1)**2/2
Let x = -10222/5 + 2037. Let v = x - -41/5. Factor 2/5*w + 0*w**3 - 4/5*w**2 - 2/5*w**5 + 0 + v*w**4.
-2*w*(w - 1)**3*(w + 1)/5
Let v = -16 - -18. Suppose -3*n = -v - 4. Factor 2*s**3 - 4/5*s**n - 2*s + 4/5.
2*(s - 1)*(s + 1)*(5*s - 2)/5
Let g(c) be the first derivative of c**6/3 + 2*c**5 + 2*c**4 - 32*c**3/3 - 32*c**2 - 32*c + 6. Suppose g(b) = 0. What is b?
-2, -1, 2
Let h(t) = -t - 1. Let g(v) = -v**2 + 5*v - 6. Let w be g(5). Let d(z) = -z + 5*z**2 - 8*z - 4*z**2 - 4. Let n(p) = w*h(p) + d(p). Factor n(x).
(x - 2)*(x - 1)
Suppose 0*g - 44 = 4*g. Let p = g + 15. Suppose -8/7*w**p + 8/7*w**2 - 2/7*w + 2/7*w**3 + 0 = 0. Calculate w.
-1, 0, 1/4, 1
Suppose v - 16 = -4*i, -2*i - v = -6*i + 8. Solve -4 + 6*d - 3*d**2 + 1/2*d**i = 0 for d.
2
Let q(f) = -f**3 + 5*f**2 + f - 3. Let h be q(5). Let j = 726/5 + -145. Factor -1/5*r**4 - r + 2/5 + 3/5*r**h + j*r**3.
-(r - 1)**3*(r + 2)/5
Factor 4/3*c**2 + 2/3*c**4 + 0*c + 0 + 2*c**3.
2*c**2*(c + 1)*(c + 2)/3
Suppose -3*l = -3*j - 6*l + 15, 0 = j + 2*l - 10. Find c such that 0*c**4 + 0 + 0*c + j*c**2 + 2/13*c**5 + 0*c**3 = 0.
0
Let t(c) be the second derivative of -c**4/78 - 8*c**3/39 - 16*c**2/13 - 24*c. Factor t(m).
-2*(m + 4)**2/13
Let f(c) = -9*c**2 - 3*c + 5. Let h(u) = 14*u**2 + 4*u - 8. Let w(p) = -8*f(p) - 5*h(p). Suppose w(y) = 0. What is y?
-2, 0
Determine l, given that 51/2*l**4 + 33*l**2 + 42*l**3 + 12*l + 3/2 + 6*l**5 = 0.
-1, -1/4
Suppose q - l + 19 = l, 0 = 4*q - 3*l + 61. Let m = 27/2 + q. Determine i so that 0 + m*i - 1/4*i**2 = 0.
0, 2
Suppose 0 = -x + 6*x + 2*x. Suppose -r - 3/2*r**4 + x + 1/2*r**5 + 3/2*r**2 + 1/2*r**3 = 0. Calculate r.
-1, 0, 1, 2
Factor -2*x + 2 + 2 - 2*x**2 + 0*x**2.
-2*(x - 1)*(x + 2)
Let w(c) be the first derivative of 0*c + 0*c**3 + 7/40*c**6 - 2*c**2 + 3 + 1/2*c**4 - 4/5*c**5. Let q(f) be the second derivative of w(f). Solve q(o) = 0.
0, 2/7, 2
Let z(l) = -4*l**5 - 4*l**4 + 8*l**3 + 15*l**2 + 3*l. Let b(d) = -d**5 - d**4 + d**2 + d. Let r(i) = 3*b(i) - z(i). Factor r(k).
k**2*(k - 3)*(k + 2)**2
Suppose 1 + 1 = b. Suppose b*v - 4 = -0. Determine c so that 0*c + 0*c + c**4 + 2*c**3 + c**v = 0.
-1, 0
Factor 26/3*v + 26/3*v**2 + 2*v**3 + 2.
2*(v + 1)*(v + 3)*(3*v + 1)/3
Let i(g) be the second derivative of -g**7/1680 - g**6/240 - g**5/80 - g**4/4 + g. Let p(w) be the third derivative of i(w). Find q, given that p(q) = 0.
-1
Let n(q) = q**2 + q + 2. Let b be n(0). Determine u, given that -1 + 5*u**b - 14*u**2 - 1 - 17*u - 27*u**2 = 0.
-1/4, -2/9
Factor -5/6*t**3 + 4/3*t**2 - 2/3*t + 1/6*t**4 + 0.
t*(t - 2)**2*(t - 1)/6
Let w be (-14)/(-32) - 87/(-1392). Let -g**2 + 0 + 1/2*g**5 + 0*g**3 + g**4 - w*g = 0. What is g?
-1, 0, 1
Let t = 23 - 20. Let o be (t + -1)/10 + 0. Factor o + 1/5*x**2 - 2/5*x.
