Solve 0 + 2/3*m - j*m**2 = 0.
0, 1
Let y(w) = -w**2 + 1. Let o = 1 - 0. Let x(b) be the second derivative of b**4/6 - b**3/6 - 3*b**2/2 + 3*b. Let t(i) = o*x(i) + 3*y(i). Solve t(v) = 0.
-1, 0
Factor -6/7*u + 0*u**2 - 3/7*u**4 + 6/7*u**3 + 3/7.
-3*(u - 1)**3*(u + 1)/7
Let v = -1 + 4. Suppose 5*m = -3*j + 9, -2*j = -v*j + 3. Let m*x - 2/7*x**4 + 0 + 0*x**2 + 4/7*x**3 = 0. Calculate x.
0, 2
Let y be ((-7)/(-28))/((-15)/(-4)). Let x(f) be the first derivative of 0*f**2 - 4/25*f**5 + 2 - y*f**6 + 0*f - 1/10*f**4 + 0*f**3. Factor x(p).
-2*p**3*(p + 1)**2/5
Let y(d) be the first derivative of -d**7/21 - d**6/5 - 3*d**5/10 - d**4/6 - 3*d**2/2 + 6. Let v(k) be the second derivative of y(k). Factor v(h).
-2*h*(h + 1)**2*(5*h + 2)
Let c(y) = -y**4 + 13*y**3 - 26*y**2 + 22*y - 3. Let s(h) = h**4 - 12*h**3 + 25*h**2 - 22*h + 4. Let z(u) = 4*c(u) + 5*s(u). What is x in z(x) = 0?
1, 2, 4
Suppose 3*f**3 - 2*f**2 + 3*f**4 + 0*f**5 - 2*f**2 + f**2 - 3*f**5 = 0. What is f?
-1, 0, 1
Let f(m) be the first derivative of m**5/20 + m**4/8 + m**3/12 + 6. What is j in f(j) = 0?
-1, 0
Let b(i) be the second derivative of -3*i**8/8960 + i**7/672 + i**6/240 - i**5/40 - i**4/2 - 9*i. Let z(k) be the third derivative of b(k). Factor z(x).
-3*(x - 2)*(x + 1)*(3*x - 2)/4
Let b be 3/(-5)*3/(-27). Let k(i) be the second derivative of -i + 0 + b*i**3 + 0*i**2 + 1/30*i**4. Factor k(h).
2*h*(h + 1)/5
Let c(z) be the first derivative of -27*z - z**3 + 7*z**2 - 7 - 5 + 4 + 2*z**2. Determine s, given that c(s) = 0.
3
Factor 0 + 12/7*a - 6/7*a**2.
-6*a*(a - 2)/7
Suppose 4*t - 8 = 2*t. Suppose 0 = -4*s + 19 - 3. Find v such that -s*v**t - 4*v**2 - 2*v + 2*v**5 + 0*v + 8*v**4 = 0.
-1, 0, 1
Let f(j) be the second derivative of 0 - j + 1/12*j**3 + 1/8*j**2 + 1/48*j**4. Factor f(t).
(t + 1)**2/4
Let f(m) = m - 2. Let h(a) = -2*a + 1. Let r be h(-3). Let g be f(r). Determine b, given that -2/11*b**2 - 6/11*b**3 + 0 - 6/11*b**4 + 0*b - 2/11*b**g = 0.
-1, 0
Factor -1/4*d + 3/8 - 1/8*d**2.
-(d - 1)*(d + 3)/8
Let d = -403/5 - -81. Suppose -p - 18 = -4*w, 0 = 4*p - 6*p + 5*w - 21. Suppose -d*r - 2/5 + 4/5*r**p = 0. Calculate r.
-1/2, 1
Let y = -13 + 18. Suppose 13 = -r + y*u, 0 = -0*r + 2*r - 5*u + 11. Find w such that -r*w**2 + 3*w - 3*w = 0.
0
Let f = -97 + 99. Let b(a) be the first derivative of 2*a**f - 2/3*a**3 - 2*a + 2. Determine z, given that b(z) = 0.
1
Let r(h) = -h - 9. Let c be r(-8). Let k be -12*c/(1 - -1). Factor -4*u - 6*u**2 + k*u + 0*u**2.
-2*u*(3*u - 1)
Let d(p) be the first derivative of -p**4/28 + 3*p**2/14 + 2*p/7 - 8. Factor d(h).
-(h - 2)*(h + 1)**2/7
Let c = -423/5 + 85. Find z, given that 0*z - 2/5 + 4/5*z**2 + 0*z**3 - c*z**4 = 0.
-1, 1
Suppose 449*s**2 + 3*s**3 - 2*s**3 - 448*s**2 = 0. Calculate s.
