/107 - -2/535. Find c such that 1/5*c**4 - 1/5*c + 0 + s*c**3 - 1/5*c**2 = 0.
-1, 0, 1
Let o be 3/(-2) - 21/(-6). Suppose o*p + p = 0. Factor p*h - 4*h + 6*h - 2*h**3.
-2*h*(h - 1)*(h + 1)
Let p be (2 - 8)/(6/(-3)). Let x = -7/3 + p. Find b such that 0*b**2 + 0*b + 0*b**3 + 0 - x*b**4 = 0.
0
Let r(n) = -4*n**3 - 22*n**2 - 28*n - 14. Let g(k) = -k**2 - 1. Let u(h) = 2*g(h) - r(h). Factor u(t).
4*(t + 1)**2*(t + 3)
Suppose 0*k + 3*k - 4 = n, -3*n = 4*k - 14. Factor w - 8*w**2 - w**3 + 8*w**k + 2*w**2 - 2.
-(w - 2)*(w - 1)*(w + 1)
Let x(p) be the third derivative of p**6/160 + p**5/80 - p**4/16 - 8*p**2. Solve x(k) = 0 for k.
-2, 0, 1
Suppose -6 = -2*a - 3*t, -2*t + 16 = -5*a + 12. Solve 0*l**3 - 1/4*l**2 + 0*l + a + 1/4*l**4 = 0.
-1, 0, 1
Let k(p) be the first derivative of p**4/36 - p**2/6 + p - 3. Let a(u) be the first derivative of k(u). Suppose a(g) = 0. What is g?
-1, 1
Determine c so that -6/7*c**3 - 4/7*c**4 + 2/7*c + 0 + 0*c**2 = 0.
-1, 0, 1/2
Factor 0 - 1/2*v**2 - 1/2*v**3 + v.
-v*(v - 1)*(v + 2)/2
Factor 14*c**4 + 54*c**2 + 84*c + 24*c**3 - 13 - 160*c**2 - 3.
2*(c - 1)**2*(c + 4)*(7*c - 2)
Let d(s) = s**2 + 1. Let r(g) be the first derivative of 4*g**3/3 + 6*g - 5. Let f(k) = -12*d(k) + 2*r(k). Factor f(i).
-4*i**2
Let c = -23/1281 + 4/61. Let v(g) be the second derivative of 1/105*g**6 - 3/70*g**5 + 0*g**2 + 0 + 1/14*g**4 - 2*g - c*g**3. Determine t, given that v(t) = 0.
0, 1
Let k be 4/18 + (0 - 0). Suppose 3*a + 1 = -2*z + 3, -5*z - 4 = 3*a. Let 4/9*x**a + k*x - 2/9*x**3 - 4/9 = 0. What is x?
-1, 1, 2
Find d such that -1/9*d**3 + 1/9*d - 8/9 + 8/9*d**2 = 0.
-1, 1, 8
Let z be 5 + (3 - (0 + 4)). Let u(h) be the third derivative of 2*h**2 + 0*h - 1/24*h**z + 1/60*h**5 + 0*h**3 + 0. What is r in u(r) = 0?
0, 1
Let q(f) be the first derivative of -3*f**5/5 - 3*f**4 - 6*f**3 - 6*f**2 - 3*f - 39. Find i such that q(i) = 0.
-1
Let a(k) = -5*k**2 + 17*k - 8. Let l(j) = 35*j**2 - 120*j + 55. Let m(u) = -15*a(u) - 2*l(u). Factor m(y).
5*(y - 2)*(y - 1)
Let y(t) be the third derivative of t**7/1155 - t**6/660 - t**2. Solve y(z) = 0.
0, 1
Let i = 12 + -12. Let n(f) be the second derivative of 1/36*f**4 + i*f**3 - 2*f - 1/6*f**2 + 0. Find k such that n(k) = 0.
-1, 1
Let q(r) = 417*r**4 + 576*r**3 - 327*r**2 + 81*r. Let f(w) = -52*w**4 - 72*w**3 + 41*w**2 - 10*w. Let l(k) = 33*f(k) + 4*q(k). Factor l(t).
-3*t*(t + 2)*(4*t - 1)**2
Let s(n) = -14*n**3 - 48*n**2 + 20*n. Let l(b) = -b**2 - b. Let x(u) = -4*l(u) - s(u). Suppose x(w) = 0. What is w?
-4, 0, 2/7
Let r(f) be the first derivative of -f**5/120 - f**4/24 - f**2 + 1. Let k(g) be the second derivative of r(g). Factor k(t).
-t*(t + 2)/2
Let c = 4 - 2. Find x, given that 3*x**4 + 4*x**3 + 8*x**3 + 11*x**2 + 3 + 12*x + 7*x**c = 0.
-1
Let c(h) be the third derivative of 0*h**3 + h**2 - 13/120*h**6 + 7/180*h**5 + 1/36*h**4 + 0 + 0*h. Factor c(s).
