4 = 0. Calculate k.
0, 1
Suppose 0 = 4*x + 5*q + 13, 5*x - 2*q - 1 = 8*x. Factor -15/2*p**x - 21/2*p + 33/2*p**2 + 3/2.
-3*(p - 1)**2*(5*p - 1)/2
Determine i, given that 0 + 1/6*i**3 - 1/2*i**2 + 1/3*i = 0.
0, 1, 2
Let m = -48 + 146/3. Factor m + 2*q**2 - 8/3*q.
2*(q - 1)*(3*q - 1)/3
Let i = 27 + -27. Let m(w) be the second derivative of 1/6*w**4 + i*w**2 + w + 0*w**3 - 1/10*w**6 + 0 - 1/20*w**5. Factor m(l).
-l**2*(l + 1)*(3*l - 2)
Let s = -6/23 + 88/161. Factor 0*f**3 + 0*f - s*f**4 + 0*f**2 + 0.
-2*f**4/7
Find c, given that -1/2*c**2 + 0*c + 0 - 1/4*c**3 = 0.
-2, 0
Let j(b) be the first derivative of b**6/24 - b**5/5 + b**4/4 + b**3/6 - 5*b**2/8 + b/2 - 22. Determine h so that j(h) = 0.
-1, 1, 2
Factor -2/5*t - 1/10*t**2 + 1/2.
-(t - 1)*(t + 5)/10
Let m(v) be the second derivative of -v**9/37800 + v**7/6300 - 2*v**4/3 - 7*v. Let z(s) be the third derivative of m(s). Find n such that z(n) = 0.
-1, 0, 1
Let u(i) = -i - 1. Let r be u(-5). Factor -1/5*a**5 + 0*a + 4/5*a**r - 4/5*a**3 + 0*a**2 + 0.
-a**3*(a - 2)**2/5
Suppose 0*h = 5*p + 3*h - 3, 3*h + 24 = 4*p. Let i(x) be the second derivative of 0*x**4 + 0*x**5 + 0*x**p - 2*x + 0*x**2 + 1/105*x**6 + 0. Factor i(w).
2*w**4/7
Let z(c) = c + 8. Let h be z(-5). Factor 2/3*a + 4/3*a**4 + 0*a**2 - 2*a**h + 0.
2*a*(a - 1)**2*(2*a + 1)/3
Let z(f) be the second derivative of -3*f**2 - 2/3*f**3 - f - 1/18*f**4 + 0. Factor z(y).
-2*(y + 3)**2/3
Let s(u) be the second derivative of u**10/105840 + u**9/26460 + u**8/23520 - u**4/4 + 2*u. Let q(w) be the third derivative of s(w). What is r in q(r) = 0?
-1, 0
Let d(i) = 16*i**3 + 6*i**2 - 7*i + 3. Let b(z) = -16*z**3 - 5*z**2 + 7*z - 4. Let a(o) = 2*b(o) + 3*d(o). Factor a(v).
(v + 1)*(4*v - 1)**2
Let m(j) be the first derivative of j**8/1176 - j**6/210 + j**4/84 + j**2 + 2. Let c(z) be the second derivative of m(z). Factor c(s).
2*s*(s - 1)**2*(s + 1)**2/7
Let n(y) be the third derivative of 3/245*y**7 - 3*y**2 + 1/70*y**6 + 0*y + 4/21*y**3 - 1/21*y**4 - 11/210*y**5 + 0. What is t in n(t) = 0?
-1, 2/3
Let x(n) be the second derivative of -n - 1/2*n**2 + 1/6*n**5 + 1/3*n**3 - 1/2*n**4 + 0. Let a(s) be the first derivative of x(s). Factor a(b).
2*(b - 1)*(5*b - 1)
Let f be 8/(-2) + 0/6. Let i(t) = 2*t**3 - 5*t. Let q(j) = 2*j**3 - 4*j. Let v(z) = f*i(z) + 5*q(z). What is r in v(r) = 0?
0
Suppose -4*c - 12 = a, 3*a + 2*c - 12 = -2*a. Suppose -6 - 6 = -a*w. Find t, given that -3*t**3 - w*t**4 - 2*t**2 - 3*t**4 - 2*t**5 - 3*t**3 = 0.
-1, 0
Let s(f) be the second derivative of f**4/9 + f**3/6 - f. Factor s(d).
d*(4*d + 3)/3
Let r(h) be the first derivative of h**5/180 - h**4/36 + h**3/18 + 3*h**2/2 + 2. Let f(p) be the second derivative of r(p). What is z in f(z) = 0?
1
Suppose 2*n - 7*n - 3 = -t, -5*n - t + 3 = 0. Factor -2/7*c**4 + 0*c - 2/7*c**3 + 2/7*c**5 + n + 2/7*c**2.