(x - 1)**2/5
Suppose q = 3*q. Suppose 0 = -3*j - q*j - 5*x + 31, 5*x - 27 = -j. Factor -8/3*f - 2*f**j - 2/3.
-2*(f + 1)*(3*f + 1)/3
Let b be (-138)/(-30) + 6/(-10). Suppose 6*g + 11*g**4 + 39*g**2 + 24*g**5 + 70*g**b + 87*g**3 + 3*g**5 = 0. What is g?
-1, -2/3, -1/3, 0
Let q(v) be the first derivative of v**4/16 + v**3/12 - v**2/8 - v/4 + 12. Factor q(h).
(h - 1)*(h + 1)**2/4
Let u(n) be the third derivative of n**6/810 + n**5/540 - n**4/108 + 5*n**3/6 + 6*n**2. Let a(p) be the first derivative of u(p). Factor a(z).
2*(z + 1)*(2*z - 1)/9
Let g(f) = 9*f**5 + 24*f**4 + 34*f**3 + 16*f**2 + 9*f - 4. Let t(u) = u**5 + u**4 + u**3 - u**2 + u - 1. Let y(c) = g(c) - 4*t(c). Factor y(z).
5*z*(z + 1)**4
Let g(v) = -6*v**3 + 6*v**2 - 17. Let r(k) = 2*k**3 - 2*k**2 + 6. Let y(q) = 6*g(q) + 17*r(q). Find s, given that y(s) = 0.
0, 1
Let w(o) be the first derivative of o**3/12 - 3*o**2/8 - 11. Factor w(t).
t*(t - 3)/4
Factor f - 30*f**2 - 27*f**2 + 3*f**3 + f**4 + 60*f**2.
f*(f + 1)**3
Find i such that i**3 + 1/3*i**5 - 4/3*i - 4/3*i**2 + 4/3*i**4 + 0 = 0.
-2, -1, 0, 1
Let l = 341 - 339. Factor 9/2*r + 3/4*r**l + 27/4.
3*(r + 3)**2/4
Let f(d) be the first derivative of -d**6/15 - 3*d**5/5 - 2*d**4 - 8*d**3/3 + 3*d + 2. Let g(n) be the first derivative of f(n). Determine x so that g(x) = 0.
-2, 0
Let k(y) = -3*y**3 + 2*y + 1. Suppose 19*b - 3 = 22*b. Let f be k(b). Suppose 0*t**f + 2/5*t**3 + 0*t + 2/5*t**4 + 0 = 0. What is t?
-1, 0
Suppose -22*j = -20*j. Let g(v) be the first derivative of -2/5*v**5 - 2*v**2 - 1 + 2*v**3 + 0*v**4 + j*v. Factor g(i).
-2*i*(i - 1)**2*(i + 2)
Factor 0 - 3/7*i**2 + 9/7*i.
-3*i*(i - 3)/7
Suppose -y + 0 = -2. Factor 0*m**5 + 2*m**4 - 7*m**y + 4*m**4 + m**2 - 3*m**5 + 3*m.
-3*m*(m - 1)**3*(m + 1)
Let z(b) = -b**2 + 11*b + 15. Let i(r) be the third derivative of -r**5/60 - r**4/24 - r**3/6 - 9*r**2. Let w(j) = 3*i(j) + z(j). Factor w(d).
-4*(d - 3)*(d + 1)
Suppose 0 = 4*c - 14 - 2. Suppose -c*v = 5*w, 5*w - 2*v = 2*v. Factor -2/9*p**2 + w + 0*p.
-2*p**2/9
Let p(f) = -12*f**4 + 6*f**2 + 3*f + 3. Let o(l) = -23*l**4 - l**3 + 13*l**2 + 6*l + 5. Suppose -q + 2 + 3 = 0. Let j(m) = q*p(m) - 3*o(m). Factor j(b).
3*b*(b - 1)*(b + 1)*(3*b + 1)
Let k(b) be the second derivative of 3*b**8/4480 - 13*b**7/10080 + b**6/1440 - 7*b**4/12 + 7*b. Let n(m) be the third derivative of k(m). Solve n(z) = 0 for z.
0, 2/9, 1/2
Let j = 46 - 44. Let f(h) be the second derivative of -1/3*h**3 - 1/3*h**4 - 1/10*h**5 + 0 + 3*h + 0*h**j. Factor f(m).
-2*m*(m + 1)**2
Let s be (1/(-3))/(3/(-45)). Suppose -1 = -2*w + s. Factor w*p + 2*p**5 + 10*p**4 + 14*p**2 - 8*p**3 + p + 26*p**3.
2*p*(p + 1)**3*(p + 2)
Let g(k) be the third derivative of 9*k**8/112 + 9*k**7/70 - 3*k**6/20 - k**5/6 + 7*k**4/24 - k**3/6 - 7*k**2. Factor g(w).