-s*(3*s - 1)*(13*s + 2)/3
Let q be 5/(-90)*(-6)/4. Let d(k) be the second derivative of 0*k**2 - 3/40*k**5 + 1/5*k**6 - k - q*k**7 + 0 - 1/12*k**4 + 0*k**3. Solve d(h) = 0.
-2/7, 0, 1
Let m(z) be the first derivative of 2/3*z**3 - 1/6*z**6 - 2/5*z**5 + 1/2*z**2 - 6 + 0*z + 0*z**4. Factor m(h).
-h*(h - 1)*(h + 1)**3
Let h(s) = s**2 - 4*s + 2. Let t be h(4). Factor -2 - 3*u - 4*u**2 + 0*u + 3*u**t.
-(u + 1)*(u + 2)
Let b(d) be the third derivative of -d**6/120 + d**5/15 - d**4/24 - d**3 + 2*d**2 - 39. Find l, given that b(l) = 0.
-1, 2, 3
Let y(s) = s**3 - 3*s. Let d = 5 + -2. Let n(g) = d*g**3 + g - 5*g**3 + 7*g. Let k(u) = 3*n(u) + 8*y(u). Factor k(v).
2*v**3
Let c(i) be the third derivative of 0 + 1/600*i**6 + 1/1050*i**7 + 0*i**3 + 0*i**4 + 0*i - i**2 + 0*i**5. Factor c(z).
z**3*(z + 1)/5
Let t(f) be the first derivative of -f**8/5880 - f**7/1470 + f**5/210 + f**4/84 + f**3 + 1. Let z(n) be the third derivative of t(n). Factor z(c).
-2*(c - 1)*(c + 1)**3/7
Solve -29*l**2 - 8*l + 30*l**3 - 18*l**4 + 7*l**2 - 2*l**2 + 20*l**3 = 0.
-2/9, 0, 1, 2
Let p(g) = -7*g**5 - 19*g**4 - 41*g**3 - 35*g**2 - 11*g - 5. Let b(h) = -h**5 - h**4 - h**3 + h**2 + h - 1. Let k(t) = -5*b(t) + p(t). Solve k(v) = 0.
-2, -1, 0
Let t(b) be the third derivative of 0*b + 1/105*b**5 + 0*b**3 + 0 - 8*b**2 + 0*b**6 - 1/1176*b**8 + 1/84*b**4 - 2/735*b**7. Factor t(v).
-2*v*(v - 1)*(v + 1)**3/7
Let u(s) be the first derivative of s**7/840 - s**6/240 - s**5/240 + s**4/48 + s**2/2 - 3. Let t(v) be the second derivative of u(v). Solve t(y) = 0.
-1, 0, 1, 2
Solve -1 + 2*h**2 + 2*h**3 - 3*h**4 + 2*h**4 - 2*h**3 = 0 for h.
-1, 1
Let x(r) be the third derivative of 0 + 0*r + r**2 + 1/270*r**5 + 1/27*r**4 + 4/27*r**3. Suppose x(h) = 0. Calculate h.
-2
Let h = -7 + 10. Suppose 0 = -z + h*t + 2*t - 10, 0 = z - 4*t + 8. Suppose z - 2/3*q**2 + q**3 + 0*q = 0. What is q?
0, 2/3
Let b(o) be the second derivative of o**6/180 - o**5/30 + o**4/18 - 5*o**2/2 + 4*o. Let c(k) be the first derivative of b(k). Factor c(r).
2*r*(r - 2)*(r - 1)/3
Factor 2/3*c + 8/3*c**2 + 0.
2*c*(4*c + 1)/3
Let w be 4/18*(1257/(-420) + 3). Let m(o) be the third derivative of 0*o**3 + 1/36*o**5 - 1/36*o**4 + w*o**7 + 0 + 4*o**2 - 1/90*o**6 + 0*o. Factor m(s).
s*(s - 2)*(s - 1)**2/3
Let g = -97 + 389/4. Factor -1/4*w**2 - g + 1/2*w.
-(w - 1)**2/4
Let p be 210/42 - (4 - 1)/1. Factor 0*f + 4/7*f**3 + 0 - 2/7*f**p.
2*f**2*(2*f - 1)/7
Let r(d) = d - 1. Let m be r(7). Suppose -m*i - i**3 + 2*i + 4*i**2 + 0*i = 0. Calculate i.
0, 2
Let c be 26/(-8)*2*-2. Suppose 5 = w + 3*z - 12, 4*w = -z + c. Factor -2*o**4 + 0*o**3 + 0*o**3 + w*o**3.
-2*o**3*(o - 1)
Let k(d) be the second derivative of -d**5/5 - 2*d**4/3 + 2*d**3/3 + 4*d**2 - 6*d. Factor k(s).
