2*(a + 1)
Suppose 4*z + 2*b = -352, 7*z = 2*z + 4*b - 466. Let w be 21/(-35) - 74/z. Factor -w*g**2 + 4/9*g - 2/9.
-2*(g - 1)**2/9
Let w = -1 - 1. Let s be (-12)/w*(-2)/(-6). Solve 0*v - 4*v + 14*v**s - 4 + 2 - 8*v**3 = 0.
-1/4, 1
Let j(b) = 132*b**3 + 101*b**2 - 17*b - 7. Let x(h) = 44*h**3 + 34*h**2 - 6*h - 2. Let t(g) = -2*j(g) + 7*x(g). Factor t(f).
4*f*(f + 1)*(11*f - 2)
Let w = -242 - -247. Factor 0*g**2 + 1/6*g**w + 0 + 1/6*g**4 + 0*g**3 + 0*g.
g**4*(g + 1)/6
Let -543*z**4 + 8*z**2 + 0*z**2 + 563*z**4 + 28*z**3 = 0. Calculate z.
-1, -2/5, 0
Determine d so that 5*d**3 - 3 - 9*d + 4*d - 2 - 10*d**4 + 10*d**2 + 5*d**2 = 0.
-1, -1/2, 1
Let c = 1249 - 6239/5. Determine g so that -9/5*g + c + 3/5*g**2 = 0.
1, 2
Determine z, given that -2 - 1/2*z**2 + 2*z = 0.
2
Suppose -6/19 + 8/19*v + 2/19*v**2 - 4/19*v**3 = 0. What is v?
-3/2, 1
Let a(m) be the first derivative of 3*m**5/20 + 5*m + 4. Let d(r) be the first derivative of a(r). Let d(k) = 0. Calculate k.
0
Suppose 1/4*t**5 + 9/4*t**2 + 0*t + 0 + 3/4*t**3 - 5/4*t**4 = 0. Calculate t.
-1, 0, 3
Suppose 17*k - 16*k - 11 = 0. Let r = 15 - k. Let -4/3 + 7/3*u**2 + r*u = 0. What is u?
-2, 2/7
Determine k so that -2/15*k**3 + 16/15 - 4/3*k**2 + 8/15*k**4 + 8/15*k - 2/15*k**5 = 0.
-1, 2
Determine p, given that p**4 + 4*p**4 - 2*p**3 - 3*p**4 + 4*p**3 = 0.
-1, 0
Let n(a) = 27*a**3 - 27*a**2 + 9*a - 12. Let j(b) = 1 + 1 - 3. Let k(u) = 22*j(u) - 2*n(u). Solve k(f) = 0 for f.
1/3
Let n = -1 + 6. Factor 5*z**4 + 1 + 3*z**2 + 2*z**5 + 10*z**3 - z**5 + 7*z**2 + n*z.
(z + 1)**5
Suppose -2*y = -16 + 4. Let o(j) = -3*j**2 + 9. Let x(v) = -9*v**2 + 26. Let g be (-2)/6 - (-50)/(-3). Let c(a) = g*o(a) + y*x(a). Factor c(u).
-3*(u - 1)*(u + 1)
Let x = 374 - 1487/4. Factor 0*u + x*u**5 - 5/4*u**3 + 1 - 15/4*u**2 + 15/4*u**4.
(u + 1)**3*(3*u - 2)**2/4
Let g(r) be the second derivative of r**7/210 - r**5/50 + r**3/30 - 3*r. Factor g(h).
h*(h - 1)**2*(h + 1)**2/5
Let d(f) be the third derivative of -f**6/96 + 7*f**5/48 - 25*f**4/32 + 15*f**3/8 - 16*f**2. Factor d(c).
-5*(c - 3)**2*(c - 1)/4
Let j(r) be the third derivative of -r**7/42 + r**5/3 + r**2. Factor j(g).
-5*g**2*(g - 2)*(g + 2)
Let t(g) be the second derivative of g**5/90 - g**4/18 - 32*g. Factor t(a).
2*a**2*(a - 3)/9
Let l = 6 + -2. Let i(o) be the second derivative of 0 - o**2 - o + 1/10*o**5 - 1/3*o**3 + 1/6*o**l. Factor i(g).
2*(g - 1)*(g + 1)**2
Solve 0 - 2/7*a**3 + 2/7*a**2 + 0*a = 0.
0, 1
Factor 1/3*s**2 + 2*s + 3.
(s + 3)**2/3
Suppose -5*u = -3*q - 26, -2*q = 5*u - 10 - 6. Let t = 117 + -344/3. Find r, given that -8/3*r**2 + 4/3*r - r**3 + 0 - 2/3*r**5 + t*r**u = 0.
-1, 0, 1/2, 2
Find r, given that 2/7*r + 1/7 - r**2 + 4/7*r**3 = 0.
