5 = 0.
-2
Let f = -393/4 + 99. Let o(l) be the first derivative of -2*l + f*l**4 - 3/2*l**2 - 2 + 2/3*l**3. Solve o(h) = 0 for h.
-1, -2/3, 1
Suppose -2 = -h - 0*h. Suppose -2*i + h*z = -4*i + 4, 0 = -4*i + 2*z + 20. Let 1/3*n**5 + 0 + 1/3*n - 4/3*n**2 + 2*n**3 - 4/3*n**i = 0. Calculate n.
0, 1
Solve -2*q**2 + 2 + 0*q**2 + 89*q**5 - 90*q**5 - 3*q + 4*q**3 = 0.
-2, -1, 1
Let y(d) = 13*d**3 - d**2 - d + 1. Let s be y(1). Suppose -3*c**2 + 20*c - 4 + 28*c**4 - 9*c**3 + c**3 - s*c**5 - 21*c**2 = 0. What is c?
-1, 1/3, 1
Let y be 5/2 - 2/(-4). Factor 2*i + 18 + i + 44*i**y - 14 - 5*i + 6*i**5 - 24*i**2 - 28*i**4.
2*(i - 2)*(i - 1)**3*(3*i + 1)
Let g(j) be the second derivative of 0*j**6 - 1/273*j**7 + 0 + 2*j + 0*j**5 + 0*j**3 + 0*j**2 + 0*j**4. What is b in g(b) = 0?
0
Let y(o) = -o**2 + 2*o. Let v be y(3). Let j = v - -5. Factor 0*b**j - 2*b**3 + b**3 + 0*b**2 + 2*b**2 - b.
-b*(b - 1)**2
Let s = -19 + 31. Suppose 3*t = -5*y + 69, 0 = -t - 3*y + s + 15. Let -31*h**3 - 69*h**4 + 24*h**4 + 9*h**2 + 2*h + t*h**3 - 25*h**5 = 0. Calculate h.
-1, -1/5, 0, 2/5
Let w(m) be the second derivative of 9*m**5/10 - 7*m**4/6 - 2*m**3/3 - 33*m. Suppose w(y) = 0. Calculate y.
-2/9, 0, 1
Let a(u) be the first derivative of -3*u**4/16 - 11*u**3/12 + u**2/2 + 31. Determine n, given that a(n) = 0.
-4, 0, 1/3
Let o be (-9 - -4) + (-34)/(-4). Factor 9/2*d**2 + 1 - 5/2*d**3 - o*d + 1/2*d**4.
(d - 2)*(d - 1)**3/2
Suppose -5*z - 5*x - 16 - 29 = 0, 0 = 4*z - 2*x + 48. Let y be 3/(-1 - z/2). Factor y + 1/3*f**2 + f.
(f + 1)*(f + 2)/3
Let r = 2/5 - 1/15. Let u = 466/3 - 155. Let -u*c + r*c**2 + 0 = 0. What is c?
0, 1
Let q(o) be the second derivative of o**8/13440 - o**7/5040 - o**6/720 + o**4/6 + 3*o. Let x(r) be the third derivative of q(r). Factor x(v).
v*(v - 2)*(v + 1)/2
Let o(f) be the third derivative of -1/420*f**7 - 1/120*f**6 + 0*f - 4*f**2 + 1/672*f**8 + 1/60*f**5 + 1/48*f**4 - 1/12*f**3 + 0. Factor o(w).
(w - 1)**3*(w + 1)**2/2
Let a(z) be the third derivative of -z**5/300 + z**4/60 - z**3/30 + 11*z**2. Factor a(c).
-(c - 1)**2/5
Let g = 60 - 60. Determine h so that g*h + 2/9*h**3 + 0 + 0*h**2 - 8/9*h**4 = 0.
0, 1/4
Let t = -209/4 + 2331/44. Suppose t - 8/11*k + 6/11*k**4 - 14/11*k**2 + 8/11*k**3 = 0. Calculate k.
-2, -1, 2/3, 1
Let v(q) = -q + 2. Let u be v(-7). Suppose 6*t - 3*t = u. Factor 0*z**3 - 2*z**3 + 0*z**3 + z**t - z**2.
-z**2*(z + 1)
Let r be (-9)/(-6) - 4/(-8). Solve -k - 4 + 8*k - 3*k**r + k**2 - k = 0.
1, 2
Let f(z) be the second derivative of -2*z**6/15 - 3*z**5/5 - z**4/3 + 2*z**3 + 4*z**2 - 16*z + 2. Let f(a) = 0. Calculate a.
-2, -1, 1
Factor -1/3*r**5 + 0*r**2 + 2/3*r**4 + 0 + 0*r - 1/3*r**3.
-r**3*(r - 1)**2/3
Let a(f) = 32*f**2 + 2. Let r(k) = 11*k**2 + 1. Let u(t) = 6*a(t) - 17*r(t). Let u(g) = 0. What is g?
