 + 1)/2
Solve 0*g + 0*g**2 + 0*g**3 - 1/2*g**5 + 0 + 5/2*g**4 = 0 for g.
0, 5
Let a(f) = 7*f**2 + 13*f + 2. Let m(h) = -8*h + 2 + 6*h**2 + 20*h + 1. Let x(u) = 3*a(u) - 4*m(u). Factor x(i).
-3*(i + 1)*(i + 2)
Let s = 3 - -1. Suppose 2*j = -y - 3*j + 12, -10 = -s*y - j. Solve -2*a**3 + 4*a + 0*a - y*a = 0 for a.
-1, 0, 1
Suppose -4*z - 1 - 27 = -4*m, -10 = -m + 2*z. Suppose -m*s + 3*k = 9, 4*k - 12 = 8*s - 3*s. Factor s + 2/3*i**3 + 0*i**2 + 0*i.
2*i**3/3
Let c(g) be the second derivative of -5/3*g**4 - 23/30*g**5 - 1/9*g**6 + 0 - 4/9*g**3 + 8/3*g**2 + g. Determine m, given that c(m) = 0.
-2, -1, 2/5
Let r = 7 - -1. Let q(z) = -z + 8. Let w be q(r). Suppose 0*p + 2/3*p**3 + w + 0*p**2 = 0. What is p?
0
Let k(s) be the first derivative of s**5/150 + 2*s**4/15 + 16*s**3/15 - 9*s**2/2 + 1. Let j(u) be the second derivative of k(u). Factor j(g).
2*(g + 4)**2/5
Let v(r) = -r**2 + 9*r - 4. Let j be v(7). Suppose -j = 5*b - 25. Factor -8*x**2 + 3 - 2*x**b + 2*x + 8*x**4 - 3.
2*x*(x - 1)*(x + 1)*(4*x - 1)
Suppose -8*h - 87 = -37*h. Factor -2/3*c**2 + 0 + c - 1/3*c**h.
-c*(c - 1)*(c + 3)/3
Let u(z) be the first derivative of -8/5*z + 1 - 34/15*z**3 + 4*z**2 + 2/5*z**4. Factor u(t).
2*(t - 2)**2*(4*t - 1)/5
Let j(q) = q + 6. Let d(t) = 1. Let a(w) = 4*d(w) - j(w). Let s be a(-5). Suppose 0 - 6/7*n**s + 0*n**2 + 2/7*n**4 + 8/7*n = 0. Calculate n.
-1, 0, 2
Factor 1/7*u**3 + 8/7 - 4/7*u - 2/7*u**2.
(u - 2)**2*(u + 2)/7
Let y(w) = -w**4 + w**3 - w**2 + w - 1. Let r(j) = 6*j**4 + 6*j**3 + 12*j**2 + 3. Let a(g) = -r(g) - 3*y(g). Factor a(n).
-3*n*(n + 1)**3
Let s(f) = -f**5 - 2*f**2 - 3. Let y(t) = t**3 + 1. Let o(b) = s(b) + 3*y(b). Let o(u) = 0. Calculate u.
-2, 0, 1
Let j be (5/30)/((-6)/(-180)) + -2. Let 1/2*z + 9/2*z**3 + 0 - 2*z**4 - j*z**2 = 0. What is z?
0, 1/4, 1
Let u(j) = j**3 + 9*j**2 + 8*j + 2. Let b be u(-8). Suppose -9/4*p**b - 3/4 - 9/4*p - 3/4*p**3 = 0. What is p?
-1
Let w(n) be the third derivative of -n**7/1260 + n**5/360 - 4*n**2. Factor w(m).
-m**2*(m - 1)*(m + 1)/6
Let o(n) be the second derivative of -n**8/168 - 2*n**7/105 + n**5/15 + n**4/12 + 3*n**2/2 + 3*n. Let t(g) be the first derivative of o(g). Factor t(h).
-2*h*(h - 1)*(h + 1)**3
Let w(t) be the first derivative of -2*t**5/5 - 2*t**4/3 - 2*t**3/9 + 13. Suppose w(j) = 0. What is j?
-1, -1/3, 0
Let n(y) be the third derivative of -y**8/16800 + y**4/8 - 3*y**2. Let f(w) be the second derivative of n(w). Find v such that f(v) = 0.
0
Let n(i) = -4*i**5 + 8*i**4 + 4*i**3 + 8*i**2 + 8*i + 8. Let b(x) = x**5 - x**2 - x - 1. Let m(c) = -8*b(c) - n(c). Factor m(z).
-4*z**3*(z + 1)**2
Factor -4 + 9 + 1 + 2*q**2 - 2 - 6*q.
2*(q - 2)*(q - 1)
Let z be 0/((3 + -7)/(-4)). Let q(l) be the first derivative of z*l + 1/2*l**2 - 1 - 1/3*l**3. Suppose q(j) = 0. Calculate j.
