) = 0. Calculate l.
-3, 0
Let a be 2/15*-3*(-15)/12. Find l such that 0 + 1/2*l**2 - 1/2*l**4 + 1/2*l**5 - a*l**3 + 0*l = 0.
-1, 0, 1
Let h = -5 + 5. Determine y, given that 0*y + h*y - y**2 + y + 0*y = 0.
0, 1
Let v be 0 + 0 + 0/2. Let 2*c**2 + 4*c + v*c - 3*c - c**2 - 2*c**3 = 0. Calculate c.
-1/2, 0, 1
Solve -1/6*o - 1/6*o**2 + 1/3 = 0 for o.
-2, 1
Let m(y) be the first derivative of -y**6/12 + 9*y**5/5 - 97*y**4/8 + 24*y**3 - 16*y**2 + 11. Suppose m(j) = 0. Calculate j.
0, 1, 8
Factor d**4 - 1/2*d**5 - d**2 + 0 + 0*d**3 + 1/2*d.
-d*(d - 1)**3*(d + 1)/2
Let w be 35/30 + (-2)/4. Let c be 0 + 10/3 - 2. What is g in 0 - c*g + w*g**2 = 0?
0, 2
Let k(y) be the first derivative of y**6/24 + 3*y**5/20 - y**3/3 + 2. Solve k(s) = 0.
-2, 0, 1
Let -3*p - p**3 + 2*p**2 - p**3 + 7*p = 0. Calculate p.
-1, 0, 2
Let s be ((-5)/150)/((-22)/4). Let j = s + 131/165. Factor 4/5*d**2 + 2/5*d - 2/5*d**5 + 0*d**3 - j*d**4 + 0.
-2*d*(d - 1)*(d + 1)**3/5
Let f be -13 + 18 + (3 - 2 - 4). Factor -1/3*r**3 - 1/3*r - 2/3*r**f + 0.
-r*(r + 1)**2/3
Factor 35 - 228*d**4 + 6*d**4 + 1641*d**2 - 2000*d**3 - 415*d - 21*d**2 - 98*d**4.
-5*(d + 7)*(4*d - 1)**3
Let b be 98/(-56)*-5*3/21. Let 5/2*u**3 - 5/4*u**4 + b*u - 1/4 + 1/4*u**5 - 5/2*u**2 = 0. Calculate u.
1
Let p(i) = -i**2 + 21*i + 16. Let k(h) = -10*h - 8. Let l(z) = 5*k(z) + 2*p(z). Determine y so that l(y) = 0.
-2
Suppose -2*o - v - 31 = 0, -2*v - 2*v - 12 = 0. Let p(l) = 2*l**2 - 11*l + 8. Let k(t) = 4*t**2 - 23*t + 16. Let g(f) = o*p(f) + 6*k(f). Factor g(m).
-4*(m - 2)**2
Let u = 53 + -51. Factor 0*q + 2/3*q**u + 0.
2*q**2/3
Factor 0 + 9/7*w**2 + 6/7*w**3 + 1/7*w**4 + 4/7*w.
w*(w + 1)**2*(w + 4)/7
Let z(y) be the third derivative of y**5/12 + 5*y**4/3 + 40*y**3/3 + 12*y**2. Factor z(a).
5*(a + 4)**2
Let z = 25 - 25. Let -11*t + 3*t + 0*t**2 - 4*t**2 + z*t**2 = 0. What is t?
-2, 0
Let t(f) = -f + 2. Let g be t(4). Let x be (-2)/(0 - g/(-6)). What is j in -2*j + j**4 - 2*j**4 + x*j**3 - 4*j**3 + 1 = 0?
-1, 1
Let n(p) = -35*p**2 - 8*p + 8. Let y(a) = -a + 1. Let u(m) = n(m) - 4*y(m). Factor u(h).
-(5*h + 2)*(7*h - 2)
Let q(s) = -2*s**3 + 7*s**2 + s + 2. Let i(h) = -3*h**3 + 8*h**2 + 2. Let v(n) = -3*i(n) + 4*q(n). Let o be v(-2). Let -5*c**2 + 6*c**2 - o*c**2 = 0. What is c?
0
Let w(f) = f**5 + f**4 + f**3 + f**2 - f. Let l(v) = -3*v**5 + 2*v + 3*v**4 + v**2 - 4*v**4 - 3*v**2. Let z(x) = -l(x) - 2*w(x). Factor z(r).
r**3*(r - 2)*(r + 1)
Factor 7/2*f**4 + 0 - 1/2*f**5 + 9/2*f**2 + 0*f - 15/2*f**3.
-f**2*(f - 3)**2*(f - 1)/2
Let -2/15*x**2 + 0 - 2/15*x**3 + 0*x = 0. What is x?
