 2*f. Let l(s) be the third derivative of -s**2 + 0*s + 1/30*s**5 + 1/6*s**4 + f + 1/3*s**3. Let l(n) = 0. What is n?
-1
Let o(f) be the first derivative of -f**3 + 3*f**2 - 3*f - 3. Factor o(m).
-3*(m - 1)**2
Let h be 8/(16/3) + -1. Factor v**3 + 1/2*v**2 - h*v**4 + 0 - v.
-v*(v - 2)*(v - 1)*(v + 1)/2
Let b(p) be the second derivative of -3*p + 1/30*p**6 - 1/168*p**7 - 1/24*p**3 + 1/12*p**4 + 0*p**2 - 3/40*p**5 + 0. Factor b(l).
-l*(l - 1)**4/4
Let p(z) be the third derivative of z**5/12 + 5*z**4/4 + 25*z**3/6 - 29*z**2. Factor p(o).
5*(o + 1)*(o + 5)
Factor 27*f - 4*f**4 + 18*f**3 + 1/3*f**5 - 36*f**2 + 0.
f*(f - 3)**4/3
Let y(a) be the second derivative of a**4/18 + a**3/9 + 8*a. Let y(p) = 0. What is p?
-1, 0
Suppose 5*n - 6 = -j + 5, -j = 4. Let l(m) be the first derivative of 0*m + 0*m**2 + 1/8*m**4 + 1/6*m**n + 2. Let l(s) = 0. Calculate s.
-1, 0
Let g(z) be the second derivative of z**7/98 - 3*z**6/70 + 3*z**5/140 + 3*z**4/28 - z**3/7 + 2*z. Determine o so that g(o) = 0.
-1, 0, 1, 2
Let s = -9 + 11. Let t(d) be the third derivative of 0 + 0*d + 1/24*d**3 + 1/240*d**5 - 1/48*d**4 - 3*d**s. Factor t(z).
(z - 1)**2/4
Let h be (91/(-4))/7 - -4. Let i(q) = q**2 + 8*q + 7. Let y be i(-7). Solve -3/4*p + y - h*p**3 + 3/2*p**2 = 0 for p.
0, 1
Let f be ((0/(-1))/(5 - 8))/(-1). Let t(j) be the third derivative of 3*j**2 - 1/3*j**3 + f*j - 1/60*j**5 + 1/8*j**4 + 0. Factor t(l).
-(l - 2)*(l - 1)
Let n(i) be the third derivative of 1/9*i**4 - 1/9*i**3 + 0*i + 4*i**2 + 0 - 1/30*i**5. Factor n(b).
-2*(b - 1)*(3*b - 1)/3
Let f = 27 + 5. Find o, given that -20*o**2 + 0*o**3 + f*o**2 - 3*o**3 - 9*o = 0.
0, 1, 3
Factor -10 + 5*y + 2 + 2*y + y**2 - 9*y.
(y - 4)*(y + 2)
Suppose -32*p + 56 + 8 = 0. Factor -2/7*g**3 - 4/7*g**p + 2/7*g + 4/7.
-2*(g - 1)*(g + 1)*(g + 2)/7
Let a(o) be the second derivative of 1/150*o**6 - 1/30*o**4 + 0 + 1/10*o**2 - o + 0*o**5 + 0*o**3. Factor a(g).
(g - 1)**2*(g + 1)**2/5
Let w(k) be the third derivative of 0*k**4 - 5*k**2 - 2/15*k**3 + 1/75*k**5 + 0 + 0*k. Suppose w(c) = 0. What is c?
-1, 1
Let w be -3*2/(-6) + -2. Let o be 5/(1/w)*-1. Factor -15*c**4 - 14*c**2 + 6*c**o + 17*c**2 + 9*c**3 - c - 2*c.
3*c*(c - 1)**3*(2*c + 1)
Suppose 2*f - 6 = -h, -4*f = -2*h - 5 + 1. Suppose 0 = 4*u - h*u. What is y in 6/7*y - 2/7*y**3 + u*y**2 + 4/7 = 0?
-1, 2
Suppose 4 = -4*p - 0*p. Let z(v) = -4*v**2 + v + 1. Let j be z(p). Let t(k) = k. Let r(q) = 2*q**2 + 6*q - 4. Let y(a) = j*t(a) + r(a). Factor y(b).
2*(b - 1)*(b + 2)
Let x(b) = b**2 - b + 2. Let s be x(6). Find a such that -14*a**5 - 4*a**2 + 8*a**3 + 8*a**2 - 30*a**3 + s*a**4 = 0.
0, 2/7, 1
Suppose -1308 = k - 1310. Factor -2*n - 10/7*n**3 + 4/7 + 18/7*n**k + 2/7*n**4.
2*(n - 2)*(n - 1)**3/7
Let i = 79 + -392/5. Suppose -i*g**2 - 6/5*g - 3/5 = 0. Calculate g.