2*c**2*(c - 1)**2*(c + 1)/7
Let w(v) be the third derivative of -2*v**2 + 0*v + 1/60*v**5 + 0 + 0*v**4 + 0*v**3. Find h such that w(h) = 0.
0
Let p = -11 - -15. Factor -p*y**2 + y + 2*y + y**2.
-3*y*(y - 1)
Let x(v) = v**3 - 2*v**2 - 10*v + 10. Let w be x(4). Factor -8/3*y**2 - 2/3*y + 0 - w*y**3.
-2*y*(y + 1)*(3*y + 1)/3
Let j(v) be the second derivative of -v**7/21 + 2*v**5/5 + v**4/3 - v**3 - 2*v**2 + v. Factor j(a).
-2*(a - 2)*(a - 1)*(a + 1)**3
Suppose 0 = 23*d - 24*d + 6. Let s(i) be the first derivative of 1/3*i**d + 0*i - 1 + 0*i**2 - 1/2*i**4 + 2/5*i**5 - 2/3*i**3. What is p in s(p) = 0?
-1, 0, 1
Let n be (-12)/(-3) + (315/(-10))/9. Factor 3/2*h**3 - 1/2*h**4 + n*h - 3/2*h**2 + 0.
-h*(h - 1)**3/2
Let c(g) be the first derivative of -g**6/2 + 12*g**5/5 - 9*g**4/2 + 4*g**3 - 3*g**2/2 - 8. Solve c(k) = 0.
0, 1
Let n(w) = w**2 + 1. Let k(i) = -2 + 4*i + 1 - 1 - 10*i**2. Let p(h) = k(h) + 8*n(h). What is d in p(d) = 0?
-1, 3
Let p = 15 + -16. Let j be p/(-2)*(-3)/(-2). Determine v, given that 9/4*v**2 + 0 + 3/2*v - 9/4*v**4 - 3/4*v**3 - j*v**5 = 0.
-2, -1, 0, 1
Let s(l) be the second derivative of -l**6/60 + l**5/10 - l**4/4 + l**3/3 - l**2/4 - 50*l. Determine o so that s(o) = 0.
1
Let a(s) be the first derivative of -s**7/21 - s**6/15 + 3*s**5/10 + 5*s**4/6 + 2*s**3/3 - 2*s - 1. Let i(c) be the first derivative of a(c). Factor i(q).
-2*q*(q - 2)*(q + 1)**3
Let o(q) be the third derivative of q**8/6720 + q**7/4200 - q**6/1800 + q**4/12 - 4*q**2. Let w(d) be the second derivative of o(d). Solve w(y) = 0 for y.
-1, 0, 2/5
Suppose 5 = 5*o - 5. Let w(f) be the first derivative of -1/8*f**4 - 2 - 3/4*f**o - 1/2*f**3 - 1/2*f. Solve w(a) = 0 for a.
-1
Determine b so that 6*b**3 - 2*b + 112*b**4 - 3 - 121*b**4 - 4*b + 12*b**2 = 0.
-1, -1/3, 1
Suppose -9*f - 11*f = -5*f. Factor -1/2*n + f + 1/4*n**2.
n*(n - 2)/4
Let l(t) = -t**2 + 8*t - 2. Let c be l(8). Let v = c - -4. Suppose -1/3 + 1/3*b**v + 0*b = 0. What is b?
-1, 1
Solve -9/8 + 3/8*g**2 + 3/4*g = 0 for g.
-3, 1
Let i(r) be the third derivative of 0*r**4 + 0 + 0*r**3 + 0*r**6 - 1/270*r**5 + 4*r**2 + 1/945*r**7 + 0*r. Factor i(b).
2*b**2*(b - 1)*(b + 1)/9
Let m be -6*(2 + 8/(-3)). Solve -x**2 + m + 1 - 1 - 2*x - x**2 = 0.
-2, 1
Let q(u) be the second derivative of 0 - 5/6*u**4 + 0*u**2 - 7/10*u**5 - 1/3*u**3 - 2*u - 1/5*u**6. Factor q(m).
-2*m*(m + 1)**2*(3*m + 1)
Let t = 41/4 + -256/25. Let y(s) be the second derivative of 0*s**2 + s + 0 + 1/30*s**3 + 1/30*s**4 + t*s**5. Factor y(i).
i*(i + 1)**2/5
Factor 2/5*x**2 + 4/5*x - 6/5.
2*(x - 1)*(x + 3)/5
Let k(d) = d**2 - d - 1. Let t(p) = -1. Let r(j) = 3*k(j) + 3*t(j). Factor r(h).
3*(h - 2)*(h + 1)
Let s(j) be the third derivative of j**5/450 - j**4/45 + j**3/15 + 15*j**2. Factor s(z).
