+ 1/2*v**2 + z*v.
-(v - 1)**2*(v + 1)/2
Determine j so that 48*j**4 + 28*j**5 - 8*j + 7*j**4 - 19*j**4 - 36*j**2 - 20*j**3 = 0.
-1, -2/7, 0, 1
Let g(a) be the third derivative of -a**6/24 + 13*a**5/60 - a**4/6 - 2*a**3/3 - 2*a**2. Determine s so that g(s) = 0.
-2/5, 1, 2
Let v(l) be the second derivative of -l**5/20 + 13*l**4/6 - 169*l**3/6 + 14*l. Factor v(r).
-r*(r - 13)**2
Let h(k) be the third derivative of k**8/10080 + k**7/2520 - k**6/180 + k**5/20 - 7*k**2. Let p(s) be the third derivative of h(s). Factor p(q).
2*(q - 1)*(q + 2)
Suppose 0 - 8*s**2 + 4/3*s**3 + 12*s = 0. What is s?
0, 3
Let q(y) be the first derivative of -3/16*y**4 - 1/2*y**3 + 7 + 0*y**2 + 0*y. Let q(v) = 0. Calculate v.
-2, 0
Suppose r = 2*i - i + 1, -3*r = 5*i + 5. Determine p, given that r*p - 2*p**3 + 4/3*p**2 + 2/3*p**4 + 0 = 0.
0, 1, 2
Let n(b) be the second derivative of b**4/12 - b**3/6 - b**2 - 6*b. Solve n(l) = 0 for l.
-1, 2
Let y(a) = -a**3 - a**5 + 6*a - 4*a - 2*a + 1. Let p(f) = -3*f**4 + 7*f**3 - 5. Let n(t) = 3*p(t) + 15*y(t). Factor n(k).
-3*k**3*(k + 1)*(5*k - 2)
Suppose 0 = -2*r - 10, b = -b + 3*r + 19. Let l be (1 - -1) + (5 - b). Factor -4/3*t**3 + 0 + 8/9*t**2 - 2/9*t**l + 8/9*t**4 - 2/9*t.
-2*t*(t - 1)**4/9
Let r(n) be the second derivative of -n**7/84 - n**6/30 + n**5/20 + n**4/6 - n**3/12 - n**2/2 - 11*n. What is g in r(g) = 0?
-2, -1, 1
Factor 0*u - 7/6*u**4 + 0*u**2 + 1/3*u**3 + 5/6*u**5 + 0.
u**3*(u - 1)*(5*u - 2)/6
Let b(k) be the second derivative of k**5/30 + k**4/6 + 2*k**2 + 4*k. Let u(g) be the first derivative of b(g). Factor u(a).
2*a*(a + 2)
Suppose 2*a = 5*a - 21. Let c be (-3)/a - (-3)/7. What is b in -2/7*b**2 + 0*b + c + 2/7*b**3 = 0?
0, 1
Let l be 22/4 - (14 + -9). Let -y**4 + y**2 + 1/2*y**5 - l*y + 0*y**3 + 0 = 0. What is y?
-1, 0, 1
Suppose g + 4*g = 205. Factor -4 + 2 - 21*q**4 + 5*q**5 - q**5 + 6*q**2 + g*q**3 + 15*q - 43*q**2.
(q - 2)*(q - 1)**3*(4*q - 1)
Let n be (-112)/5 - (-3)/(-5). Let t = n + 25. Factor -4/7*d + 6/7 - 2/7*d**t.
-2*(d - 1)*(d + 3)/7
Let -2/7*j + 2/7 - 2/7*j**2 + 2/7*j**3 = 0. What is j?
-1, 1
Let c(y) = 6*y**3 - 40*y**2 - 50*y - 4. Suppose 0 = -p + 5*p - 12. Let v(j) = -j**3 + 8*j**2 + 10*j + 1. Let s(g) = p*c(g) + 16*v(g). Factor s(t).
2*(t + 1)**2*(t + 2)
Suppose 0 = 3*c - 1 - 14. Suppose -t - i = 4*t - 12, -15 = c*i. Let 1/2*p - 1/2*p**t + 0*p**2 + 0 = 0. What is p?
-1, 0, 1
Let j(f) be the third derivative of -f**7/42 - f**6/8 + 20*f**2. Factor j(x).
-5*x**3*(x + 3)
Suppose 2*f + 2*x + x = -4, 0 = 3*x. Let d(q) = -2*q**3 - 12*q**2 - 6*q + 2. Let o(u) = 9*u**3 + 60*u**2 + 29*u - 11. Let l(t) = f*o(t) - 11*d(t). Factor l(c).
4*c*(c + 1)*(c + 2)
Let -4/5*c**2 + 14/5*c - 6/5 = 0. What is c?
1/2, 3
Let q = 11/25 + -8/75. Factor q*v**2 + 1/3 + 2/3*v.