-1/4, 1
Factor -2/7*h**2 + 0 + 16/7*h.
-2*h*(h - 8)/7
Let h = -1076/7 + 154. Let r be ((-6)/(-4))/(5/10). Factor -h*p**4 + 6/7*p**5 + 0*p + 0 + 0*p**2 + 0*p**r.
2*p**4*(3*p - 1)/7
Let g(h) be the second derivative of -h**7/210 - h**6/45 - h**3/2 - 2*h. Let i(a) be the second derivative of g(a). Solve i(o) = 0 for o.
-2, 0
Factor 0*u + 6/5*u**3 - 2/5*u**2 + 0.
2*u**2*(3*u - 1)/5
Let g(d) be the first derivative of d**4/4 + 4*d**3 + 24*d**2 + 64*d + 3. Let g(z) = 0. Calculate z.
-4
Let c(j) be the first derivative of j**4/2 - 4*j**3 + 12*j**2 - 16*j - 7. Solve c(y) = 0 for y.
2
Let w(k) = k**5 - 2*k**4 + 8*k**3 - 2*k**2 + 3*k + 2. Let q(j) = j**4 + j**3 + j**2 + j + 1. Let o(z) = 2*q(z) - w(z). Determine v, given that o(v) = 0.
0, 1
Let 173 - 36*j - 8*j**2 - 157 - 2*j**2 = 0. Calculate j.
-4, 2/5
Suppose -3 = -2*v + 5. Suppose 2*p = v*p. What is d in p - d**2 + 0*d**3 + d**4 + 1/2*d**5 - 1/2*d = 0?
-1, 0, 1
Let o(l) be the first derivative of 2*l**3/3 + 5*l**2/2 + 2*l - 6. Find s, given that o(s) = 0.
-2, -1/2
Suppose -3*r - 1 = -7. Solve -7*o**2 - 4*o**3 + 10*o**4 + 2*o - o**r - 4*o**5 + 6*o - 2 + 0*o = 0.
-1, 1/2, 1
Let r(k) be the first derivative of 1/6*k**4 - 2/3*k + k**2 - 1 - 2/3*k**3. Factor r(l).
2*(l - 1)**3/3
Let t(j) be the first derivative of -4/5*j - 8/15*j**3 - j**2 - 1/10*j**4 - 3. Solve t(o) = 0 for o.
-2, -1
Let m(h) = 12*h**2 + 4*h - 2. Let o(s) = -s**2 + 1. Let i(x) = 2*m(x) + 4*o(x). Factor i(t).
4*t*(5*t + 2)
Let z be 1*(-1 - -1)/2. Let a(q) be the first derivative of 1 + q**2 + z*q + 2/3*q**3. Factor a(p).
2*p*(p + 1)
Let a(g) = g**4 + g**3 + g**2 - g. Let o(q) = 2*q**5 - 18*q**4 + 18*q**3 - 22*q**2 + 6*q. Suppose 2*d + 2 = 4*d. Let f(z) = d*o(z) + 6*a(z). Factor f(n).
2*n**2*(n - 2)**3
Let u(g) be the third derivative of 0*g + g**2 - 1/108*g**4 - 1/540*g**6 + 0 + 0*g**3 - 1/135*g**5. Factor u(c).
-2*c*(c + 1)**2/9
Let i(h) be the second derivative of h**4/138 + h**3/69 - 3*h. Factor i(x).
2*x*(x + 1)/23
Let a(b) be the first derivative of b**6/30 - b**5/6 - b**4/3 - b**3 + 1. Let d(f) be the third derivative of a(f). Factor d(c).
4*(c - 2)*(3*c + 1)
Let z be -4 + 36/10 + (-9)/(-10). Determine j, given that z*j**4 - j**3 + 0 + 1/2*j**2 + 0*j = 0.
0, 1
Suppose -4*u + 2*u + 2 = 0. Let r(w) be the first derivative of 1/6*w**3 - u - 1/2*w - 1/4*w**2 + 1/8*w**4. Factor r(c).
(c - 1)*(c + 1)**2/2
Suppose 3*x - 5*l - 20 + 4 = 0, 5*x - 14 = 2*l. Let o be (4/(-8))/(x/(-20)). Suppose -m**4 - 2*m**5 - 2*m**2 - 6*m**3 - o*m**4 + 0*m**2 = 0. Calculate m.
-1, 0
Suppose 0 = -4*k - 3*l - 15, 5*l = k - 0*l - 25. Factor 1/5*w**2 + k*w + 0.
w**2/5
Let b = 185 - 185. Suppose b*d + 0*d**3 - 3*d**2 + 3/2*d**4 + 3/2 = 0. What is d?
-1, 1
Let k(s) be the second derivative of 4/105*s**6 - 2/7*s**2 + 0 + 5/21*s**3 - 1/21*s**4 - 2/35*s**5 - 1/147*s**7 - s. Solve k(y) = 0.
