
Let r(d) be the third derivative of 0*d + 0*d**3 + 0 + 1/120*d**5 + 1/240*d**6 - 5*d**2 + 0*d**4. Find k, given that r(k) = 0.
-1, 0
Let p(h) be the third derivative of h**7/105 - h**5/10 - h**4/6 + 4*h**2. Let p(t) = 0. What is t?
-1, 0, 2
Let x(r) = -8*r**2 - 137*r - 13. Let l be x(-17). Factor 0 + 1/2*q**2 + 0*q - 1/2*q**l + 0*q**3.
-q**2*(q - 1)*(q + 1)/2
Let p(w) be the third derivative of -w**8/336 - 2*w**7/105 - w**6/20 - w**5/15 - w**4/24 + 4*w**2. Factor p(v).
-v*(v + 1)**4
Suppose 0 = 3*i + 5*h - 22, -6*h = 2*i - 3*h - 14. Let -1/4*n**i - 1/4*n + 3/4*n**2 + 1/4*n**3 - 1/2 = 0. Calculate n.
-1, 1, 2
Let c(q) be the second derivative of 0*q**2 - 3/70*q**5 + 0 + 3*q - 1/147*q**7 + 1/35*q**6 + 0*q**3 + 1/42*q**4. Factor c(x).
-2*x**2*(x - 1)**3/7
Let q(w) be the first derivative of -3*w**4/14 - 5*w**3/7 + 6*w**2/7 + 9*w/7 + 1. Solve q(h) = 0 for h.
-3, -1/2, 1
Let k(d) = 4*d**2 + 22*d + 6. Let l(x) = -4*x**2 - 23*x - 5. Let w(j) = 7*k(j) + 6*l(j). What is g in w(g) = 0?
-3, -1
Let s(p) = p**3 - 2*p**2 + 2. Suppose 11 = z - 3*z - 3*f, -f = z + 3. Let x be s(z). Suppose 0 + x*d**2 - 2*d - 1/2*d**3 = 0. What is d?
0, 2
Let m(q) = -4*q**3 - 28*q**2 - 40*q + 4. Let g(f) = -4*f**3 - 29*f**2 - 41*f + 5. Let u(l) = 4*g(l) - 5*m(l). Factor u(h).
4*h*(h + 3)**2
Let n be ((-2)/4 - 105/(-180))*9. Find r such that -1/2*r**3 + n*r**5 - r**4 + 0 + r**2 - 1/4*r = 0.
-1, 0, 1/3, 1
Let c(u) be the third derivative of u**9/10080 + u**8/2016 + u**7/1260 - u**5/20 + 2*u**2. Let n(i) be the third derivative of c(i). Factor n(p).
2*p*(p + 1)*(3*p + 2)
Let b(i) = -3 - 5 + i + 3. Let f be b(7). Factor -3*h**f + h**2 + h**2.
-h**2
Let c(v) be the second derivative of v**4/72 + v**3/12 + v**2/6 - 4*v. Factor c(q).
(q + 1)*(q + 2)/6
Suppose 2*u = 2*h, 0 = -4*u + 3*h - 5*h + 24. Suppose d = -u*m + 2*m + 8, -3 = -m. Factor -1/4*l**d + 0*l - 1/4*l**3 + 0.
-l**2*(l + 1)/4
Suppose -2*p + 4 = -k - 4, -5*k - 4 = -4*p. Let f = -1 + p. Factor c**3 + c**3 + f*c - 3*c + 3*c**2 + c**2.
2*c*(c + 1)**2
Let f(y) be the third derivative of -y**5/60 + y**4/8 - y**3/3 - y**2 + 42. What is s in f(s) = 0?
1, 2
Let h(j) = -j**3 - 10*j**2 + 10*j - 9. Let t be h(-11). Let b(s) = 2*s - 2. Let z be b(t). Factor 6/7*c + 2/7*c**3 + 2/7 + 6/7*c**z.
2*(c + 1)**3/7
Factor 0*v**3 + 2*v**3 + 4*v**4 - 16*v**2 + 2*v**3 - 16*v.
4*v*(v - 2)*(v + 1)*(v + 2)
Let a(s) = 9*s**3 - 6*s**2 - 9*s - 6. Let i(k) = -k**3 + k**2 + k + 1. Let c(o) = a(o) + 6*i(o). Factor c(v).
3*v*(v - 1)*(v + 1)
Let z be 59 - (-1 - 2)/3. Factor -28*i**3 - 35*i - i + i**3 + 6 - 3*i + z*i**2.
-3*(i - 1)**2*(9*i - 2)
Factor 28*l**2 - 2*l**3 + 2*l**4 - 24*l**2 - 3*l**4 - l**4.
-2*l**2*(l - 1)*(l + 2)
Factor 0*j**3 + 0 - 4/13*j**2 + 4/13*j**4 - 2/13*j + 2/13*j**5.