-1
Let p(r) = 2*r**2 + r - 3. Let k be p(-2). Determine d, given that 0 + 3/2*d**2 + 1/2*d**4 - 1/2*d - 3/2*d**k = 0.
0, 1
Suppose 0 = -n + 3 - 1. Let p(f) = -4*f**2 - 24*f - 32. Let w be p(-4). Let -2/9*g - 2/9*g**n + w = 0. What is g?
-1, 0
Let f(s) be the first derivative of 2*s**3/3 - 3*s**2 - 8*s - 18. Let f(w) = 0. Calculate w.
-1, 4
Let w(k) be the second derivative of -1/15*k**3 + 3*k + 0 - 1/60*k**4 - 1/10*k**2. Let w(p) = 0. Calculate p.
-1
Let u(o) = -o**2 + o. Let f(q) = 4*q**2 - 4*q. Let k(i) = -f(i) - 5*u(i). Let k(s) = 0. Calculate s.
0, 1
Suppose 2/3*p - 2/9 + 2/9*p**3 - 2/3*p**2 = 0. Calculate p.
1
Let z(q) be the second derivative of q**8/13440 + q**7/5040 + q**4/6 - 2*q. Let w(j) be the third derivative of z(j). Factor w(s).
s**2*(s + 1)/2
Let c(d) be the first derivative of -3/2*d**2 - 3 + 0*d - 1/240*d**5 + 0*d**3 + 1/96*d**4. Let q(v) be the second derivative of c(v). What is z in q(z) = 0?
0, 1
Suppose -21*a + 60 = -a. Factor -l + 0 - 3/2*l**2 - 1/2*l**a.
-l*(l + 1)*(l + 2)/2
Suppose 5*l + 1 = -4. Let z be 2 + 2 + (-2 - l). Factor -4*r**3 + 4*r**3 - r**z.
-r**3
Let j = -20411/42 - -486. Let n(q) be the second derivative of j*q**4 + 0 - 1/21*q**3 + 0*q**2 + 4*q. Let n(v) = 0. What is v?
0, 1
Factor 4 + 0 - 12 - 5*n**2 - 12*n + n**2.
-4*(n + 1)*(n + 2)
Let y(d) = 2*d**4 + 27*d**3 - 29*d**2 + 11*d - 11. Let r(h) = h**4 + 9*h**3 - 10*h**2 + 4*h - 4. Let g(l) = 11*r(l) - 4*y(l). Find t such that g(t) = 0.
0, 1, 2
Let w(i) be the third derivative of 5*i**2 - 1/20*i**6 + 2/3*i**3 + 0 + 0*i - 2/15*i**5 + 1/12*i**4. What is u in w(u) = 0?
-1, 2/3
Let l be 341/186 + (5/(-6) - -1). Suppose 0 - 2/5*r + 0*r**4 + 4/5*r**3 + 0*r**l - 2/5*r**5 = 0. Calculate r.
-1, 0, 1
Let r(c) = -c. Let g(n) = -n + 1. Let w be g(4). Let o be r(w). Factor 0*t**o + 5*t**3 - 3*t**3.
2*t**3
Factor -2*a**5 + 3*a**5 + 1 - a**3 - 1.
a**3*(a - 1)*(a + 1)
Let t(a) be the first derivative of -2/3*a**3 - 7/15*a**6 - 2/5*a**2 + 9/10*a**4 - 2 + 2/5*a**5 + 0*a. Solve t(x) = 0 for x.
-1, -2/7, 0, 1
Suppose -11*z = -2*z. Factor z - 1/3*v - 1/3*v**2.
-v*(v + 1)/3
Suppose -1/5*m**3 + 0*m**2 + 0*m + 0 = 0. What is m?
0
Let j(p) = 4*p**4 - 7*p**3 + 12*p**2 - 7*p + 4. Let f(h) = -5*h**4 + 6*h**3 - 11*h**2 + 6*h - 5. Let m(l) = -2*f(l) - 3*j(l). Factor m(i).
-(i - 2)*(i - 1)**2*(2*i - 1)
Suppose b + 3228 = -2*m, 0 = 3*b - 5*m + 5349 + 4280. Let a = b + 22636/7. Solve -8/7 + 46/7*x**2 - a*x**4 - 38/7*x**3 + 16/7*x - 50/7*x**5 = 0.
-1, 2/5
Let j be (10/4)/(3/30). Suppose -j = -6*o + o. Let 3*a**4 - 2*a**3 + a**4 + 4*a**3 + 2*a**o = 0. What is a?
-1, 0
Suppose 32/7*q**2 + 28 + 22*q + 2/7*q**3 = 0. Calculate q.
-7, -2
Let f = 98 - 98. Suppose -8/3*w**2 - 2/3*w + f = 0. What is w?