-1, 1
Let b(l) = 2*l**2 - 8*l - 8. Let z be b(5). Factor 2/3*d**3 + 0*d + 1/3*d**4 + 1/3*d**z + 0.
d**2*(d + 1)**2/3
Let m(l) be the third derivative of 1/42*l**7 - 1/15*l**6 + 0*l + 0*l**4 + 1/15*l**5 + 0*l**3 + 0 - 1/336*l**8 - l**2. Find w such that m(w) = 0.
0, 1, 2
Let z(a) = 8*a**2 - 4*a - 12. Suppose 3*w + 30 = -2*w. Let f(n) = n**2 - 1. Let c(j) = w*f(j) + z(j). Let c(i) = 0. What is i?
-1, 3
Let u = -44 - -22. Let i be (-1)/u*(8 - 4). Let -2/11 - 4/11*x - i*x**2 = 0. Calculate x.
-1
Let k(p) be the second derivative of -p**4/3 + 8*p**3/3 - 6*p**2 - 5*p. Factor k(q).
-4*(q - 3)*(q - 1)
Suppose 0*j = -4*j - 12. Let n(h) = -4*h**2 + 2*h. Let c(m) = -3*m**2 + m. Let a(u) = j*c(u) + 2*n(u). Factor a(y).
y*(y + 1)
Let z = -472/3 - -158. Determine j so that 2/9 + 2/3*j**2 - z*j - 2/9*j**3 = 0.
1
Suppose 0 = -5*w - 0*w + 10. Suppose -4*u = -u. Let t + 2*t**w - 3*t**2 + u*t**2 = 0. Calculate t.
0, 1
Factor -12 + 37*o**3 + 3*o - 39*o**3 + 6*o + 5*o.
-2*(o - 2)*(o - 1)*(o + 3)
Suppose -5*n - 1 + 26 = 0. Suppose 5*l - 16 + 1 = n*y, 4*l = 3*y + 12. Solve -8*f**4 + 24/5*f**5 - 4/5*f**2 + 0*f + 22/5*f**l + 0 = 0.
0, 1/2, 2/3
Factor 16*k + 10*k - 2*k**2 + 7*k**2 - 41*k.
5*k*(k - 3)
Let a(v) = v**2 - v + 5*v**2 - 7*v**2. Let t(b) = 2*b**3 + 6*b**2 + 2*b - 2. Let z(s) = 4*a(s) + t(s). Factor z(i).
2*(i - 1)*(i + 1)**2
Let p(d) be the third derivative of -2*d**7/175 + 2*d**6/75 - d**5/75 + 6*d**2. Suppose p(k) = 0. What is k?
0, 1/3, 1
Suppose -2/7*y**2 + 4/7 - 2/7*y = 0. Calculate y.
-2, 1
Let d be (-6)/10 + (-660)/(-100). Suppose f - 4*l - 6 - d = 0, -5*f = -l - 22. Let 6*u - 15/2*u**5 + 0 + 3/2*u**3 + 18*u**f - 18*u**2 = 0. What is u?
-1, 0, 2/5, 1, 2
Let d(g) be the first derivative of -g**4/12 + g**3/9 + g**2/3 - 4. Factor d(j).
-j*(j - 2)*(j + 1)/3
Let t(i) be the third derivative of -i**8/1512 - i**7/945 + 21*i**2. Factor t(y).
-2*y**4*(y + 1)/9
Let z(c) be the second derivative of c**4/3 - 4*c**3/3 + 2*c**2 - 5*c. Factor z(o).
4*(o - 1)**2
Let p(c) = -c**2 + 4*c + 1. Let i(t) = t + 1. Let z(v) = -10*i(v) + 5*p(v). Factor z(h).
-5*(h - 1)**2
Let q(l) be the first derivative of -l**4/16 - l**3/12 + 4. Determine m, given that q(m) = 0.
-1, 0
Let b(w) = -w**2 + w + 1. Let z(x) = -8*x**2 - 2*x. Let a(f) = -12*b(f) + 2*z(f). Suppose a(d) = 0. What is d?
-3, -1
Let k(z) = -z + 1. Let x be k(1). Let n(d) be the third derivative of 0*d + 1/30*d**5 + 0 + d**2 + x*d**3 + 0*d**4. Suppose n(b) = 0. What is b?
0
Suppose -4*u + 2 = -6. Find b, given that -1/2*b**u + b - 1/2 = 0.
1
Let u(z) be the third derivative of 1/210*z**5 + 0*z + 0 - 1/42*z**4 + 2*z**2 + 1/21*z**3. Solve u(f) = 0.
1
Let z(c) = 6*c**4 + 2*c**3. Let s(p) = -7*p**4 - 3*p**3. Suppose -5*u + 40 = 3*x, 2*x + 2*x = u + 15. Let j(r) = x*z(r) + 4*s(r). Find q such that j(q) = 0.
