e the third derivative of -f**5/240 - f**4/32 + 10*f**2. Let q(w) = 0. What is w?
-3, 0
Let z(b) be the second derivative of -b**4/6 + 2*b**3/3 - b**2 - 2*b. Determine o, given that z(o) = 0.
1
Let l = -7 - -11. Suppose -2*v = 8, 5*k + 0*v - l*v = 21. Factor 2*o**3 - 3*o**4 + 0*o**2 + k + o**5 + 3*o**2 - o**2 - 3*o.
(o - 1)**4*(o + 1)
Let c(p) = 3*p**3 - p. Let w be c(1). Let s be 100/36 - w/(-9). Factor -2 + 2*b**2 - b - b + 2*b**3 + 0*b**s.
2*(b - 1)*(b + 1)**2
Factor z**2 + 4 - 8*z + 5*z - z.
(z - 2)**2
Determine q, given that -4*q + 8*q**5 - 4*q**2 - 6*q**3 + 3*q - 30*q**4 + 3*q + 38*q**4 = 0.
-1, 0, 1/2
Let k(o) be the second derivative of -o**6/150 + o**4/60 + 23*o. Factor k(c).
-c**2*(c - 1)*(c + 1)/5
Factor 0*r + 0 + r**4 - 2/3*r**2 + 1/3*r**3.
r**2*(r + 1)*(3*r - 2)/3
Let x(n) be the first derivative of -2 + 2*n - 1/12*n**3 + 1/4*n**2 - 1/24*n**4 + 1/40*n**5. Let f(o) be the first derivative of x(o). Factor f(g).
(g - 1)**2*(g + 1)/2
Let k(w) be the first derivative of -w**6/2 + 3*w**4/4 - 6. Find l, given that k(l) = 0.
-1, 0, 1
Factor -2/9 - 2/9*c**2 + 4/9*c.
-2*(c - 1)**2/9
Let z(c) be the second derivative of c**5/30 + c**4/6 + c**3/3 + c**2/3 + 20*c. Factor z(t).
2*(t + 1)**3/3
Let p = 33/5 - 94/15. Let f(j) be the first derivative of -1 - 4/9*j**3 + 0*j + p*j**2. Factor f(y).
-2*y*(2*y - 1)/3
Let i(z) be the first derivative of 2*z + 4 - 1/20*z**4 - 1/10*z**2 - 2/15*z**3. Let u(c) be the first derivative of i(c). Factor u(p).
-(p + 1)*(3*p + 1)/5
Determine k so that -44*k**2 + 0*k**4 + 2*k - k**4 - 3*k**4 - 2*k**3 + 48*k**2 = 0.
-1, -1/2, 0, 1
Let u(h) = -h**2 - 2*h + 1. Suppose -5*n + 6 = 4*v + 34, -n + 4 = -4*v. Let y(l) = l**2. Let j(s) = v*y(s) - u(s). What is k in j(k) = 0?
1
Let g = 3/55 - -376/165. Factor v**5 + 2*v**2 - g*v**4 + 2/3*v**3 + 1/3 - 5/3*v.
(v - 1)**3*(v + 1)*(3*v - 1)/3
Suppose 0 = 9*h - 14*h + 15. Factor 0 - 2/7*i**4 + 0*i + 0*i**h + 2/7*i**2.
-2*i**2*(i - 1)*(i + 1)/7
Let p(b) = -6*b**4 - 6*b**3 + 3*b**2 - 3*b. Let k(f) = -7*f**4 - 7*f**3 + 4*f**2 - 4*f. Let d(w) = w. Let i be d(3). Let j(m) = i*k(m) - 4*p(m). Factor j(v).
3*v**3*(v + 1)
Let b(y) = -y**2 + 9. Let k be b(3). Let o(q) be the second derivative of 1/36*q**4 + 0*q**3 + 0*q**2 + k + 1/60*q**5 - 2*q. Solve o(l) = 0 for l.
-1, 0
Let w(y) be the first derivative of 2*y**3/3 + 6*y**2 + 18*y - 9. What is n in w(n) = 0?
-3
Let n(l) = 9*l**4 - 5*l**3 - 2*l**2 - 17*l + 4. Suppose 0 = -3*v + 7*v - 88. Let k(f) = -f**4 + f**3 + f. Let u(w) = v*k(w) + 2*n(w). Factor u(o).
-4*(o - 2)*(o - 1)**2*(o + 1)
Determine l so that l**3 - 2*l + 4*l - 3*l**3 = 0.
-1, 0, 1
Let b = 205/3 - 68. What is m in 0 - b*m**2 + 1/3*m**4 + 1/3*m - 1/3*m**3 = 0?
-1, 0, 1
Let b = 5/42 + 3/14. Suppose 4*z + 5*p = 11 + 7, -3*z + 2 = -2*p. Factor b - 1/3*l**z + 0*l.