0, 1
Let t be -1 - 9 - (7 - 8). Let h = t + 9. Determine c so that h - 4/3*c**2 + 4/3*c + 1/3*c**3 = 0.
0, 2
Suppose 2*r - 2*l + 6*l = 26, -5*l = -25. Let d be (2/r)/((-8)/(-6)). Factor -1/4*g - 1/4*g**4 - 1/4*g**5 + d*g**2 - 1/4 + 1/2*g**3.
-(g - 1)**2*(g + 1)**3/4
Let o(l) be the third derivative of -1/140*l**6 + 1/140*l**5 + 0*l**4 + 8*l**2 + 0*l**3 + 0*l + 0 + 1/490*l**7. What is v in o(v) = 0?
0, 1
Let s = 575/6 + -286/3. Factor -3/2*p - p**2 + 0 + s*p**3.
p*(p - 3)*(p + 1)/2
Let j = 23 - 18. Factor j*t**2 - 5*t**4 + 10*t**5 + 7*t**3 + 2*t - 16*t**3 - 3*t**5.
t*(t - 1)**2*(t + 1)*(7*t + 2)
Let f(c) be the first derivative of c**4/6 - c**2 - 4*c + 4. Let g(d) be the first derivative of f(d). Determine b, given that g(b) = 0.
-1, 1
Let o(x) = 5*x**4 + 22*x**3 + 68*x**2 + 72*x + 29. Let t(v) = -51*v**4 - 219*v**3 - 681*v**2 - 720*v - 291. Let k(z) = -21*o(z) - 2*t(z). Factor k(s).
-3*(s + 1)**2*(s + 3)**2
Solve -40*m**2 + 180*m**2 + 50*m**3 + 102*m + 23*m - 37*m + 16 = 0.
-2, -2/5
Factor j**3 + 13*j**5 - 5*j**3 + 14*j**5 - 23*j**5.
4*j**3*(j - 1)*(j + 1)
Suppose 4*y - 4 = 2*s, y + s - 8 = -2*y. Suppose y*u - 6*u + 28 = -5*l, 24 = 2*u - 5*l. Factor -2 + z**3 + z**3 - z - z + 2*z**u.
2*(z - 1)*(z + 1)**2
Determine a so that 24/13*a**2 - 54/13*a + 28/13 + 2/13*a**3 = 0.
-14, 1
Factor 0 - 2/11*h**2 - 2/11*h.
-2*h*(h + 1)/11
Suppose -5*v = -0*v + 5*r + 10, 5*r + 10 = v. Factor -3/4*u**3 - 3*u**5 + 0*u + 15/4*u**4 + v + 0*u**2.
-3*u**3*(u - 1)*(4*u - 1)/4
Let s(h) = h**3 - h**2 - h + 3. Let w be s(0). Factor 2*j**2 + j + j - j + j**w + 0*j.
j*(j + 1)**2
Factor -f**2 + 16*f**4 - 6*f**5 + 349*f**3 + 5*f**2 - 363*f**3.
-2*f**2*(f - 1)**2*(3*f - 2)
Suppose -3*l = -4*l - 5*l. Let x(f) be the second derivative of 2*f + 1/21*f**3 + 0*f**2 + l - 1/70*f**5 + 0*f**4. Factor x(c).
-2*c*(c - 1)*(c + 1)/7
Let h(b) be the second derivative of b**6/15 + 3*b**5/10 - 5*b**4/2 + 17*b**3/3 - 6*b**2 + 23*b. Suppose h(t) = 0. What is t?
-6, 1
Suppose -4*z = -10 - 2. Factor 2*r**4 + 2*r**z - 2*r**2 - r**3 + 0*r**2 - r.
r*(r - 1)*(r + 1)*(2*r + 1)
What is w in -1/9*w**2 + 0*w - 2/9*w**3 - 1/9*w**4 + 0 = 0?
-1, 0
Factor -3 + 13*p**2 + 3 - 5*p**2 + 4*p**3 + 4*p.
4*p*(p + 1)**2
Let j(g) be the first derivative of g**4/6 + 22*g**3/9 + 8*g**2 - 24*g - 11. Find t, given that j(t) = 0.
-6, 1
Let c(t) be the second derivative of -1/27*t**3 - 1/9*t**2 + t + 0 + 1/54*t**4 + 1/90*t**5. Factor c(k).
2*(k - 1)*(k + 1)**2/9
Let m be ((-236)/15)/4 - -4. Let n(a) be the second derivative of 0*a**4 + 2/3*a**3 - 1/5*a**5 + 2*a + m*a**6 - a**2 + 0. Factor n(j).
2*(j - 1)**3*(j + 1)
Let g(u) = -2*u**3 - 2*u**2 - 2. Let z be g(-2). Factor 3*l**2 - 4*l**2 + l - l**3 + z*l**2 - 2 + 0*l**4 - 3*l**4.
