 x(n) = n**2. Let b(k) be the third derivative of k**4/6 + k**3/3 + k**2. Let t be 8/2 - (-4 - -8) - 1. Let w(y) = t*b(y) - 2*x(y). What is p in w(p) = 0?
-1
Let r(m) be the third derivative of -m**7/2940 + m**6/315 - m**5/105 + 4*m**3/3 + 7*m**2. Let s(d) be the first derivative of r(d). Factor s(t).
-2*t*(t - 2)**2/7
Let 2*d**2 + 175 - 175 - 3*d + d**3 = 0. What is d?
-3, 0, 1
Let u(w) be the second derivative of 0 + 1/150*w**5 + w - w**2 - 1/15*w**3 + 0*w**4. Let r(o) be the first derivative of u(o). Factor r(i).
2*(i - 1)*(i + 1)/5
Let g(b) = -3*b**2 + 2*b + 5. Let p(y) = y**2 + 8*y + 5. Let t be p(-7). Let w(r) = -6*r**2 + 5*r + 11. Let x(o) = t*w(o) + 5*g(o). Factor x(z).
-3*(z - 1)*(z + 1)
Let w(x) = 2*x**3 - x + 1. Suppose 5*b = 28 - 3. Suppose -4*a + a - 21 = -3*q, 0 = -a - b. Let r(f) = -f**3 - 1. Let p(s) = q*r(s) + 2*w(s). Solve p(y) = 0.
-1, 0, 1
Let w = -2 - -9. Let b be 2/42 - (-2)/w. Solve 2/3*n**3 + 1/3*n**4 + b*n**2 + 0*n + 0 = 0.
-1, 0
Let n(p) be the second derivative of -p**5/210 - p**4/42 + p**3/7 - 3*p**2 - 6*p. Let a(d) be the first derivative of n(d). Solve a(r) = 0 for r.
-3, 1
Let p(o) = 2*o**4 - 6*o**2 - 6. Let t(d) = d**5 - 5*d**4 + 17*d**2 + 17. Let a(m) = 17*p(m) + 6*t(m). Solve a(w) = 0.
-2/3, 0
Let f(c) be the first derivative of -c**4/20 + 2*c**3/15 + 2. Factor f(b).
-b**2*(b - 2)/5
Let s(t) be the second derivative of t**5/30 - t**4/54 + 6*t. What is o in s(o) = 0?
0, 1/3
Suppose -4*n = 2*t - 14, n + 33*t = 29*t + 14. Solve -1/5*o - 1/5*o**n + 1/5*o**3 + 1/5 = 0 for o.
-1, 1
Let v(q) be the second derivative of 1/3*q**6 + q - 7/6*q**4 + 2*q**2 + 0 + q**3 - 3/10*q**5. Factor v(r).
2*(r - 1)**2*(r + 1)*(5*r + 2)
Let u = -5 - -8. Let y(t) be the second derivative of t**4/12 + t**2 + t. Let j(a) = 2*a**2 + 5. Let s(n) = u*j(n) - 7*y(n). Let s(m) = 0. Calculate m.
-1, 1
Suppose -2*n = n - 9. Solve 0*o**2 + 3/2*o - 2*o**n - 1/2 = 0 for o.
-1, 1/2
Factor -5/2*m**4 - 1/4*m + 0 - 3*m**3 - 3/4*m**5 - 3/2*m**2.
-m*(m + 1)**3*(3*m + 1)/4
Let r(x) be the second derivative of x**6/240 - x**5/120 - x**4/24 + 2*x**2 - 6*x. Let c(h) be the first derivative of r(h). Factor c(b).
b*(b - 2)*(b + 1)/2
Let z be 385/(-528) + (-2)/(-3). Let k = z + 21/80. Factor -k - 1/5*j**2 + 2/5*j.
-(j - 1)**2/5
Factor -6*h**2 + 21/4*h + 3/4.
-3*(h - 1)*(8*h + 1)/4
Let o = 340/1141 - 2/163. What is t in 0 + 2/7*t + 0*t**2 - o*t**3 = 0?
-1, 0, 1
Let n be ((-7)/(-2))/(2/48). Let d be 66/n - 2/4. Suppose -d*j**2 + 0 - 2/7*j = 0. What is j?
-1, 0
Let n be (-8)/(-44) + (-40)/(-22). Let -6/5*x + 0*x**n + 2/5*x**3 + 4/5 = 0. Calculate x.
-2, 1
Find j, given that 8/9*j - 8/9*j**2 + 4/9*j**4 + 2/9*j**5 + 0 - 2/3*j**3 = 0.
-2, 0, 1
Let w = -7 - -7. Let y(o) be the first derivative of -2/3*o**3 + 0*o**2 + 1/3*o**6 + w*o + 2/5*o**5 + 2 - 1/2*o**4. Factor y(v).