2*j*(j - 1)*(j + 1)**3/13
Let x(y) be the first derivative of 10*y**3/3 - 15*y**2/2 - 5. Let x(n) = 0. What is n?
0, 3/2
Suppose 3 = -u + 1. Let b be -1 + (2 - u) - 1. Solve -2*d - 2*d**b - 1/2*d**3 + 0 = 0.
-2, 0
Let q be 1 - (-1 - (-2)/(-2)). Let c(h) be the first derivative of -2/27*h**q - 2/9*h**2 - 2/9*h - 1. Factor c(n).
-2*(n + 1)**2/9
Suppose -2*c - 5*s - 32 = 0, -4*s - 29 = 3*c + 5. Let g be c/15 - 2/(-5). Factor 0 + 0*a**3 + g*a**2 + 0*a + 1/6*a**4.
a**4/6
Let p be ((-1)/(-2))/((-8)/(-48)). Factor -2/9*a**2 - 2/9*a**p + 0 + 0*a.
-2*a**2*(a + 1)/9
Let u(x) = 2*x + 21. Let z be u(-13). Let p be 35/(-21)*4/z. Factor 14/3*g**4 + 8*g**3 + 2*g**2 + 0 - p*g.
2*g*(g + 1)**2*(7*g - 2)/3
Factor -19*w**2 - 16*w**2 - 2 + 37*w**2.
2*(w - 1)*(w + 1)
Let f(o) = o**2 - 5*o - 6. Let w be f(6). Solve w + 2/9*h**2 - 2/9*h**3 + 4/9*h = 0.
-1, 0, 2
Let v = 8 - 6. Factor -16*d + 39*d**v + 3*d**2 + 19*d + 8 + 18*d**3 + 29*d.
2*(d + 1)*(3*d + 2)**2
Let r = -350 + 1753/5. Factor 1/5*x**2 + 2/5 + r*x.
(x + 1)*(x + 2)/5
Let -21/2*j**3 + 27/2*j**2 + 18*j - 6 = 0. What is j?
-1, 2/7, 2
Factor -12/7*x - 18/7 - 2/7*x**2.
-2*(x + 3)**2/7
Let x(j) be the first derivative of j**6/360 + j**5/180 + j**2/2 - 6. Let w(r) be the second derivative of x(r). Solve w(f) = 0.
-1, 0
Let a(r) = 3*r + 8. Let t be a(-2). Factor 2/7*c**5 + 0 + 4/7*c**4 + 0*c**3 - 4/7*c**t - 2/7*c.
2*c*(c - 1)*(c + 1)**3/7
Suppose -2*u + p + 1 = 0, 4*p - 23 - 3 = -2*u. Suppose 3 - 4 + 2*l**2 + u - 2*l - 6 = 0. Calculate l.
-1, 2
Suppose -5*z - 4*d + 37 = -6*d, -4*d = z - 3. Suppose 0 = 3*k - v - 3, -k + 2*v + z = 1. Factor 2/5*w**5 + k + 0*w + 0*w**2 + 2/5*w**3 + 4/5*w**4.
2*w**3*(w + 1)**2/5
Let t(m) = -9*m**2 - 6*m - 6. Let z(y) = 8*y**2 + 7*y + 7. Let c(b) = 5*t(b) + 6*z(b). Suppose c(o) = 0. What is o?
-2
Suppose -5*u + 57 = 22. Let t(h) = -h**2 + 8*h - 4. Let f be t(u). Determine p, given that 2*p**3 + 0*p**3 + p - f*p = 0.
-1, 0, 1
Determine j so that -2*j**2 + 4 - 1/4*j**5 + 4*j - 7/4*j**4 - 4*j**3 = 0.
-2, 1
Let r(p) be the second derivative of -p**7/105 - p**6/15 - p**5/5 - p**4/3 - p**3/3 + 3*p**2/2 + 6*p. Let v(d) be the first derivative of r(d). Factor v(c).
-2*(c + 1)**4
Let d(n) be the third derivative of 7*n**5/20 - 19*n**4/8 - 3*n**3 + 4*n**2. Find m such that d(m) = 0.
-2/7, 3
Let 8/5*h - 4/5*h**2 - 4/5 = 0. What is h?
1
Let i(g) be the second derivative of -g**6/540 + 2*g**2 + 4*g. Let k(s) be the first derivative of i(s). Factor k(a).
-2*a**3/9
Factor 20*c**5 + 20*c**5 + 16*c + 16*c**2 - 12*c**3 - 8*c**4 - 36*c**5.
4*c*(c - 2)**2*(c + 1)**2
Suppose 2*r + 5*r = 0. Suppose 4/13*v - 2/13*v**4 + 2/13 + r*v**2 - 4/13*v**3 = 0. What is v?
-1, 1
Factor -1/2*u + 1/6*u**2 + 1/6*u**4 + 1/2*u**3 - 1/3.