-1/4, 0
Let j be 1 + (0 + -1)/3. Let c = 16/21 + -2/21. Determine k, given that -3*k**3 + c - j*k**2 + 3*k = 0.
-1, -2/9, 1
Solve 2/5*z**4 - 8/5*z + 0 - 2*z**3 + 16/5*z**2 = 0.
0, 1, 2
Let z(f) be the second derivative of f**7/840 - 7*f**6/720 + f**5/60 + f**4/12 - f**3/3 + 6*f. Let j(u) be the second derivative of z(u). Solve j(c) = 0 for c.
-1/2, 2
Let u(r) = -r**4 - r**3 - r + 1. Let m(c) = 9*c**4 + 8*c**3 + 2*c**2 + 11*c - 11. Let a(n) = -4*m(n) - 44*u(n). Let a(l) = 0. Calculate l.
-2, 0, 1/2
Let c(x) be the third derivative of x**6/120 - x**4/8 + x**3/3 - 4*x**2. Suppose c(h) = 0. What is h?
-2, 1
Let i(f) be the first derivative of 2*f**5/5 + f**4 - 2*f**2 - 2*f - 6. Suppose i(o) = 0. What is o?
-1, 1
Let r(n) be the third derivative of n**5/15 + 2*n**4/3 + 8*n**3/3 - n**2. Let r(k) = 0. Calculate k.
-2
Let v(l) be the first derivative of -2*l**5/15 + 2*l**4/3 - 8*l**3/9 + 14. Suppose v(z) = 0. Calculate z.
0, 2
Let n = 77 - 461/6. Factor n*w**2 - 1/6*w**3 + 1/6*w - 1/6.
-(w - 1)**2*(w + 1)/6
Let p(m) = m**2 + 1. Let q be p(-1). Find a, given that -1/3*a**q - 1/3*a + 2/3 = 0.
-2, 1
Let p(i) be the second derivative of 1/48*i**4 + 1/4*i**2 + 3*i - 1/8*i**3 + 0. Solve p(x) = 0 for x.
1, 2
Let q be 162/(-42) + 7 - (-2)/(-14). Find y, given that -1/3*y**4 + 0 + 2/3*y + y**2 + 0*y**q = 0.
-1, 0, 2
Let i be 77/35 + 2/(-10). Factor -4 + 46*d**3 - 34*d**i - 14*d**4 - 20*d**2 + 30*d - 4*d.
-2*(d - 1)**3*(7*d - 2)
Factor 3*a - 2*a**3 - 1 - 5 - a**3 + 0*a**3 + 6*a**2.
-3*(a - 2)*(a - 1)*(a + 1)
Determine m, given that 24/17*m - 72/17 - 2/17*m**2 = 0.
6
Let i(j) be the first derivative of 2*j**5/55 + j**4/11 - 2*j**3/33 - 2*j**2/11 + 6. What is q in i(q) = 0?
-2, -1, 0, 1
Factor 1/2*p**2 + 0 - p.
p*(p - 2)/2
Let x be 1 + -1 + 2/7. Let w(z) = -z**3 - z**2 - 3*z + 2. Let l be w(0). Solve 2/7*d**l + 4/7*d + x = 0 for d.
-1
Let x = -7 + 10. Factor 5*q**3 - 2*q**5 + 2*q**4 - 2*q**2 + 4*q**5 - 4*q**5 - x*q**3.
-2*q**2*(q - 1)**2*(q + 1)
Factor -809*s**4 - 5*s**3 - s**5 + 5*s**5 + 17*s**3 + 821*s**4 + 4*s**2.
4*s**2*(s + 1)**3
Let z(k) = -13*k**2 + 24*k - 11. Let p(n) = -6*n**2 + 12*n - 6. Let y(d) = -5*p(d) + 2*z(d). Suppose y(q) = 0. What is q?
1, 2
Solve -22*v**3 - 68*v - 5*v**4 - v**4 + 5*v**2 + 60*v - 29*v**2 = 0 for v.
-2, -1, -2/3, 0
Let b(w) be the first derivative of -2*w**3/21 + 4*w**2/7 - 8*w/7 + 9. Factor b(p).
-2*(p - 2)**2/7
Let j(m) = -m**3 + 5*m**2 + 2*m - 8. Let t be j(5). Solve 8/3 + t*z**2 + 16/3*z = 0.
-2, -2/3
Let j(v) be the third derivative of 0*v**5 + 1/945*v**7 - 3*v**2 + 0*v**6 + 0 - 1/1512*v**8 + 0*v**4 + 0*v**3 + 0*v. What is m in j(m) = 0?
0, 1
Suppose v = -0*f + 3*f + 14, 4*f - 3 = -3*v. Let n = v + -3. Let -n*l**5 + 1/2*l + 3/2*l**3 + 2*l**4 + 0 - 2*l**2 = 0. Calc