-1, 0
Let a(b) be the first derivative of -28/3*b**3 + 4*b - 12*b**2 + 5. Determine l so that a(l) = 0.
-1, 1/7
Let t(u) = u**2 - 6*u + 4. Let v be t(6). Factor -4*q**2 - 4*q + 2*q**5 + v*q**4 + 3*q - q.
2*q*(q - 1)*(q + 1)**3
Let l(x) be the second derivative of -4*x**7/735 - x**6/60 - x**5/105 + x**4/84 - 3*x**2/2 - 4*x. Let d(a) be the first derivative of l(a). Factor d(v).
-2*v*(v + 1)**2*(4*v - 1)/7
Let g = 6 + -4. Factor -1 + g*r + 5/4*r**2.
(r + 2)*(5*r - 2)/4
Suppose 4 = 2*v - 10. Factor -g**2 + 3 - v*g**2 + 5*g**2.
-3*(g - 1)*(g + 1)
Factor 12*a**4 + a**5 - 3*a**5 - 15*a**4 - a**5.
-3*a**4*(a + 1)
Let m(j) be the second derivative of 1/18*j**4 + 0*j**2 + 0 + 0*j**3 + j - 1/30*j**5. Factor m(b).
-2*b**2*(b - 1)/3
Let c(s) be the first derivative of 3*s**3 - 3*s**2 - 3*s - 6. Solve c(m) = 0.
-1/3, 1
Let s(v) = -v**3 - 18*v**2 + 19*v + 2. Let g be s(-19). Determine m, given that 3/4*m**g - 3/4*m - 3/2 = 0.
-1, 2
Let h(w) = -7*w**2 - 9*w + 3. Let k(o) = -o**2 + o + 1. Let u(x) = h(x) - 3*k(x). Determine m, given that u(m) = 0.
-3, 0
Solve 0*o**2 + 0 + 2/7*o**3 - 2/7*o = 0 for o.
-1, 0, 1
Let w = 3 - -11. Let t = w - 10. Factor 3*k**2 + t*k - 4 - 3*k**2 - k**2.
-(k - 2)**2
Let f = 5/2 + -2. Determine k so that -1/2*k + 1/2 - f*k**2 + 1/2*k**3 = 0.
-1, 1
Factor 42*n - 50*n + n**3 + n**3.
2*n*(n - 2)*(n + 2)
Determine b, given that -6/5*b**3 + 0*b**2 + 6/5*b + 3/5 - 3/5*b**4 = 0.
-1, 1
Let u be (2/91)/((-19)/(-133)). Factor 0 - u*l + 2/13*l**2.
2*l*(l - 1)/13
Suppose -t = x - 7, -2*x + 4*t - 3 = 7. Let o = -3 + x. Find g such that 2/9*g**2 - 2/9*g + o = 0.
0, 1
Let r(o) be the second derivative of -o**7/84 - o**6/30 - o**5/160 + 7*o**4/96 + 5*o**3/48 + o**2/16 - 11*o. Solve r(t) = 0 for t.
-1, -1/2, 1
Let j(u) = -u**2 - 21*u - 75. Let n be j(-5). Factor 30*b**2 + 0 - 12*b + 21/2*b**4 - 3/2*b**n - 27*b**3.
-3*b*(b - 2)**3*(b - 1)/2
Let f(r) = r - 6*r**2 + 10*r + r**2 - 11. Let i(b) = 2*b**2 - 4*b + 4. Let w(k) = 4*f(k) + 11*i(k). Suppose w(g) = 0. Calculate g.
0
Let d(u) be the second derivative of -u**10/45360 + u**8/3360 - u**7/1890 + u**4/3 + 4*u. Let j(q) be the third derivative of d(q). Factor j(w).
-2*w**2*(w - 1)**2*(w + 2)/3
Suppose 0 = 4*s - 8, 2*n - s = -0*s + 4. Let y(t) be the second derivative of 0 + 0*t**2 - 1/10*t**n + 1/20*t**4 - t. Factor y(b).
3*b*(b - 1)/5
Let l(h) be the third derivative of 0*h**3 + 0*h - 1/70*h**7 - 2*h**2 + 1/40*h**6 + 1/20*h**5 + 0 - 1/8*h**4. Let l(m) = 0. Calculate m.
-1, 0, 1
Let z = 1/78 + 131/1950. Let o(j) be the first derivative of 0*j**4 + 0*j + 2/15*j**3 - z*j**5 + 3 + 0*j**2. Factor o(b).
-2*b**2*(b - 1)*(b + 1)/5
Let h(y) be the third derivative of -2*y**7/105 - 2*y**6/15 - y**5/3 - y**4/3 + 8*y**2. Factor h(w).