(w + 1)**2*(3*w - 1)**3
Let q(m) be the third derivative of m**7/210 + m**6/40 - m**5/30 - m**4/2 - 4*m**3/3 + 4*m**2. Factor q(k).
(k - 2)*(k + 1)*(k + 2)**2
Suppose 17*t - 30 = 12*t. Suppose -4*n + t = -2*o + 4*o, 2*n - 9 = 5*o. What is r in r**4 - 1/3*r**3 + 0*r + 0 - 2/3*r**n = 0?
-2/3, 0, 1
Let t(l) be the first derivative of l**6/120 - l**5/15 + 5*l**4/24 - l**3/3 + 5*l**2/2 + 2. Let c(s) be the second derivative of t(s). Factor c(b).
(b - 2)*(b - 1)**2
Let r be -6*(1 - 4/3). Factor r*s + 2*s**2 + 0*s - 2 - 2*s**3 + 0*s**3.
-2*(s - 1)**2*(s + 1)
Let z = 89 + -89. Factor 0*h**2 + 2/5*h**3 + z + 0*h.
2*h**3/5
Factor -10/19*u + 2/19*u**3 - 4/19 - 6/19*u**2 + 2/19*u**4.
2*(u - 2)*(u + 1)**3/19
Suppose -3*j = -8*j - 3*d + 138, 4*d = 4*j - 136. Suppose -5*y + 4*k - 5 = 0, -5*y = k + 2*k - j. Factor 1/2*w**2 + 1/2*w**5 + 3/2*w**y + 0*w + 0 + 3/2*w**4.
w**2*(w + 1)**3/2
Let r(i) be the third derivative of i**7/420 + i**6/240 - i**5/40 - i**4/48 + i**3/6 - 6*i**2 - 5*i. Factor r(d).
(d - 1)**2*(d + 1)*(d + 2)/2
Let p be (20/30)/(10/45). Determine r so that -1/2*r**2 + 1/2 + 1/2*r - 1/2*r**p = 0.
-1, 1
Determine y, given that 0 + 1/5*y**2 - 1/5*y = 0.
0, 1
Let l(u) be the second derivative of 14*u**6/45 - u**5/3 - u**4 + 10*u**3/9 + 4*u**2/3 - 3*u. Suppose l(q) = 0. Calculate q.
-1, -2/7, 1
Let w(h) be the first derivative of -7*h**5 + 20*h**4 - 55*h**3/3 + 5*h**2 + 11. Suppose w(s) = 0. Calculate s.
0, 2/7, 1
Let i = 57 + -227/4. Let j = 5 + -2. Solve i*q - 1/4*q**5 + 1/2*q**2 - 1/2*q**4 + 0 + 0*q**j = 0.
-1, 0, 1
Let u = 125 - 118. Let i(t) be the second derivative of 0*t**3 + 1/35*t**6 + 0 + 0*t**2 - t - 1/21*t**4 - 2/147*t**u + 3/70*t**5. Determine j so that i(j) = 0.
-1, 0, 1/2, 2
Let j(y) = 2*y**4 - 5*y**3 - 9*y**2 + 7*y - 1. Let i(m) = -2*m**4 + 6*m**3 + 10*m**2 - 6*m. Let l(b) = 3*i(b) + 4*j(b). Factor l(h).
2*(h - 1)**3*(h + 2)
Suppose -2*j + 5*j - 4*q = -214, 3*j + 218 = 2*q. Let y = -516/7 - j. Suppose 12/7*f**2 - y + 0*f + 6/7*f**4 - 16/7*f**3 = 0. Calculate f.
-1/3, 1
Let x = -11 + 13. Factor 2*r**3 + x + 2*r**2 + 3*r**2 + 6*r + r**2.
2*(r + 1)**3
Let k(u) be the first derivative of 5*u**4/2 + 4*u**3 - 36*u**2/5 + 16*u/5 - 2. Factor k(l).
2*(l + 2)*(5*l - 2)**2/5
Let w(j) be the first derivative of -2*j**5/15 + j**4/6 + 2*j**3/9 - j**2/3 + 60. Find c such that w(c) = 0.
-1, 0, 1
Let j(z) be the third derivative of z**2 + 0*z**3 + 0 - 1/24*z**4 - 1/120*z**6 + 0*z + 1/30*z**5. Factor j(x).
-x*(x - 1)**2
Let j = 78 - 73. Factor -11/2*o**3 + o**2 + 0*o + 8*o**4 + 0 - 7/2*o**j.
-o**2*(o - 1)**2*(7*o - 2)/2
Let x be 2/4 + 3/(-6). Factor 1 - u**2 - u**2 + x*u**2 - 8*u - 7.
-2*(u + 1)*(u + 3)
Let b(p) = 9*p**5 - 3*p**4 + 6*p**2 - 3*p + 3. Let d(w) = 10*w**5 - 