2*(z - 3)*(z - 1)/15
Let k(d) be the third derivative of 7/72*d**4 + 1/36*d**5 + 1/360*d**6 + 2*d**2 + 0 + 1/6*d**3 + 0*d. Factor k(q).
(q + 1)**2*(q + 3)/3
Let t(w) be the second derivative of -1/12*w**3 - 2*w - 1/80*w**5 + 0 + 0*w**2 + 1/16*w**4. Find k, given that t(k) = 0.
0, 1, 2
Let h = 210 - 208. Let k(z) be the second derivative of 1/10*z**5 + 0*z**4 + 0 - z**3 - 2*z**h + 4*z. What is m in k(m) = 0?
-1, 2
Let n(q) = -3*q**2 - 4*q + 3. Let b(z) = -z**2. Let i(j) = -4*b(j) + n(j). Factor i(a).
(a - 3)*(a - 1)
Suppose 5*j = -r + 31, -4*j - r - 2*r + 27 = 0. Suppose 0 = -3*z + z + 4. Factor -p**2 + j*p - 5*p + z + 0.
-(p - 2)*(p + 1)
Let q(f) be the second derivative of 3*f - 1/2*f**2 + 1/12*f**3 + 0 + 1/24*f**4. Factor q(x).
(x - 1)*(x + 2)/2
Let h(v) = -v**4 + v**3 + v. Let p(u) = -2*u**3 + 3*u**2. Let i(w) = h(w) - p(w). Let i(o) = 0. Calculate o.
0, 1
Let b(t) be the third derivative of -1/150*t**5 + 0 - 3*t**2 + 0*t - 1/30*t**4 - 1/15*t**3. Factor b(d).
-2*(d + 1)**2/5
Determine c, given that 0*c**2 + 0*c**3 + 0*c + 0 - 2/7*c**4 = 0.
0
Find w such that -w + w - w + 7*w - 9*w**2 + 3*w**3 = 0.
0, 1, 2
Let b = 27316 - 1638883/60. Let f = 1/20 + b. Factor -2/3*j**3 - 2/3*j + 0 - f*j**2.
-2*j*(j + 1)**2/3
Suppose -3*g - 14 + 0 = 5*s, 0 = -4*g + 4*s + 24. Factor -2/3 - 1/3*x**g - x.
-(x + 1)*(x + 2)/3
Suppose 19 = -3*x + 4*a, 13 = -2*x - 3*x + 2*a. Let k be (-54)/(-12)*x/(-3). Factor -k*b**3 + 0 - 6*b - 6*b**2.
-3*b*(b + 2)**2/2
Suppose 0 = 3*i + 12, 4*z = -3*i - 4 - 0. Let h(k) = 10*k**2 + 7*k. Let a(j) = 3*j**2 + 2*j. Let p(c) = z*h(c) - 7*a(c). Factor p(v).
-v**2
Suppose 4*h = -5*f - 10, -2*h + 0*h = -f - 2. Factor h + 14/5*s**3 - 4/5*s + 2*s**2.
2*s*(s + 1)*(7*s - 2)/5
Suppose 12 = 30*i - 27*i. Let d(m) be the second derivative of 3*m + 0 - 1/40*m**5 - 1/4*m**2 + 1/24*m**i + 1/12*m**3. Factor d(r).
-(r - 1)**2*(r + 1)/2
Let j(u) be the third derivative of 1/15*u**5 + 0 + 0*u + 1/3*u**3 + u**2 + 5/24*u**4 + 1/120*u**6. Factor j(t).
(t + 1)**2*(t + 2)
Factor 1/2*q + 0 + 1/2*q**2.
q*(q + 1)/2
Let c(y) = 2*y**3 - 2*y**2 + 2*y - 2. Let s be c(2). Factor -6*j**2 + 2*j**3 - 5*j**3 + s + j**3 - 2.
-2*(j - 1)*(j + 2)**2
Let g(t) be the first derivative of -3 - 1/24*t**4 + 1/40*t**5 + 0*t + t**2 - 1/12*t**3. Let n(k) be the second derivative of g(k). Let n(d) = 0. Calculate d.
-1/3, 1
Factor 85*v**2 - v**4 - 26*v**4 - 37*v - 18*v**4 + 22*v - 105*v**3.
-5*v*(v + 3)*(3*v - 1)**2
Let g(i) be the first derivative of -2*i**2 + 1/4*i**4 + 3 - 2/3*i**3 + 8*i. Factor g(m).
(m - 2)**2*(m + 2)
Suppose -2*v**3 + 0*v - 2*v**2 + 0 - 1/2*v**4 = 0. Calculate v.
-2, 0
Suppose -2*h**2 - 14*h**2 + 175*h**3 + 9*h**2 + 180*h**4 - 8*