-1, 0
Let r(f) = -f**3 + 29*f**2 - 40*f + 20. Let q(m) = 5*m**3 - 115*m**2 + 160*m - 80. Let s(x) = 4*q(x) + 15*r(x). What is n in s(n) = 0?
1, 2
Factor 10*n + 3*n**2 + 14*n**2 - 12*n**2.
5*n*(n + 2)
Let t(h) = -h**3 - 6*h**2 + h - 3. Let w be t(-6). Let i be (-2)/(30/w + 0). Determine f so that 19/5*f**3 - 11/5*f**2 + 0 - 13/5*f**4 + i*f**5 + 2/5*f = 0.
0, 1/3, 1, 2
Let y(d) be the first derivative of -1 - 2/3*d**3 - d**2 + 0*d - 1/2*d**4 - 1/12*d**5. Let g(u) be the second derivative of y(u). Factor g(m).
-(m + 2)*(5*m + 2)
Let h(t) be the second derivative of t**6/105 - 2*t**5/35 + t**4/7 - 4*t**3/21 + t**2/7 + 13*t. Solve h(i) = 0.
1
Determine v so that v**2 + 1/3*v**3 + 2/3*v + 0 = 0.
-2, -1, 0
Factor 2/13*k**3 + 2/13*k**4 - 2/13*k**2 + 0 - 2/13*k.
2*k*(k - 1)*(k + 1)**2/13
Let p(w) be the first derivative of -w**8/504 + w**7/315 + w**6/180 - w**5/90 - 2*w**2 + 1. Let d(t) be the second derivative of p(t). Factor d(z).
-2*z**2*(z - 1)**2*(z + 1)/3
Let q(t) be the second derivative of t**7/1260 - t**6/120 + t**5/30 + t**4/12 - 5*t. Let y(k) be the third derivative of q(k). Factor y(m).
2*(m - 2)*(m - 1)
Let r(m) be the first derivative of m**8/1680 - m**7/420 + m**6/360 + m**3/3 + 2. Let c(o) be the third derivative of r(o). Suppose c(g) = 0. What is g?
0, 1
Let w(i) = 9*i**5 - i**4 - 3*i**3 - 13*i**2 + 4*i + 4. Let y(c) = 14*c**5 - 2*c**4 - 4*c**3 - 20*c**2 + 6*c + 6. Let p(q) = -8*w(q) + 5*y(q). Factor p(j).
-2*(j - 1)**2*(j + 1)**3
Let f be 1/(-3)*(-1362)/20. Let s = -45/2 + f. Factor s*p + 0 + 1/5*p**2.
p*(p + 1)/5
Let f(d) be the first derivative of d**5/10 + d**4/72 - d**3/4 + d**2/6 + d + 1. Let i(h) be the first derivative of f(h). Suppose i(a) = 0. What is a?
-1, 1/4, 2/3
Let k(u) be the second derivative of u**4/48 - u**3/2 + 9*u**2/2 + 15*u. Solve k(d) = 0.
6
Let y = -50 - -50. Let p(h) be the third derivative of 0*h**3 + 0*h**5 - 1/560*h**8 + 0 - h**2 + 0*h**4 + 1/200*h**6 + y*h + 0*h**7. Factor p(l).
-3*l**3*(l - 1)*(l + 1)/5
Let h(b) be the third derivative of -b**6/180 - b**5/90 + b**4/18 - 16*b**2. Solve h(c) = 0.
-2, 0, 1
Let c = -139 + 422/3. Let s(d) be the first derivative of 3 - c*d**2 + 4/3*d - 14/9*d**3. Factor s(v).
-2*(v + 1)*(7*v - 2)/3
Find f such that -105*f**2 - 6*f**3 - 1 + 101*f**2 + 2*f**5 + 1 = 0.
-1, 0, 2
Suppose 0 + 2 = n. Let o(s) = 2*s**2 - 5*s - 4. Let w(b) = -2*b**2 + 4*b + 4. Let j(k) = n*o(k) + 3*w(k). Factor j(z).
-2*(z - 2)*(z + 1)
Suppose 2*q = -3*q + 15. Factor 3*p**4 - 3*p**2 - 4*p**4 - 4*p + 0*p**4 + 3*p**q + 5*p.
-p*(p - 1)**3
Factor 0*z**2 + 0*z - 4/7*z**5 - 8/7*z**4 + 0 + 0*z**3.
-4*z**4*(z + 2)/7
Let k(n) be the first derivative of -4*n**3/9 - 44*n**2/3 - 484*n/3 - 8. Determine d, given that k(d) = 0.
-11
Let y = 157 + -155. Factor 2*w - 11/2*w**y - 9/4*w**4 - 1/4 + 6*w**3.