-(l - 1)*(l + 1)/3
Let x be 3 - (-4 - -4)/(-1). Let w(f) be the first derivative of 0*f + 3 - 1/4*f**2 - 1/6*f**x. Factor w(z).
-z*(z + 1)/2
Let u(l) be the first derivative of 1/3*l**2 + 2/9*l**3 + 0*l + 2. Factor u(v).
2*v*(v + 1)/3
Let f(v) be the second derivative of 0 - 2/45*v**6 - 1/12*v**5 + 1/12*v**4 + 1/6*v**2 + 4*v + 5/18*v**3. Find c such that f(c) = 0.
-1, -1/4, 1
Factor 3*n**3 - 3*n**4 + n**2 + 4*n**5 - 3*n**5 - 2*n**2.
n**2*(n - 1)**3
Let s(l) be the second derivative of l**6/1980 + l**5/660 + l**3/2 - 3*l. Let r(m) be the second derivative of s(m). Solve r(f) = 0.
-1, 0
Suppose b = -1 + 3. Determine r, given that 0*r**2 + 5*r**b + 12*r + 7*r**2 + 4*r**3 + 4 = 0.
-1
Factor 16*o**2 + 2*o**2 - 23 + 7*o**2 + 15*o + 5*o**3 - 22.
5*(o - 1)*(o + 3)**2
Determine z so that 0 + 1/3*z**2 - 2/3*z + 1/3*z**3 = 0.
-2, 0, 1
Let r(d) be the third derivative of d**2 + 0 + 5/24*d**4 + 0*d + 1/30*d**5 + 1/3*d**3. Suppose r(l) = 0. Calculate l.
-2, -1/2
Let j(u) = u**4 - u**3. Let q(w) = 2*w**5 - 15*w**4 + 31*w**3 - 32*w**2 + 18*w - 4. Let p(h) = -3*j(h) - q(h). Let p(i) = 0. Calculate i.
1, 2
Let p(v) = -v**3 - 12*v**2 - 11*v + 3. Let k be p(-11). Let x = 2/5 + -1/15. Factor -1/3*g + x*g**k - 1/3*g**2 + 1/3.
(g - 1)**2*(g + 1)/3
Let c be ((-1)/(-4) + 12/(-144))/1. Factor -c*x**3 + 1/3*x**2 - 1/6*x + 0.
-x*(x - 1)**2/6
Let z(j) be the first derivative of 25/16*j**4 - 3 - 2*j - 5/2*j**3 - 9/2*j**2. Let z(u) = 0. Calculate u.
-2/5, 2
Let o = -134/3 + 415/6. Let 4 + 22*c + o*c**4 + 9*c**2 - 119/2*c**3 = 0. What is c?
-2/7, 1, 2
Let o(t) be the second derivative of t**4/30 - t**3/15 - 6*t**2/5 + 34*t. Factor o(z).
2*(z - 3)*(z + 2)/5
Let a(x) = 15*x + 5. Let c be a(-3). Let w = c + 42. Determine q, given that -2*q + 4/3 - 10/3*q**w = 0.
-1, 2/5
Determine h so that -34/3*h**3 + 8/3*h**4 + 0 + 7/3*h**2 + 4/3*h = 0.
-1/4, 0, 1/2, 4
Let f(m) be the second derivative of -m**6/30 + 7*m**5/20 - 5*m**4/4 + 3*m**3/2 - 2*m. Suppose f(u) = 0. What is u?
0, 1, 3
Let 3/5*t**2 + 12/5*t + 4/5 - t**3 = 0. Calculate t.
-1, -2/5, 2
Suppose -9 = 5*f + 1. Let o be 3*1*(-1 - f). Suppose 2*w**2 + 1/2*w**o + 0 - 1/2*w - 2*w**4 = 0. Calculate w.
-1, 0, 1/4, 1
Let k(i) be the third derivative of 1/32*i**4 - 1/240*i**6 + 3*i**2 + 0*i + 1/120*i**5 + 0 - 1/1344*i**8 + 1/24*i**3 - 1/280*i**7. Factor k(v).
-(v - 1)*(v + 1)**4/4
Let h(w) be the first derivative of -2*w**3/21 - 4*w**2/7 - 8*w/7 - 6. What is d in h(d) = 0?
-2
Let a = 139 - 1667/12. Let l(z) be the second derivative of 1/24*z**3 - a*z**4 + 3/80*z**5 - 2*z + 0 + 0*z**2. Factor l(h).
h*(h - 1)*(3*h - 1)/4
Let g(z) be the first derivative of 5*z**6/18 + 4*z**5/3 + 25*z**4/12 + 10*z**3/9 - 2. Factor g(r).
