e the third derivative of 0*j**3 - 4*j**2 + 1/60*j**4 - 1/75*j**o + 0*j + 1/300*j**6 + 0. Find i such that h(i) = 0.
0, 1
Let g = -6 + 11. Suppose g*s + 1 = 11. Factor 0*c + 0 + 1/2*c**3 - 1/2*c**s.
c**2*(c - 1)/2
Suppose 12*x - 147*x**5 - 180*x**3 - 2283*x**2 + 2559*x**2 - 35*x - 651*x**4 - 25*x = 0. What is x?
-4, -1, 0, 2/7
Let b be ((-4)/(-12))/(4/6). Suppose -2 = -2*y + 6. Factor 0 - 1/2*k**5 - 1/2*k**2 + b*k**y + 1/2*k**3 + 0*k.
-k**2*(k - 1)**2*(k + 1)/2
Suppose -3*d - 6*d = 6*d. Let b(q) be the third derivative of q**2 + 0*q + 0 + d*q**3 + 1/100*q**6 - 1/75*q**5 - 1/525*q**7 + 0*q**4. Let b(k) = 0. Calculate k.
0, 1, 2
Let c(p) be the second derivative of -p**9/15120 + p**8/13440 + p**4/4 - 3*p. Let t(q) be the third derivative of c(q). Determine w, given that t(w) = 0.
0, 1/2
Let r be 1 - (0 + -3 - -1). Suppose 4*y + 12 = i, -3*y - 12 = r*i - 3. Determine g, given that 1/3*g**3 - 1/3*g**2 + i + 0*g = 0.
0, 1
Find v such that -188*v**3 - 2*v**4 + 190*v**3 + 2*v - 5*v + 2*v**2 + v = 0.
-1, 0, 1
Let u be 18/240*8/30. Let g(v) be the third derivative of -u*v**5 + 0*v + 1/100*v**6 + 0 + 1/60*v**4 + 2*v**2 - 1/525*v**7 + 0*v**3. Let g(r) = 0. Calculate r.
0, 1
Let x = 1753/4 + -438. Factor 1/4*u**2 - 1/4*u**3 - 1/4 + x*u.
-(u - 1)**2*(u + 1)/4
Let b(x) be the second derivative of -x**5/120 - 3*x. Suppose b(t) = 0. Calculate t.
0
Suppose 0 = 2*j + 5*f - 15, -6*j + j = 2*f - 6. Factor 2/3 + j*n - 2/3*n**2.
-2*(n - 1)*(n + 1)/3
Let j be (-4)/18 - 169/(-234). Let w(t) be the first derivative of 0*t + 2/5*t**5 - 2/3*t**3 + j*t**4 + 2 - t**2. Let w(b) = 0. What is b?
-1, 0, 1
Let q = 7 + -5. Solve -q*i + 6*i**2 - 2*i**2 + 1 - 3*i**2 = 0.
1
Suppose 0 = 4*c - 4*z - 16, -c - 4*z - 3 = -2. Let v(k) be the first derivative of 0*k**c - 12*k + 12*k**2 + 3 + 0*k**3 - 2*k**3 - k**3. Solve v(l) = 0.
2/3, 2
Suppose 0 = -5*i, 5*g + 2*i = g + 8. Solve -1/4*a**3 + 0 + 1/4*a**g + 1/4*a - 1/4*a**4 = 0.
-1, 0, 1
Suppose 37 = 4*v - 27. Factor 20*q - 60*q**2 + v*q - 12*q**4 - 3 - 5 + 44*q**3.
-4*(q - 1)**3*(3*q - 2)
Let y = -17 - -89/5. Suppose 1/5*v + 0 - 3/5*v**3 + 4/5*v**5 + y*v**4 - 2/5*v**2 = 0. What is v?
-1, 0, 1/2
Let s = -161 + 163. Find p such that -2*p + 3*p**s - 2*p**3 + 1/2 + 1/2*p**4 = 0.
1
Suppose -j = -4*j - 3*i - 12, 3*j + 15 = -2*i. Let l = j + 9. Let 5 - 2*z**4 + 3 - l*z - 6 - 2*z + 4*z**3 = 0. What is z?
-1, 1
Suppose -4*w + 20 = w. Determine p so that -4*p**3 + 29*p**4 + 3*p**5 + 7*p**3 - 35*p**w = 0.
0, 1
Let j be -4 + (5 - (-8)/(-20)). Let 0 + 3/5*z + j*z**3 - 6/5*z**2 = 0. What is z?
0, 1
Let a(u) be the third derivative of u**10/151200 - u**8/16800 + u**6/3600 - 3*u**4/8 - 2*u**2. Let r(d) be the second derivative of a(d). Factor r(j).
j*(j - 1)**2*(j + 1)**2/5
Let s be (-63)/(-54) - 2/4. Let w(u) be the second derivative of 0 + s*u**3 + 2*u - 2*u**2 - 1/12*u**4. Factor w(o).