-4*(s - 1)*(s + 1)*(s + 2)
Suppose 2/5*h**3 + 0 - 2/5*h**4 + 8/5*h**2 - 8/5*h = 0. Calculate h.
-2, 0, 1, 2
Let t(w) be the second derivative of 0*w**2 + 0 - 3*w + 1/3*w**3 - 1/180*w**6 + 1/6*w**4 - 1/60*w**5. Let p(v) be the second derivative of t(v). Factor p(n).
-2*(n - 1)*(n + 2)
Let s be 6/1 - (120/(-18))/10. What is t in 28/3*t**4 + s*t**3 - 12*t**2 + 8/3 - 20/3*t = 0?
-1, 2/7, 1
Factor -g**2 - 2*g**3 - 6 - 11*g**2 - 14*g + 0*g**3 + 2*g**2.
-2*(g + 1)**2*(g + 3)
Suppose -2*t = 2 - 0, 4*w - 11 = 3*t. Factor -2/5*y**w + 8/5 + 0*y.
-2*(y - 2)*(y + 2)/5
Factor 8*p**3 - 26*p**2 + 12*p**3 + 11*p**2 - 5*p**4.
-5*p**2*(p - 3)*(p - 1)
Let f(z) be the first derivative of z**4/24 - 7*z**3/18 + 5*z**2/4 - 3*z/2 + 6. Find s, given that f(s) = 0.
1, 3
Let v(f) = -6*f**3 - 3*f**2 + 3*f + 6. Let c = -18 + 12. Let x(s) = 5*s**3 + 3*s**2 - 3*s - 5. Let u(n) = c*v(n) - 7*x(n). Factor u(m).
(m - 1)**3
Let p = 4 - 4. Suppose 0 = -c - p + 3. Factor g**3 + 3*g + g**c + g**2 - 5*g**3 + 2 + 5*g**4 - 8*g**2.
(g - 1)**2*(g + 1)*(5*g + 2)
Let q be 1/4*2*0. Let c(j) be the second derivative of -1/3*j**3 + 1/12*j**4 - 1/10*j**6 - 2*j + 0*j**2 + q + 1/5*j**5. Factor c(v).
-v*(v - 1)**2*(3*v + 2)
Let g = 2 + 0. Let s be (3/g)/(3/8). Find r such that -4*r - r**4 + 1 + 2*r**5 + 2*r**2 + 2*r**2 - 4*r**s + 2*r**3 = 0.
-1, 1/2, 1
Let m(l) = l**2. Let v(c) = 2*c**3 - 6*c**2 - 8*c + 16. Let t(h) = 2*m(h) + v(h). Factor t(b).
2*(b - 2)**2*(b + 2)
Let i be (0 - -1) + (-1 - (-6 + 6)). Factor 4/5*o**2 + 6/5*o**3 + 0*o - 2/5*o**5 + 0 + i*o**4.
-2*o**2*(o - 2)*(o + 1)**2/5
Factor -5*k**3 + k**4 + 0*k**4 - 6*k**4.
-5*k**3*(k + 1)
Suppose -8 = g - 3*g. Let s(u) = 6*u**2 + 4*u - 4. Let o(q) = -q**2 + 1. Let i(h) = g*o(h) + s(h). Solve i(p) = 0 for p.
-2, 0
Suppose 3*f + 8 = f. Let p(d) = d**2 + 5*d + 6. Let l be p(f). Solve -l*x - x**3 + x**2 - x**2 - 3*x**2 = 0.
-2, -1, 0
Let l(j) = j**4 + 17*j**3 + 27*j**2 + 21*j + 6. Let z(s) = -s**4 - 35*s**3 - 54*s**2 - 42*s - 12. Let g(q) = -5*l(q) - 2*z(q). Factor g(y).
-3*(y + 1)**3*(y + 2)
Let h(f) be the third derivative of -f**6/360 + f**5/30 - f**4/6 + 4*f**3/3 + 6*f**2. Let o(s) be the first derivative of h(s). Factor o(x).
-(x - 2)**2
Let q = -60707/18 - -3367. Let y = -31/6 - q. Suppose y*p - 2/9*p**2 - 2/9 = 0. Calculate p.
1
Suppose -2*j - 5 = -k, 4*k + 3*j - 10 = 6*j. Solve 1 - k + r**3 = 0 for r.
0
Let z(p) = 3 - 1 + 2 - p. Let l be z(0). Find h, given that -2 - 44*h**2 - 51*h**3 - 34*h**l - 5*h**3 - 16*h + 0 - 8*h**5 = 0.
-1, -1/4
Let a(w) = w**4 + 4*w**3 + 2*w**2 + 5*w + 3. Let v(c) = -c**4 - 4*c**3 - 3*c**2 - 4*c - 2. Let b(t) = 2*a(t) + 3*v(t). Determine g so that b(g) = 0.
-2