-1, 1, 2
Find w, given that -18/5*w**3 + 4/5*w + 0 - 14/5*w**2 = 0.
-1, 0, 2/9
Let f(t) be the first derivative of -t**4 - 8*t**3/3 + 2*t**2 + 8*t - 1. Factor f(n).
-4*(n - 1)*(n + 1)*(n + 2)
Suppose 3*i - 4*i = -2. What is q in -3*q - 3*q**i + 2*q**2 + q = 0?
-2, 0
Let r = -935/9 + 105. Find x such that 62/9*x**2 + 8/9 - r*x**5 + 26/9*x**3 + 40/9*x - 14/9*x**4 = 0.
-1, -2/5, 2
Let c(q) be the first derivative of -q**4 + 4*q**3/3 - 13. Find y such that c(y) = 0.
0, 1
Let y = -9 - -13. Suppose -3*b + 16 = b. Determine w so that -2 + 2*w**5 - y*w**2 - 6*w + 0*w**3 + 0*w**3 + b*w**3 + 6*w**4 = 0.
-1, 1
Let v = -4 - -6. Suppose -5*a + 28 = v*c, 28 = -3*c + 6*c + 4*a. Factor 5*n**5 - 6*n**c + 5*n**2 + 3*n**2 - 7*n**5.
-2*n**2*(n - 1)*(n + 2)**2
Let z(t) be the first derivative of 0*t - t**3 + 2 + 9/2*t**2. Factor z(i).
-3*i*(i - 3)
Let c(k) be the second derivative of -k**7/252 + k**6/180 + k**5/120 - k**4/72 - 51*k. What is h in c(h) = 0?
-1, 0, 1
Let k = 57 - 283/5. Let 4/5*n**5 - 2/5*n**3 - k*n + 6/5*n**4 + 0 - 6/5*n**2 = 0. Calculate n.
-1, -1/2, 0, 1
Determine j so that -11/2*j - 1 + 13/2*j**2 = 0.
-2/13, 1
Find u, given that 4*u**3 - 28*u**2 - 4*u**4 + 17*u**2 + 8 + 23*u**2 - 20*u = 0.
-2, 1
Factor 2/13 + 14/13*k**2 + 6/13*k**3 + 10/13*k.
2*(k + 1)**2*(3*k + 1)/13
Let z = 0 - -2. Suppose a - 7 = 3*p, z*a + 4*p - 4 = -0*a. Factor 12/5*n**3 - 6/5*n + 0 - 9/5*n**a + 3/5*n**2.
-3*n*(n - 1)**2*(3*n + 2)/5
Let y(p) be the first derivative of -p**3/3 - 6*p + 3. Let n(t) = 2*t**2 + 13. Let o(j) = 6*n(j) + 13*y(j). Suppose o(s) = 0. What is s?
0
Let f(z) = z**2 - 8*z - 3. Let o(i) = -i - 1. Let k(m) = f(m) - 3*o(m). Let l be k(5). Factor -4/9*s + 2/9*s**2 + l.
2*s*(s - 2)/9
Solve -8/5*f**2 + 2/5*f + 6/5*f**3 + 0 = 0 for f.
0, 1/3, 1
Let q(k) = 4*k**2 + k - 1. Let a be q(1). Factor -106*r + 106*r + a*r**2 + 2*r**3.
2*r**2*(r + 2)
Suppose -10*r + 18*r = 3*r. Solve -4/9*d**4 + 2/3*d**3 - 2/9*d**2 + 0 + r*d = 0.
0, 1/2, 1
Let j(q) be the first derivative of -q**4/24 - q**3/12 + q**2/2 - 9*q - 4. Let z(b) be the first derivative of j(b). Factor z(i).
-(i - 1)*(i + 2)/2
Let f(v) = -8*v**5 - 13*v**4 - 5*v**3 - v**2 + 7. Let y(j) = -j**5 - j**4 + j**3 + j**2 + 1. Let x(r) = 2*f(r) - 14*y(r). Solve x(u) = 0.
-2, 0
Let b(t) = t**2 + t - 1. Let a be b(2). Suppose a*r**4 - 4*r + r**4 - 6*r**2 + 3*r**5 - r**5 + 2*r**3 = 0. What is r?
-2, -1, 0, 1
Factor -96*l + 4 + 94*l + 2*l**3 + 3*l**2 - 7*l**2.
2*(l - 2)*(l - 1)*(l + 1)
Let h(z) be the first derivative of -z**3/9 + z**2/6 - 47. What is g in h(g) = 0?
0, 1
Let k(o) be the first derivative of o**8/112 + o**7/35 + o**6/40 - 3*o**2/2 - 4. Let f(y) be the second derivative of k(y). Factor f(b).
3*b**3*(b + 1)**2
Let j(l) be th