0, 1
Let r(p) be the second derivative of -p**8/15120 - p**7/2268 - p**6/810 - p**5/540 - p**4/6 + 3*p. Let a(g) be the third derivative of r(g). Factor a(v).
-2*(v + 1)**2*(2*v + 1)/9
Let 20*u + 20 - 100*u**3 - 38*u**2 - 17*u**2 - 8*u**5 - 55*u**4 + 4*u**5 - 6*u**5 = 0. What is u?
-2, -1, 1/2
Find g such that -6 + 36*g**3 - 20*g**3 - 17*g**3 + 7*g = 0.
-3, 1, 2
Let z = -1/18 + 2/9. Let v(t) be the first derivative of -3 + 1/9*t**3 - 1/3*t + 1/12*t**4 - z*t**2. Factor v(s).
(s - 1)*(s + 1)**2/3
Let m(d) be the first derivative of -d**6/12 + d**4/4 - d**2/4 - 5. Factor m(x).
-x*(x - 1)**2*(x + 1)**2/2
What is u in -u**4 - 25 + 9*u**2 + 11*u - 21 + 50 + u**3 = 0?
-1, 4
Suppose 0 = -3*k - 0*i - 3*i + 24, 3*k = 4*i - 4. Factor 8*g**3 - 5*g**3 + 2*g**k - g**3.
2*g**3*(g + 1)
Suppose -3*k - 18 = -0*k. Let z be (-4)/k*2/6. Factor 0*a + 2/9*a**2 - z.
2*(a - 1)*(a + 1)/9
Let c(j) = -19*j**2 + 27*j + 3. Let t(a) = 10*a**2 - 14*a - 2. Let h(q) = 6*c(q) + 11*t(q). Let h(p) = 0. Calculate p.
1
Let r = -1/329 - -2635/987. Factor 2/3*u**2 + 8/3*u + r.
2*(u + 2)**2/3
Let q = 3 + -2. Let o = 2 + q. Factor -3*w**3 - 4*w**2 + 5*w**3 + 5*w - o*w.
2*w*(w - 1)**2
Suppose 4*l + 2 - 6 = 0. Let h be (6/9)/(l - 0). Find c, given that h + 2/3*c**2 - 4/3*c = 0.
1
Let i(p) be the second derivative of p**6/120 + 26*p. Let i(t) = 0. Calculate t.
0
Let -3*z**4 + 0*z**2 + 0*z + 0 + 0*z**3 + 3/2*z**5 = 0. What is z?
0, 2
Suppose -5*k = -k. Let i = k + 2. What is r in -9*r**3 + r**i + 3*r - 3*r**4 - 3 + 3*r**3 + 5*r**2 + 3*r**5 = 0?
-1, 1
Let c = 45 + -45. Let o(g) be the third derivative of -1/80*g**5 + c*g**4 - 3*g**2 + 0*g + 0 + 1/8*g**3. Factor o(z).
-3*(z - 1)*(z + 1)/4
Determine r so that 10*r + 3368 - 3353 - 7*r**2 + 2*r**2 = 0.
-1, 3
Let b = 0 + 3. Suppose -b*d + 5 + 4 = 0. Suppose -t**3 - 2*t**2 + 2*t**3 - 3*t**d = 0. Calculate t.
-1, 0
Let o be (16/(-12))/((-21)/9). Let c = 83/119 - 7/17. Find n such that 2/7*n + 0 + c*n**3 + o*n**2 = 0.
-1, 0
Suppose -16/13*j**2 + 18/13 + 12/13*j**3 - 2/13*j**4 - 12/13*j = 0. What is j?
-1, 1, 3
Let y = -69 + 73. Let h = -13/34 - -363/238. Factor 4/7*d + 2/7*d**y + h*d**3 + 10/7*d**2 + 0.
2*d*(d + 1)**2*(d + 2)/7
Factor 0*u**2 - 1/4*u**3 + 0 + 1/4*u.
-u*(u - 1)*(u + 1)/4
Let z(l) = l - 5. Let v be z(6). Suppose 2 = -h + 2*k, -4*h + v = k - 0. Factor -1/2*t**3 + 0*t + h + t**4 + 0*t**2 - 1/2*t**5.
-t**3*(t - 1)**2/2
Let p = -1 - -5. Let c(k) be the third derivative of -1/20*k**5 + k**2 + 0*k + 1/24*k**p + 0 + 1/3*k**3. Suppose c(g) = 0. What is g?
-2/3, 1
Let a(q) be the third derivative of q**7/70 - q**6/40 - 7*q**5/20 + 13*q**4/8 - 3*q**3 - 25*q**2. Factor a(z).
3*(z - 2)*(z - 1)**2*(z + 3)
Let o(x) =