(u - 1)*(u + 1)**2*(u + 2)/6
Let n(w) = -w**3 + 27*w**2 - w + 31. Let v be n(27). Factor 0*m + 2/5*m**v - 1/5*m**5 + 0*m**2 - 1/5*m**3 + 0.
-m**3*(m - 1)**2/5
Let d(w) = -3*w**2 + 3*w - 2. Let c(l) be the first derivative of 3 + 13/2*l**2 - 13/3*l**3 - 9*l. Let o(h) = -2*c(h) + 9*d(h). Factor o(v).
-v*(v - 1)
Let v be (-2)/10 + (-61)/(-5). Factor 14*w + 2 - 2*w**2 - 2*w**3 + 0 - v*w.
-2*(w - 1)*(w + 1)**2
Determine x, given that -7/8*x**2 - 5/8*x**4 - 1/8*x**5 - 1/4*x - 9/8*x**3 + 0 = 0.
-2, -1, 0
Let v(y) = -20*y**5 - 30*y**4 + 2*y**3 + 18*y**2 - 18. Let s(i) = -i**5 - i**4 + i**3 + i**2 - 1. Let u(z) = -36*s(z) + 2*v(z). Factor u(n).
-4*n**3*(n + 2)*(n + 4)
Let a = 56 - 56. Solve a*r + 2/3*r**4 + 4/3*r**3 + 2/3*r**2 + 0 = 0.
-1, 0
Factor -2/5*v**3 + 0 + 0*v + 0*v**2 - 1/5*v**4 + 1/5*v**5.
v**3*(v - 2)*(v + 1)/5
Let j = 299/132 + -50/33. Factor -3/2*y - 27/4*y**3 + 0 + 21/4*y**2 + 15/4*y**4 - j*y**5.
-3*y*(y - 2)*(y - 1)**3/4
Factor 0*k - 1/5*k**5 + 1/5*k**4 + 0 + 0*k**3 + 0*k**2.
-k**4*(k - 1)/5
Let a(s) = s - 5. Let w be a(5). Let r be w - ((-4 - 1) + 3). Factor -g**3 + 5*g**3 - r*g**3 - g**3.
g**3
Let c = 11 - 11. Let k(x) be the second derivative of -1/120*x**6 + 0*x**5 + 0 + 2*x + c*x**3 + 1/168*x**7 + 0*x**2 + 0*x**4. Determine h so that k(h) = 0.
0, 1
Let q(g) = -g - 3. Let p be q(-7). Let u = 14 + -11. Factor 6*z**2 + 3*z**2 - z**2 + 2*z**4 - p*z**3 - 4*z**u.
2*z**2*(z - 2)**2
Let b(v) be the second derivative of 4*v**4/21 - 4*v**3/7 + 9*v**2/14 + 4*v. Determine h, given that b(h) = 0.
3/4
Let j be 12/(-18) + 46/6. Suppose 2*n - d = -5, -5*n + j*d - 25 = 2*d. Factor 4*q**3 - q**2 - 2*q**3 - q**2 + n*q**3.
2*q**2*(q - 1)
Let f = 551/3 + -183. Factor -1/3 - 2/3*q**3 + 1/3*q**2 + f*q.
-(q - 1)*(q + 1)*(2*q - 1)/3
Let x(c) be the second derivative of 1/3*c**2 + 1/60*c**5 + 9*c - 1/18*c**4 - 1/18*c**3 + 0. Solve x(i) = 0 for i.
-1, 1, 2
Let u(s) be the third derivative of -1/24*s**4 + 0 + 0*s + 1/60*s**5 - 7*s**2 + 0*s**3. Factor u(l).
l*(l - 1)
Let k(q) be the first derivative of -q**5/30 - q**4/6 + q**3 + 4*q**2 - 4. Let j(u) be the second derivative of k(u). Factor j(i).
-2*(i - 1)*(i + 3)
Let p = -2 + 0. Let g be -3*(-10)/(-12)*p. Factor 0*f**4 - f**3 - f**4 + 3*f**g - f**5.
f**3*(f - 1)*(2*f + 1)
Let x(l) be the second derivative of l**7/7560 - l**6/1080 - l**5/120 + 2*l**4/3 - 7*l. Let n(z) be the third derivative of x(z). Find c such that n(c) = 0.
-1, 3
Let x(l) = 8*l**5 + 2*l**4 + 2*l**3 + 3*l**2 + 5*l. Let w(y) = -y**5 - y**4 - y**3 - y. Let p(h) = 5*w(h) + x(h). Factor p(c).
3*c**2*(c - 1)**2*(c + 1)
Solve -2/9*i**2 + 2/9*i + 4/3 = 0 for i.
-2, 3
Suppose -2*m + m + 2 = 0. Suppose 4*d - m*d = 4. Factor 2/5*t - 4/5 + 2/5*t**d.
2*(t - 1)*(t + 2)/5
Let b be 103/6*(2 + -3). Let i = b + 45/2. Factor -8*s**2 +