-(o - 2)**2
Let z(r) be the third derivative of 0 - 7*r**2 + 1/120*r**5 + 0*r + 1/1344*r**8 + 0*r**3 - 1/96*r**4 + 0*r**6 - 1/420*r**7. Factor z(n).
n*(n - 1)**3*(n + 1)/4
Let k(z) be the second derivative of 4*z + 0 + 1/18*z**3 + 0*z**2 - 1/72*z**4. Factor k(m).
-m*(m - 2)/6
Let h(w) be the second derivative of w**6/30 - 9*w**5/20 + 9*w**4/4 - 9*w**3/2 + 26*w. Factor h(j).
j*(j - 3)**3
Factor 2/3*x**2 - 26/3*x + 8.
2*(x - 12)*(x - 1)/3
Let w(y) = -5*y + 1. Let r be w(2). Let q(h) = -h**2 + 4*h + 1. Let i(d) = 3*d**2 - 17*d - 4. Let g(a) = r*q(a) - 2*i(a). Suppose g(b) = 0. What is b?
-1/3, 1
Let j(o) be the first derivative of -3*o**4/4 - o**3 + 3*o**2/2 + 3*o + 2. Factor j(p).
-3*(p - 1)*(p + 1)**2
Let l(i) be the first derivative of -6*i**5/5 + i**4/2 + 4*i**3/3 - 20. Factor l(h).
-2*h**2*(h - 1)*(3*h + 2)
Suppose -7*w + 4 + 17 = 0. Determine y, given that 2/7*y**4 + 2/7*y**w - 2/7*y**5 - 2/7*y**2 + 0 + 0*y = 0.
-1, 0, 1
Suppose -2*s + 36 = -0*s. Determine m, given that 3 + s*m**2 + 3*m**4 + 3*m + 12*m**3 + 0*m**2 + 9*m = 0.
-1
Factor -3*z**2 + 10 - 5 - 3*z + 13.
-3*(z - 2)*(z + 3)
Let t(y) be the third derivative of -y**6/24 + 13*y**5/36 - 10*y**4/9 + 10*y**3/9 - 8*y**2. Find d such that t(d) = 0.
1/3, 2
Let g be (-1)/3 + (-46)/(-15). Let x = g + -12/5. Factor r + x*r**2 + 2/3.
(r + 1)*(r + 2)/3
Let n = 6 - 3. Let -2*u**4 + 3*u**4 + 2*u**3 + 2*u**3 - 3*u**n = 0. Calculate u.
-1, 0
Let d be 3/(-42)*-7*1. Factor 0 + 0*u + d*u**2 - 1/2*u**3.
-u**2*(u - 1)/2
Let b(r) be the second derivative of -r**9/4536 + r**8/2520 + r**7/252 + r**6/180 + r**3/3 + 7*r. Let h(j) be the second derivative of b(j). Factor h(p).
-2*p**2*(p - 3)*(p + 1)**2/3
Let f(i) be the first derivative of -4 - 1/3*i**6 + 0*i + 1/2*i**4 + 0*i**2 + 2/5*i**5 - 2/3*i**3. Factor f(m).
-2*m**2*(m - 1)**2*(m + 1)
Suppose -p = 1 - 3. Let q be (-1)/(1 - p) - -1. Factor 4/3*f**q - 5/3*f + 1/3.
(f - 1)*(4*f - 1)/3
Suppose 3 = 5*n - 27. Solve -1 - n + k**2 + 6 = 0 for k.
-1, 1
Suppose -6 = -0*b - b. Suppose -5*h - b = -16. Let 1/2 + 0*a - 1/2*a**h = 0. What is a?
-1, 1
Determine a so that -2*a**3 + 68/7*a - 16/7 - 38/7*a**2 = 0.
-4, 2/7, 1
Let r(i) = i**3 + i + 1. Let b(n) = -8*n**3 - 15*n**2 - 3*n - 3. Let h(o) = -b(o) - 3*r(o). Factor h(y).
5*y**2*(y + 3)
Suppose 3*x = 2*v - 1, -2*x = 2*v - 6 - 0. Let q be 2/(-3) + (-1)/(-1). Factor 1/3 - q*s**v + 1/3*s**3 - 1/3*s.
(s - 1)**2*(s + 1)/3
Let u(k) be the second derivative of k**6/40 - 9*k**5/80 + k**4/16 + 3*k**3/8 - 3*k**2/4 - 3*k. Solve u(i) = 0.