-(w - 1)**2*(3*w - 1)**2/4
Let a = 4715/7 - 673. What is y in 0*y**2 - 2/7*y**3 + a*y**4 - 2/7*y**5 + 0*y + 0 = 0?
0, 1
Factor 0 + 224/13*z**4 - 4/13*z + 46/13*z**2 - 176/13*z**3.
2*z*(4*z - 1)**2*(7*z - 2)/13
Let t(r) be the second derivative of r + 1/12*r**4 + 0 + 1/2*r**2 + 1/3*r**3. Let t(n) = 0. What is n?
-1
Suppose 3 = -2*q + 3*w, 3*q + 4 = w + 3*w. Factor q + 0*b - 1/6*b**4 - 2/3*b**3 - 2/3*b**2.
-b**2*(b + 2)**2/6
Let a(o) be the third derivative of o**7/840 - o**5/40 + o**4/12 + 7*o**3/6 + 3*o**2. Let s(l) be the first derivative of a(l). Find x such that s(x) = 0.
-2, 1
Let i(z) be the third derivative of -z**8/23520 - z**7/2940 - z**6/840 - z**5/420 + z**4/6 + 2*z**2. Let l(d) be the second derivative of i(d). Factor l(w).
-2*(w + 1)**3/7
Suppose 93*j - 81*j = 24. Find x, given that -1/2 + 0*x + 1/2*x**j = 0.
-1, 1
Factor 3/2*z**3 + 0*z + 0 - 15/2*z**2.
3*z**2*(z - 5)/2
Let u(q) be the second derivative of -q**6/15 - q**5/10 + 2*q**4/3 + 4*q**3/3 - 10*q. What is z in u(z) = 0?
-2, -1, 0, 2
Let x be (-80)/14 + (-6)/21. Let t be 24*x/(-8)*1. Determine i, given that t - 18 - 2*i + i**2 = 0.
0, 2
Let i = -2/733 + 739/2199. Factor 1/3*o**5 + 0*o**3 + 2/3*o**2 - i*o + 0 - 2/3*o**4.
o*(o - 1)**3*(o + 1)/3
Let p(k) be the third derivative of -k**7/420 + k**6/180 + k**3/2 - k**2. Let n(j) be the first derivative of p(j). Suppose n(l) = 0. Calculate l.
0, 1
Let y(c) be the third derivative of 3*c**2 - 1/210*c**5 + 1/84*c**4 + 0 + 0*c + 0*c**3. What is b in y(b) = 0?
0, 1
Let g(r) be the third derivative of 3*r**8/560 + 4*r**7/175 + 2*r**6/75 - r**5/50 - 3*r**4/40 - r**3/15 - 41*r**2. Solve g(v) = 0 for v.
-1, -1/3, 2/3
Let c(j) be the third derivative of j**6/60 - j**5/5 + 11*j**4/12 - 2*j**3 - 14*j**2. Suppose c(s) = 0. Calculate s.
1, 2, 3
Let b(p) be the first derivative of -5*p**4/4 + 35*p**3/3 - 40*p**2 + 60*p + 12. Factor b(g).
-5*(g - 3)*(g - 2)**2
Let b(z) be the first derivative of -7*z**3/24 + 5*z**2/16 + z/4 - 3. Factor b(w).
-(w - 1)*(7*w + 2)/8
Factor 242/5 + 44/5*v + 2/5*v**2.
2*(v + 11)**2/5
Let t = -1 + 1. Factor 6/7*p + t*p**2 + 4/7 - 2/7*p**3.
-2*(p - 2)*(p + 1)**2/7
Solve 0 + 9/8*v**5 + 3/8*v**2 - 15/8*v**4 + 0*v + 3/8*v**3 = 0 for v.
-1/3, 0, 1
Let o be ((-2)/(-6))/((-2)/(-18)). Find l such that 2*l**2 - 9 - 7 - 8*l - o*l**2 = 0.
-4
Let g(n) be the second derivative of -n**5/30 + n**4/2 - 3*n**3 - n**2/2 + n. Let w(d) be the first derivative of g(d). Factor w(p).
-2*(p - 3)**2
Suppose 15*n = 46 - 46. Suppose 0 + n*l**2 + 1/5*l**4 + 0*l + 1/5*l**3 = 0. Calculate l.
-1, 0
Let x(z) be the second derivative of 5*z**6/6 + 3*z**5 + 15*z**4/4 + 5*z**3/3 + 14*z. Determine h so that x(h) = 0.
-1, -2/5, 0
Suppose 7*m - 12 = 4*m. Let q(h) be the second derivative of 2/3*h**m + 0*h**3 + 7/3*h**6 + 0*h**2 - 13/5*h**5 + 0 + 2*h + 7/6*h**7. What is y in q(y) = 0?
-2, 0, 2/7
Let t(r) be the third derivative of -3