be the first derivative of -o**4/26 - 2*o**3/13 - 2*o**2/13 - 31. Factor d(n).
-2*n*(n + 1)*(n + 2)/13
Let v(q) be the second derivative of 3*q**6/2 - 9*q**5/4 - 35*q**4/12 + 25*q**3/6 + 5*q**2 - 4*q. Determine d so that v(d) = 0.
-2/3, -1/3, 1
Let f = 12415 - 744869/60. Let g = f - -3/20. Let 1/3 - 1/3*t**4 + 0*t**2 + g*t - 2/3*t**3 = 0. What is t?
-1, 1
Suppose 3*g + 4 = 16. Let 4*z + g - 2*z - 4*z - 2*z**2 = 0. What is z?
-2, 1
Let d(g) be the second derivative of g**5/150 - g**4/60 - g**2 + 4*g. Let u(q) be the first derivative of d(q). Find k, given that u(k) = 0.
0, 1
Let q(o) be the first derivative of -o**5/20 + o**4/8 - 10. Find t, given that q(t) = 0.
0, 2
Determine y so that 2/7*y**2 + 0 + 4/7*y - 2/7*y**3 = 0.
-1, 0, 2
Let y = 837041/114 - 7342. Let k = y + 2/57. Find g, given that -1/4*g**3 + 0 + 1/4*g**4 + 0*g + 0*g**2 + k*g**5 = 0.
-1, 0, 1/2
Let d = 61/5 + -107/10. Factor 3*h + 3/2 + d*h**2.
3*(h + 1)**2/2
Let r(y) be the third derivative of 2/51*y**3 + 8/255*y**5 + 0*y + 1/2856*y**8 + 7/510*y**6 + 0 + 2/595*y**7 + 3/68*y**4 - 6*y**2. Factor r(n).
2*(n + 1)**4*(n + 2)/17
Let z(s) be the second derivative of 1/2*s**2 + 5/9*s**3 + 1/3*s**4 + 1/90*s**6 - 2*s + 1/10*s**5 + 0. Let z(k) = 0. Calculate k.
-3, -1
Let o = -427/45 - -53/5. Factor 14/9*v**2 - o*v - 4/9.
2*(v - 1)*(7*v + 2)/9
Let u(x) be the second derivative of 1/6*x**4 - 8/9*x**3 + 0 + 9*x + 16/9*x**2. Factor u(s).
2*(3*s - 4)**2/9
Suppose 4*r = 2 + 6. Let t = 7 - 5. Solve -4*c**4 + 0*c**2 + 4*c**r + c + c - t*c**5 = 0 for c.
-1, 0, 1
Let q(z) be the third derivative of z**6/240 + z**5/120 - 5*z**4/48 + z**3/4 - 5*z**2. Factor q(o).
(o - 1)**2*(o + 3)/2
Let p = 13/5 - 12/5. Let c(v) be the first derivative of 0*v + 1/12*v**6 - 1/4*v**2 - p*v**5 + 1 + 0*v**4 + 1/3*v**3. Factor c(u).
u*(u - 1)**3*(u + 1)/2
Factor c**4 - 4*c**2 - c**5 + 0*c**4 + 13*c**3 - 6*c**4 - 21*c**3.
-c**2*(c + 1)*(c + 2)**2
Suppose 2*s = -4*a + 14, 4 - 2 = a + 2*s. Suppose 3*y - 6*y = 15, 2*u = a*y + 24. Factor 0*q + 0 + 2/3*q**u.
2*q**2/3
Let b(o) = 5*o - 4. Let l be b(8). Let m be 4/l + 2/6. Factor -2/9*x**2 - m*x - 2/9.
-2*(x + 1)**2/9
Let n(p) = -2*p + 1 - 5 - 4*p**4 + 9*p**2 + 2*p**3 - 1. Let c(h) = -3*h**4 + 3*h**3 + 9*h**2 - 3*h - 6. Let f(o) = 5*c(o) - 6*n(o). Factor f(q).
3*q*(q - 1)*(q + 1)*(3*q + 1)
Let i be ((-6)/14)/(26/(-182)). Factor -3/2*x - 3/2*x**5 - 3/2*x**4 - 3/2 + 3*x**i + 3*x**2.
-3*(x - 1)**2*(x + 1)**3/2
Let r(g) be the third derivative of g**6/60 - g**5/50 - g**4/30 + 13*g**2. Suppose r(j) = 0. Calculate j.
-2/5, 0, 1
Let 7*z + 12*z**3 - 3*z - 5*z + 7*z - 15*z**2 - 3*z**4 = 0. What is z?
0, 1, 2
Let i be (3/(-90))/((-8)/20). Let t(z) be the third derivative of 1/60*z**6 - i*z**4 + 2*z**2 + 0*z**5 + 0 + 0*z + 0*z**3. Solve t(p) = 0 for p.
-1, 0, 1
Let y(v) = -2*v**3 + 14*v**2 + 18*v - 14. Let q be y(8). Solve 1/2 + 1/2*n**q - n = 0 for n.
1
Suppose -2*c + 2*r - 36 = -94, -5*r = -3*c + 91. Suppose -4*u = -c + 11. Find m such that 6/7*m**3 - 10/7*m**u - 4/7 - 6/7*m + 2*m**2 = 0.
-1, -2/5, 1
Let p(d) be the first derivative of 0*d - 1/2*d**4 - 2 + 0*d**3 + d**2. Factor p(k).
-2*k*(k - 1)*(k + 1)
Let w = 109 - 105. Let b(y) be the first derivative of 0*y - 3 - 1/6*y**w + 0*y**2 + 2/9*y**3. Factor b(u).
-2*u**2*(u - 1)