5*r**2*(r + 1)**2*(r + 2)/3
Determine j, given that -2/7*j**2 + 4/7*j + 0 = 0.
0, 2
Suppose 2*y + 14 = -2. Let m = 11 + y. Find c such that 2*c - m*c**2 - 6*c + 5*c**2 = 0.
0, 2
Suppose 0 = -v - 0*v. Let w be v/((-2)/(-2))*-1. Factor -2/9*a + w - 2/9*a**2.
-2*a*(a + 1)/9
Let p be 1/((-4)/8)*(-3)/3. Factor -1/5*g**p + 3/5*g + 0.
-g*(g - 3)/5
Let d(y) be the second derivative of y**5/70 - y**3/21 + 4*y. What is b in d(b) = 0?
-1, 0, 1
Let h(u) be the first derivative of 0*u**2 - 4/27*u**3 - 1/18*u**4 + 0*u - 4. Factor h(q).
-2*q**2*(q + 2)/9
Suppose 15*u - 6*u = 18. Factor 5/2*p**u - 1 - 3/2*p.
(p - 1)*(5*p + 2)/2
Suppose 192 = -3*k - k. Let o be k/(-20) - (-4)/(-10). Find i, given that 0*i**2 - i**2 - i**o + 2*i**4 = 0.
-1, 0, 1
Suppose 11 = 4*w - 5. Let h be (-1)/w - 5/(-10). Solve -h*t**2 + 1/4 + 0*t = 0.
-1, 1
Suppose 49 = 4*k - 15. Let w be (-40)/k + 2*2. What is v in v**3 - v**2 - 1/2 - w*v + 1/2*v**5 + 3/2*v**4 = 0?
-1, 1
Let f(r) = 9*r**2 - r. Let d be (-37)/7 + (-6)/(-21). Let o(u) = -7*u + 0*u + 13*u**2 + 6*u. Let i(s) = d*o(s) + 7*f(s). Factor i(h).
-2*h*(h + 1)
Let h(w) be the first derivative of 1/2*w**2 + w**3 + 3/4*w**4 + 2 + 0*w + 1/5*w**5. Solve h(q) = 0 for q.
-1, 0
Let h(i) be the second derivative of -i**4/28 - i**3 + 45*i**2/14 + 25*i. Factor h(t).
-3*(t - 1)*(t + 15)/7
Let m(k) be the second derivative of -k**8/3360 + k**6/120 + k**5/30 - k**4/4 - 5*k. Let x(z) be the third derivative of m(z). Factor x(a).
-2*(a - 2)*(a + 1)**2
Let u be (-1 + 7)*(-17)/8. Let s = u + 13. Factor 1/4*d**3 + s*d**2 + 0 - 1/4*d**4 - 1/4*d**5 + 0*d.
-d**2*(d - 1)*(d + 1)**2/4
Let c(q) = -16*q**5 + 12*q**4 + 4*q**3 + 12*q**2 + 12. Let o(j) = -j**2 + 0*j**4 - 2*j**3 - j**4 + 2*j**3 - 1 + j**5. Let m(s) = -c(s) - 12*o(s). Factor m(x).
4*x**3*(x - 1)*(x + 1)
What is j in 2*j**5 - j**5 + j**2 - 2*j**4 + 3*j**3 - 2*j**2 - j**4 = 0?
0, 1
Let k be (-15)/(-18) + 2/(-6). Let u(o) be the first derivative of 0*o - 1 + k*o**2 + 1/6*o**3. Let u(f) = 0. What is f?
-2, 0
Let a(l) be the first derivative of 2*l**5/105 + l**4/7 + 8*l**3/21 + 10*l**2/21 + 2*l/7 - 1. Factor a(j).
2*(j + 1)**3*(j + 3)/21
Determine q so that 0 + 0*q + 5/2*q**3 + q**2 = 0.
-2/5, 0
Let d(i) = 44*i**2 - 140*i + 144. Let h(t) = -9*t**2 + 28*t - 29. Let p(v) = -5*d(v) - 24*h(v). Find b such that p(b) = 0.
1, 6
Let f(i) be the second derivative of 1/90*i**5 + 2/27*i**4 + i + 2/9*i**2 + 5/27*i**3 + 0. Factor f(m).
2*(m + 1)**2*(m + 2)/9
Let n(d) be the second derivative of -3*d + 0 + 0*d**3 - 1/6*d**4 + 1/20*d**5 + 0*d**2. Factor n(x).
x**2*(x - 2)
Let c = 1 + 0. Let f(i) = 2*i**3 + 3*i**2 + 5*i - 5. Let t(l) = -l**2 - l + 1. Let y(w) = c*f(w) + 5*t(w). Factor y(m).
2*m**2*(m - 1)
Determine t, given that 10/3*t - 10/3*t**3 + 2*t**2 + 2/3*t**4 -