(v + 1)**2/3
Let q(y) be the first derivative of -1/54*y**4 + 2 + 3/2*y**2 + 1/54*y**5 + 0*y + 0*y**3. Let m(u) be the second derivative of q(u). Solve m(b) = 0.
0, 2/5
Let f(z) = z**2 - 2*z. Let c be f(-3). Suppose -13*t + c*t = 4. Factor -1 + 1/2*y + 1/2*y**t.
(y - 1)*(y + 2)/2
Let y(l) = l**3 + 8*l**2 + 7*l + 2. Let x be y(-7). Let n be (-2)/4*(-2 + x). Factor h + 3*h**3 - h**3 + n*h**3 - h**5 - 2*h.
-h*(h - 1)**2*(h + 1)**2
Let 0 + 0*i + 0*i**2 + 1/2*i**5 + 2*i**3 + 2*i**4 = 0. Calculate i.
-2, 0
Suppose -22*j = -20*j - 6. Let h(f) be the second derivative of 0*f**j - 2*f - 1/75*f**6 + 2/105*f**7 + 0*f**2 + 0*f**4 + 0 + 0*f**5. Factor h(x).
2*x**4*(2*x - 1)/5
Let t(l) be the second derivative of 0 - 2/3*l**4 + 0*l**2 + 4/5*l**5 + 1/6*l**3 + 2*l. What is o in t(o) = 0?
0, 1/4
Let p = 6 - 0. Let u(h) = -h**3 + h**2 + h + 1. Let x(y) = 4*y**3 + 18*y**2 - 102*y + 122. Let b(s) = p*u(s) + x(s). Find r, given that b(r) = 0.
4
Let p(q) = 2*q**2 + 30*q + 112. Let k be p(-6). Factor 1/8*n**2 + 1/8*n**5 + 1/4*n - 3/8*n**3 + 0 - 1/8*n**k.
n*(n - 2)*(n - 1)*(n + 1)**2/8
Suppose 3*k - 2*x + 4*x - 30 = 0, 4 = -k + 4*x. Let f = -4 + k. Determine w, given that -2 - w**2 + 2*w**2 + f*w - 3*w**2 = 0.
1
Let v = 5/14 - 179/462. Let n = 15/11 + v. Factor 1/3*r**2 + n - 4/3*r.
(r - 2)**2/3
Let c(p) be the second derivative of p**6/40 + p**5/4 + p**4 + 2*p**3 - 5*p**2/2 - p. Let z(d) be the first derivative of c(d). Factor z(k).
3*(k + 1)*(k + 2)**2
Factor 1/2*m**2 + 1 - 3/2*m.
(m - 2)*(m - 1)/2
Let o(b) be the second derivative of 1/4*b**4 + 3/2*b**3 + 3*b**2 + 0 - 3*b. Factor o(l).
3*(l + 1)*(l + 2)
Suppose 0*h = 4*h + 36. Let m(c) = -7*c**2 + 13*c - 9. Let i(s) = 3*s**2 - 6*s + 4. Let r(q) = h*i(q) - 4*m(q). Suppose r(j) = 0. Calculate j.
-2, 0
Let q(m) be the third derivative of -m**8/336 - m**7/70 + m**6/60 + m**5/10 - m**4/24 - m**3/2 + 58*m**2. Find w such that q(w) = 0.
-3, -1, 1
Let m = 141/4 + -123/4. Find w, given that -3*w - 1/2*w**2 - m = 0.
-3
Let g(u) = -3*u**3 - 2*u**2 + 4. Let x(w) = -2*w**3 - w**2 + 3. Suppose -3 = -z + 1. Let r(b) = z*x(b) - 3*g(b). Factor r(t).
t**2*(t + 2)
Let u(b) be the first derivative of -3*b**4/16 - b**3/2 + 3*b**2/8 + 3*b/2 - 1. Determine d so that u(d) = 0.
-2, -1, 1
Factor 18*d - 5 + 1 - 2 + 2 - 14*d**2.
-2*(d - 1)*(7*d - 2)
Factor 2*y + 4*y**3 - 5*y**2 - y**4 - 23 + 23.
-y*(y - 2)*(y - 1)**2
Let p = 467/602 + 7/86. Factor -8/7 - 2/7*r**3 + 0*r + p*r**2.
-2*(r - 2)**2*(r + 1)/7
Let g = -13 - -16. Let h(l) be the second derivative of 0*l**g + 1/80*l**5 + 0 + 1/48*l**4 + 0*l**2 + l. Let h(o) = 0. Calculate o.
-1, 0
Determine z, given that 0 + 1/2*z + 1/2*z**3 + z**2 = 0.