2*v**2*(v - 1)*(v + 1)**2
Let i(u) be the first derivative of u**4 + 4*u**3 + 4*u**2 - 5. Determine b so that i(b) = 0.
-2, -1, 0
Let u be -3 - ((-22)/5 - (-4 + 4)). Factor 0 + 8/5*a**3 - u*a**2 + 2/5*a - 3/5*a**4.
-a*(a - 1)**2*(3*a - 2)/5
Let g(r) be the first derivative of 7*r**5/80 - r**4/24 - 4*r + 3. Let z(m) be the first derivative of g(m). Factor z(l).
l**2*(7*l - 2)/4
Let y be (5 - 4)*(-1 + 0). Let l be ((0 + 0)/(-1))/y. Factor 0 + l*s + 2/5*s**2.
2*s**2/5
Let z(t) = -t**3 + 4*t**2 + 2*t**3 + 2*t - 5*t. Let y be z(-4). Factor -8*r**3 + 5*r**4 - 3*r**4 + 2 + y*r**2 - 8*r + 0*r**4.
2*(r - 1)**4
Let w(m) be the first derivative of -4*m**5/5 + 8*m**3/3 - 4*m - 5. Factor w(f).
-4*(f - 1)**2*(f + 1)**2
Let x = -15 - -5. Let b = x - -5. Let v(w) = -5*w**2 + 12*w + 9. Let a(g) = -4*g**2 + 11*g + 9. Let y(o) = b*v(o) + 6*a(o). Determine u so that y(u) = 0.
-3
Let t(v) be the third derivative of v**5/140 - v**4/56 - v**3/7 - 12*v**2. Factor t(d).
3*(d - 2)*(d + 1)/7
Factor 6/7*p - 3/7*p**2 + 9/7.
-3*(p - 3)*(p + 1)/7
Find n such that -4/7 - 2/7*n + 2/7*n**2 = 0.
-1, 2
Find l such that -l + 2*l**3 + 3*l**3 - l**3 - 3*l**3 + l**2 - l**4 = 0.
-1, 0, 1
Let m(p) = -4 + 3 - 1 + 5*p + 7 - 6*p**2. Let i(v) = 7*v**2 - 6*v - 6. Let g(k) = -5*i(k) - 6*m(k). Factor g(q).
q**2
Factor -17*k**2 + 45*k**2 - 18*k**2 + 10*k**4 + 10*k**4 + 25*k**3 + 5*k**5.
5*k**2*(k + 1)**2*(k + 2)
Suppose 0 = -3*v + 5 + 4. Let x = v + 2. Factor -2*i - 3*i**3 + 3*i**4 + x*i**2 - i**3 - 2*i**4.
i*(i - 2)*(i - 1)**2
Let z(n) be the second derivative of n**5/130 - n**4/78 - n**3/39 + n**2/13 - 16*n. Suppose z(q) = 0. What is q?
-1, 1
Suppose 12 = 2*l + l. Suppose -2*q = 2*s, -5*q - l*s + 5 = 2. Factor -19*p**3 + 0*p + q*p + 13*p**3 + 3*p**5.
3*p*(p - 1)**2*(p + 1)**2
Let z(k) be the first derivative of k**5/240 - k**4/48 - 3*k**2/2 - 3. Let l(u) be the second derivative of z(u). Factor l(s).
s*(s - 2)/4
Suppose -5*y + 30 = 5*z, z + 4*y = -3 + 18. Factor -i**3 + i**4 + 0*i**4 - 4*i - 1 + 2*i + z*i**3.
(i - 1)*(i + 1)**3
Let 8/13*q**2 - 2/13*q - 12/13*q**3 + 8/13*q**4 - 2/13*q**5 + 0 = 0. What is q?
0, 1
Let s be (-6)/9 - (129/36 - 5). Factor -s*j**5 + 0 + 0*j + 3/4*j**2 - 3/4*j**4 + 3/4*j**3.
-3*j**2*(j - 1)*(j + 1)**2/4
Let n(b) be the first derivative of -3 - 8/15*b + 16/15*b**2 - 5/6*b**4 - 2/9*b**3. Let n(r) = 0. Calculate r.
-1, 2/5
Factor -8/11*b**2 - 8/11*b - 2/11*b**3 + 0.
-2*b*(b + 2)**2/11
Let b(m) be the third derivative of m**7/1050 + m**6/300 - m**5/100 - m**4/30 + 2*m**3/15 - 19*m**2. Solve b(n) = 0 for n.
-2, 1
Let c(n) be the first derivative of 1/2*n**2 - 2/3*n**3 - 1/5*n**5 - 1/5*n + 1/2*n**4 + 5 + 1/30*n**6. What is a in c(a) = 0?