-4*w*(w + 1)**2*(w + 2)
Let h = -2 + 4. Factor 3*n**h - 9*n**2 - 4*n**3 + n**3 + 0*n**3 + 6 + 3*n.
-3*(n - 1)*(n + 1)*(n + 2)
Let y(c) be the first derivative of 5/9*c**3 - 1/3*c - 1/4*c**4 + 3 - 1/6*c**2. Solve y(k) = 0 for k.
-1/3, 1
Let h(t) = t - 3. Let j be h(6). Find x, given that 4*x**3 - x**j + x**4 - 5*x**3 + 2*x - x**2 = 0.
-1, 0, 1, 2
Suppose -5*n - 5 = -5*g, -4*g = -n + 2*n + 26. Let h be (((-18)/4)/3)/n. Suppose -h*f - 1/4*f**2 + 0 = 0. What is f?
-1, 0
Let a be 85/150 + (-3)/18. Suppose y - 2*y - 1 = -4*h, y + 1 = -2*h. Factor h - 2/5*r - a*r**2.
-2*r*(r + 1)/5
Let j(c) be the third derivative of c**6/50 + c**5/75 - c**4/15 + 28*c**2. Determine u so that j(u) = 0.
-1, 0, 2/3
Let n = -24 - -44. Let w = -79/4 + n. Let -w*h**2 + 0*h + 1/4 = 0. What is h?
-1, 1
Let o = -50 - -27. Let c = o - -23. Let 2/7*m**4 + 4/7*m + 8/7*m**3 + 10/7*m**2 + c = 0. What is m?
-2, -1, 0
Suppose 0 = -5*g + 38 + 67. Let p = 43/2 - g. Factor 1/2*t**2 + 0 - 1/2*t**4 + p*t - 1/2*t**3.
-t*(t - 1)*(t + 1)**2/2
Let q(w) = -14*w**3 + 18*w - 12. Suppose 3*b = f + 4*b + 1, -5*f - 3*b = -3. Let r(p) = 5*p**3 - 6*p + 4. Let o(u) = f*q(u) + 8*r(u). Factor o(z).
-2*(z - 1)**2*(z + 2)
Let f(l) = -4*l**4 + 7*l**3 + 35*l**2 - 11. Let g(a) = 2*a**4 - 4*a**3 - 18*a**2 + 6. Let t(y) = -6*f(y) - 11*g(y). Determine m so that t(m) = 0.
-3, 0, 2
Find j, given that -8/5 - 12/5*j + 4*j**2 = 0.
-2/5, 1
Let r(t) be the second derivative of 3*t**5/40 + 5*t**4/8 + 3*t**3/2 - 18*t. Let r(p) = 0. Calculate p.
-3, -2, 0
Let y(r) be the first derivative of r**6/180 - r**4/12 + 2*r**3/3 + 2. Let s(u) be the third derivative of y(u). Determine c, given that s(c) = 0.
-1, 1
Let j(r) = r**2. Let m(x) = 20*x**2. Let q(z) = 24*j(z) - m(z). Factor q(o).
4*o**2
Let u(i) be the first derivative of 7*i**6/15 + 4*i**5/25 - 7*i**4/10 - 4*i**3/15 + 2. What is t in u(t) = 0?
-1, -2/7, 0, 1
Let p(u) be the second derivative of u**4/54 - 21*u. What is d in p(d) = 0?
0
Let g(l) = 6*l**5 + 6*l**4 - 5*l**3 + 5. Let j(t) = -5*t**5 - 5*t**4 + 4*t**3 - 4. Let r = -7 + 3. Let o(y) = r*g(y) - 5*j(y). Find f, given that o(f) = 0.
-1, 0
Let b = -10 + 12. Determine y so that -8*y + 13*y - 5*y + b*y**2 = 0.
0
Let o = -58 - -61. Let k(i) be the first derivative of -1/6*i**o - 1/2*i - 3 - 1/2*i**2. Factor k(s).
-(s + 1)**2/2
Factor 3*g**2 - 3/2*g**3 + 0 - 3/2*g.
-3*g*(g - 1)**2/2
Let b(d) = 7*d**3 - 3*d**2. Let t(k) = -8*k**3 + 4*k**2. Let i(j) = 6*b(j) + 5*t(j). Factor i(f).
2*f**2*(f + 1)
Suppose -5*b + b + 2*a = -10, 2*b + a - 15 = 0. Suppose 3*i - 9 = r - 3*r, -b*i = -4*r + 7. Find q such that -1/3*q**r + 4/3*q**2 - 4/3*q + 0 = 0.
0, 2
Let d(m) be the first derivative of -2*m**3/39 + m**2/13 + 4*m/13 + 8. Let d(z) = 0. Calculate z.
-1, 2
Let x(d) be the first derivative of -5*