-1, 0
Suppose 8 = -5*a - 2*j, 0 = -5*j - 0*j - 20. Let w(z) be the first derivative of -1/2*z**4 - 1/3*z**6 + 0*z**2 + 0*z**3 + a*z + 1 + 4/5*z**5. Factor w(t).
-2*t**3*(t - 1)**2
Let m(z) be the first derivative of z**4/26 + 8*z**3/13 + 36*z**2/13 - 57. Solve m(d) = 0.
-6, 0
Let a = 28 - 26. Factor 1/2*r + 3/2*r**a + r**3 + 0.
r*(r + 1)*(2*r + 1)/2
Let t(g) be the second derivative of g**5/10 - 2*g**4/3 + 2*g. Factor t(y).
2*y**2*(y - 4)
Suppose -3*j - j - 4*a - 8 = 0, j = 3*a + 6. Let i(r) be the second derivative of 1/21*r**4 - 2*r + 0*r**2 + j - 1/21*r**3 - 1/70*r**5. Factor i(g).
-2*g*(g - 1)**2/7
Let a(t) be the second derivative of -t**5/5 + 2*t**3 - 4*t**2 + 6*t. Let a(k) = 0. Calculate k.
-2, 1
Let w = 37/2 + -18. Let s be (-3)/(-4) + 3 + -3. Factor -w*v**2 - s*v**3 + 0 + 1/4*v.
-v*(v + 1)*(3*v - 1)/4
Let r(m) = -m**3 - m**2 - m - 1. Let a(l) = 3*l**3 - 3*l**3 + 12 + 0*l**2 + 2*l**3 - 2*l**2. Let n(b) = a(b) + 3*r(b). Factor n(q).
-(q - 1)*(q + 3)**2
Let j(o) be the third derivative of -o**8/28 + 23*o**7/210 - 13*o**6/120 + o**5/30 + 10*o**2. Determine t, given that j(t) = 0.
0, 1/4, 2/3, 1
Let q(n) = 4*n**3 + 65*n**2 + 140*n - 209. Let v(h) = h**3 + 16*h**2 + 35*h - 52. Let m(k) = -6*q(k) + 26*v(k). Factor m(l).
2*(l - 1)*(l + 7)**2
Let m(y) be the third derivative of -y**8/1512 + 4*y**7/945 - y**6/540 - y**5/27 + y**4/27 + 8*y**3/27 - 15*y**2. Let m(w) = 0. What is w?
-1, 2
Let f(x) be the second derivative of x**5/50 - x**3/5 + 2*x**2/5 + x. Factor f(p).
2*(p - 1)**2*(p + 2)/5
Let w(v) = 24*v**5 - 16*v**4 + 5*v**3 - 5*v**2 + 5. Let x(a) = -60*a**5 + 40*a**4 - 12*a**3 + 12*a**2 - 12. Let h(i) = -12*w(i) - 5*x(i). Factor h(d).
4*d**4*(3*d - 2)
Let p(y) be the second derivative of 11/20*y**5 + 1/6*y**3 + 0 + 2/15*y**6 + 3/4*y**4 - 1/2*y**2 + 3*y. Find z such that p(z) = 0.
-1, 1/4
Let q(v) = -7*v**5 - 7*v**4 + 7*v**3 + 7*v**2. Let x(o) = 2*o**5 + 2*o**4 - 2*o**3 - 2*o**2. Let z(f) = 2*q(f) + 9*x(f). Factor z(s).
4*s**2*(s - 1)*(s + 1)**2
Let p(b) = 7*b**3 - 11*b**2 + 14*b - 10. Let s(z) = 6*z**3 - 10*z**2 + 13*z - 9. Let l(u) = 5*p(u) - 6*s(u). Solve l(v) = 0 for v.
1, 2
Let l(d) = 4*d - 4. Let r(c) = c**2 + 7*c - 8. Let u(s) = 9*l(s) - 4*r(s). Determine o, given that u(o) = 0.
1
Let f(h) be the second derivative of -h**5/4 - 5*h**4/12 - 50*h. Find d, given that f(d) = 0.
-1, 0
Determine z, given that -2*z - 3*z + 9*z + 2*z**3 - 6*z**3 = 0.
-1, 0, 1
Factor -1/4*u**3 + 1/2*u**2 + 0*u + 1/4*u**5 + 0 - 1/2*u**4.
u**2*(u - 2)*(u - 1)*(u + 1)/4
Let v(h) = -5*h**4 + h**3 + h**2 + 3*h - 3. Let f(u) = 19*u**4 - 5*u**3 - 3*u**2 - 11*u + 11. Let c(d) = 6*f(d) + 22*v(d). Factor c(m).
4*m**2*(m - 1)**2
Let m(o) be the second derivative of -o**7/21 + 2*o**6/5 - 9*o**5/10 + 2*o**4/3 + 18*o. Solve m(p) = 0 for p.
0, 1, 4
Let n(k) be the first derivative of 2*k**5/15 