1
Suppose -3*l - 4 + 10 = 0. Factor 3*r**2 - r**2 + 0*r**l - 3*r - 3*r**3 - 8*r**2.
-3*r*(r + 1)**2
Let b(g) = g**3 - 7*g**2 + 18*g - 70. Let i be b(6). Factor -3/5*t**3 + 3/5*t + 6/5*t**i - 6/5.
-3*(t - 2)*(t - 1)*(t + 1)/5
Let g be 5 + 1 - (1 + -1). Factor 4*v**4 + 2*v**3 - 2*v - g*v**4 + v**4 + 1.
-(v - 1)**3*(v + 1)
Let q(a) be the second derivative of -a**6/120 + 3*a**5/80 - a**4/24 - 5*a. What is x in q(x) = 0?
0, 1, 2
Let a(d) be the second derivative of 3*d - d**3 + 0 - 2*d**2 - 1/6*d**4. Determine b so that a(b) = 0.
-2, -1
Let r(l) be the first derivative of l**7/210 - l**5/30 + l**3/6 - 5*l**2/2 - 2. Let i(q) be the second derivative of r(q). Suppose i(k) = 0. What is k?
-1, 1
Factor 0*w - 24/5*w**2 + 21/5*w**3 + 0 + 3/5*w**4.
3*w**2*(w - 1)*(w + 8)/5
Let u(j) be the third derivative of 0*j + 0 - 7*j**2 + 13/108*j**4 + 2/27*j**5 + 1/60*j**6 + 2/27*j**3. Determine b so that u(b) = 0.
-1, -2/9
Let a(m) be the first derivative of -m**5/15 - m**4/4 - m**3/3 - m**2/6 + 32. Factor a(t).
-t*(t + 1)**3/3
Let t(k) be the second derivative of k**4/84 - 2*k**2/7 + 41*k. Factor t(v).
(v - 2)*(v + 2)/7
Let c(k) = -3*k**3 + 18*k**2 - 21*k + 12. Let m(a) = -24 - 28*a**2 - 7*a**2 + 6*a**3 - 14*a + 57*a. Let i(b) = -5*c(b) - 3*m(b). Factor i(r).
-3*(r - 2)**2*(r - 1)
Let a(k) = k - 4. Let r be a(6). Suppose 21 = m - 3*m + 5*i, 3*m = -4*i + 26. Factor -4*h**r + h**2 + 4*h**m - h.
h*(h - 1)
Let a(y) be the third derivative of y**5/90 + y**4/18 - y**3/3 + 3*y**2. Factor a(r).
2*(r - 1)*(r + 3)/3
Let i(c) be the first derivative of -2*c - 2/3*c**3 - 2 - 2*c**2. Factor i(g).
-2*(g + 1)**2
Suppose 4*j - 5*l - 41 = 0, 3*l + 10 = 3*j - 17. Find g such that 1 - 2*g**2 - 4*g + 1 - j = 0.
-1
Let z be (-48)/(-252)*7/(-3) - -4. Find o, given that 0 + 2/9*o**2 + 16/9*o**3 + 0*o + z*o**5 + 40/9*o**4 = 0.
-1/2, -1/4, 0
Let b(p) be the first derivative of -p**6/180 - p**5/60 + p**4/6 + 2*p**3 + 5. Let w(j) be the third derivative of b(j). Suppose w(g) = 0. What is g?
-2, 1
Let g(j) be the third derivative of j**8/112 + j**7/70 - j**6/40 - j**5/20 - 3*j**2. Suppose g(s) = 0. What is s?
-1, 0, 1
Let w(u) be the second derivative of 2*u**7/105 - 4*u**6/75 + 2*u**4/15 - 2*u**3/15 + 2*u. What is c in w(c) = 0?
-1, 0, 1
Let l(b) be the second derivative of -b**9/25200 + b**8/11200 + b**4/3 + 4*b. Let w(s) be the third derivative of l(s). Factor w(j).
-3*j**3*(j - 1)/5
Let 27*l**2 + 18*l**2 + 5*l**4 + 13*l**3 + 35*l + 12*l**3 + 10 = 0. What is l?
-2, -1
Let v be (13 - 4)/3 - 0. Let o(m) be the first derivative of -2/21*m**v + 1/7*m**2 + 0*m - 2. Factor o(f).
-2*f*(f - 1)/7
Let v(j) = -j**3 - 26*j**2 + 2*j + 56. Let o be v(-26). Let c = -7 - -12. Let -1/4*m**c + 0*m**3 + 0 + 1/4*m + 1/2*m**2 - 1/2*m**o = 0. What is m?
-1,