-1, 1, 2
Let o(f) = -17*f**5 - 41*f**4 - 31*f**3 - 7*f**2. Let p(b) = -6*b**5 - 14*b**4 - 10*b**3 - 2*b**2. Let q(w) = 4*o(w) - 11*p(w). Factor q(i).
-2*i**2*(i + 1)**2*(i + 3)
Factor 15*s - 18*s - 2*s**4 + 5*s**4 - 3*s**2 + 3*s**3.
3*s*(s - 1)*(s + 1)**2
Let f(x) be the third derivative of -x**5/80 - x**4/32 + x**3/4 - 7*x**2. Find s such that f(s) = 0.
-2, 1
Let g(j) = -j**2 + 20*j + 4. Let m be g(20). Let k(v) be the second derivative of 1/6*v**3 + 0 + 1/6*v**m - 1/2*v**2 + v. Factor k(o).
(o + 1)*(2*o - 1)
Let v(a) be the third derivative of 7*a**5/90 - a**4/9 - 11*a**2. Factor v(q).
2*q*(7*q - 4)/3
Let y(a) be the second derivative of 22/5*a**5 - 5*a + 0 + 0*a**3 - 2/3*a**4 - 121/15*a**6 + 0*a**2. Let y(v) = 0. Calculate v.
0, 2/11
Let r(m) = m**3 - 3*m**2 + m + 4. Let u be r(2). Let d(j) be the third derivative of -j**u + 0 + 0*j + 1/24*j**4 + 0*j**3 + 1/20*j**5 - 1/30*j**6. Factor d(k).
-k*(k - 1)*(4*k + 1)
Let q(d) be the second derivative of d**4/30 - d**3/15 - 6*d**2/5 + 12*d. Solve q(z) = 0.
-2, 3
Let o(z) be the first derivative of -z**5/180 + z**4/72 + 3*z**2/2 - 2. Let r(x) be the second derivative of o(x). Let r(m) = 0. Calculate m.
0, 1
Determine i so that 0 - 1/8*i**2 + 0*i - 1/8*i**3 = 0.
-1, 0
Let z(h) be the third derivative of h**6/120 - h**5/30 + h**4/24 + 63*h**2. Suppose z(a) = 0. What is a?
0, 1
Let l(p) = 2*p**3 + 9*p**2 - 2*p - 22. Let m be l(-4). Let 1/6*z**m + 0*z + 0 = 0. What is z?
0
Let f be 2 - 6/3 - -2. Suppose d = -f*d. Factor d + 0*c + 0*c**2 - 1/2*c**4 - 1/2*c**3.
-c**3*(c + 1)/2
Let q = -23 + 34. Let c = q + -5. Factor -2*m - c*m**2 + 4*m**2 + 4*m**2.
2*m*(m - 1)
Let b(v) be the third derivative of 0 + 1/24*v**3 - 6*v**2 + 1/240*v**5 + 0*v - 1/48*v**4. What is u in b(u) = 0?
1
Let c = -3 - -6. Factor c - 2 + j**2 - 2*j**2.
-(j - 1)*(j + 1)
Let l(m) = -18*m**4 + 2*m**3 - 14*m**2 + 2*m + 12. Let t(w) = -w**4 + w**3 - w**2 + 1. Let v(s) = l(s) - 12*t(s). Factor v(u).
-2*u*(u + 1)**2*(3*u - 1)
Let t(h) be the second derivative of -5*h**6/24 + 7*h**5/8 - 11*h**4/12 + h**3/3 - 7*h. Solve t(j) = 0 for j.
0, 2/5, 2
Let a = 22/9 - 107/45. Let u(i) be the second derivative of 4/75*i**6 - 1/105*i**7 + 0*i**2 - 3/25*i**5 - a*i**3 + 2/15*i**4 + i + 0. Factor u(o).
-2*o*(o - 1)**4/5
Let f(i) be the third derivative of -1/30*i**3 + 1/300*i**5 - 1/600*i**6 - 3*i**2 + 0 + 1/120*i**4 + 0*i. Let f(h) = 0. What is h?
-1, 1
Let z(r) = 2*r**2 + 19*r + 29. Let h(t) = -8*t**2 - 75*t - 117. Let p(u) = -6*h(u) - 22*z(u). Solve p(i) = 0 for i.
-4
Let o(l) be the second derivative of l**6/120 + 3*l**5/80 + l**4/24 - 19*l + 1. Factor o(x).
x**2*(x + 1)*(x + 2)/4
Let w(v) be the second derivative of v**7/280 - 2*v**3/3 + 5*v. Let k(h) be the second derivative of w(h). Let k(j) = 0. Calculate j.
0
Factor 2/5*l - 2/5*l**2 + 0.
-2*l*(l - 1)/5
Suppose -4/3*t + 0*t**3 + 0 - 8/3*t**4 + 8/3*t**2 + 4/3*t**5 = 0. Ca