-(l - 1)*(l + 1)**2*(3*l - 2)
Let n(m) be the first derivative of -7*m**5/10 + 3*m**4/2 - 2*m**3/3 + 2*m - 3. Let v(k) be the first derivative of n(k). Factor v(p).
-2*p*(p - 1)*(7*p - 2)
Let d(y) = -3*y**3 + 6*y**2 - 6*y + 3. Let g(u) = 9*u**3 - 18*u**2 + 17*u - 8. Let p(b) = -8*d(b) - 3*g(b). Let p(q) = 0. Calculate q.
0, 1
Let b(x) = -4*x**5 - 7*x**4 + x**3 + x**2 + 3*x + 3. Let z(t) = 12*t**5 + 22*t**4 - 2*t**3 - 2*t**2 - 10*t - 10. Let g(f) = -10*b(f) - 3*z(f). Factor g(y).
4*y**2*(y - 1)*(y + 1)**2
Suppose g + 10 = 3*g + 2*j, -5*j = -10. Let y(a) be the second derivative of 0 + 0*a**4 + 0*a**2 + 1/126*a**7 - a + 0*a**g - 1/90*a**6 + 0*a**5. Factor y(r).
r**4*(r - 1)/3
Suppose 12*p = 8*p + 188. Let d = -47 + p. Determine w so that d*w**2 + 1/2*w + 0*w**4 + 0 + 1/2*w**5 - w**3 = 0.
-1, 0, 1
Suppose -k = k - 18. Suppose 0*u = u - k. Factor -2*d + u*d + 2*d**2 - 5*d.
2*d*(d + 1)
Let q(o) be the first derivative of 4/15*o**3 + 4/5*o + 4/5*o**2 + 6. Let q(s) = 0. Calculate s.
-1
Let t(n) be the second derivative of -n**5/90 + n**4/27 + 4*n**3/27 - 8*n**2/9 - 7*n. Solve t(z) = 0.
-2, 2
Suppose -z**2 - 263*z**5 + 256*z**5 + 65*z**2 - 12*z + 29*z**4 + 15*z**4 - 89*z**3 = 0. Calculate z.
0, 2/7, 1, 2, 3
Let n(o) be the second derivative of o + 0 + 0*o**3 - 1/4*o**2 + 1/24*o**4. Factor n(b).
(b - 1)*(b + 1)/2
Let n(g) be the second derivative of g**6/50 + 9*g**5/50 + 9*g**4/20 + 4*g. Suppose n(v) = 0. What is v?
-3, 0
Suppose -t - 31 = -4*t - 5*f, t = -3*f + 13. Suppose t = 2*s + 3. Factor -q**3 - 6*q**2 - 4*q**4 + 6*q**s + 2*q**5 + 3*q**3.
2*q**3*(q - 1)**2
Suppose h - 1 = -2*o - 34, -2*o + h = 23. Let u be 533/21 - 4/o. Find g such that u*g**3 + 4/3*g - 12*g**4 + 12*g**2 + 0 - 27*g**5 = 0.
-1, -2/9, 0, 1
Let o(b) be the third derivative of b**5/30 + b**4/6 + b**3/3 + 4*b**2. Factor o(r).
2*(r + 1)**2
Factor -5/2*h**5 - 15*h**3 - 5/2*h + 10*h**4 + 10*h**2 + 0.
-5*h*(h - 1)**4/2
Let c(l) be the second derivative of 4*l + 0 + 0*l**3 + 0*l**2 + 2/3*l**4 + 1/5*l**5. Let c(d) = 0. Calculate d.
-2, 0
Let d = 80 + -64. Factor -2/3 + d*v**3 - 4*v - 2/3*v**2 - 32/3*v**4.
-2*(v - 1)**2*(4*v + 1)**2/3
Let s(q) be the second derivative of -5*q**4/48 - 5*q**3/24 - 19*q. Determine h, given that s(h) = 0.
-1, 0
Let l(o) be the second derivative of o**7/168 - o**5/40 + o**3/24 - o + 4. Determine m so that l(m) = 0.
-1, 0, 1
Let x(f) be the first derivative of -f**4/8 + 4*f**3/3 + f**2/4 - 4*f + 7. Factor x(w).
-(w - 8)*(w - 1)*(w + 1)/2
Suppose 0 = -2*h + 3*h - 2. Factor 3/5*t**5 - 3/5*t**h + 0*t - 9/5*t**4 + 9/5*t**3 + 0.
3*t**2*(t - 1)**3/5
Suppose 0 = -3*i + 4*i. Let n(u) be the second derivative of i + 1/6*u**4 + 2/3*u**3 + u + u**2. Solve n(p) = 0.
-1
Let i(h) be the first derivative of h**6/21 +