t g(k) be the third derivative of k**6/120 - k**5/60 - k**4/24 + k**3/6 - 9*k**2. Suppose g(m) = 0. What is m?
-1, 1
Suppose 2*f + 1 = 7. Suppose 2*u**2 - 7 + f*u - 3*u**2 + 5 = 0. Calculate u.
1, 2
Let o(q) = -q**2 + 9*q - 7. Let m be o(6). Let t be 1/(-4) - (-9)/4. Suppose -2*b**t + m - 11 + 2*b**3 = 0. Calculate b.
0, 1
Let f be -2 - -6 - 0/2. Suppose -f = -y + 1. Let 2/7*n**y + 0*n**2 + 0*n**4 + 0 - 4/7*n**3 + 2/7*n = 0. Calculate n.
-1, 0, 1
Suppose 5*h + 0*h = 0. Determine u so that h*u**2 - 3*u + 3*u**2 + 0*u**2 + 0*u**2 = 0.
0, 1
Solve -9/4*x**3 + 9/4*x + x**4 - 1/2 - 1/2*x**2 = 0 for x.
-1, 1/4, 1, 2
Let u(a) be the first derivative of 0*a + 1/15*a**5 - 3 - 1/9*a**3 + 1/12*a**4 - 1/6*a**2. Factor u(v).
v*(v - 1)*(v + 1)**2/3
Let d be 7/1 - 427/61. Factor d - 1/4*y - y**2.
-y*(4*y + 1)/4
Let b(u) be the first derivative of -u**8/2520 - u**7/630 - u**6/540 - 2*u**3/3 + 1. Let a(g) be the third derivative of b(g). What is m in a(m) = 0?
-1, 0
Let v(o) be the second derivative of o**6/24 - o**5/8 - 5*o**4/48 + 5*o**3/12 - 9*o. Determine z, given that v(z) = 0.
-1, 0, 1, 2
Let q(r) = 4*r**2 - 11*r - 5. Let z(n) = -n**2 + n. Let v(l) = -2*q(l) - 10*z(l). Factor v(w).
2*(w + 1)*(w + 5)
Factor 1/3*r + 1/3*r**2 - 2.
(r - 2)*(r + 3)/3
Let d be (18/12)/((-6)/(-16)). Solve -5*w + d*w**2 + 7*w + 2*w = 0 for w.
-1, 0
Let t(c) be the second derivative of c**4/3 + 4*c**3 + 16*c**2 - 4*c. Find d, given that t(d) = 0.
-4, -2
Let v = -154 + 157. Determine n, given that 0 + 1/3*n**5 + 0*n**4 + 0*n + 0*n**2 - 1/3*n**v = 0.
-1, 0, 1
Let k(q) be the third derivative of q**5/180 - q**4/72 - 7*q**2. Solve k(r) = 0.
0, 1
Let l = 4 - -1. Factor -2*a**4 - 20*a**3 - a**4 - 2*a**l - 20*a**2 - 3*a**4 - 2 - 10*a - 4*a**4.
-2*(a + 1)**5
Let f = -8 + 26/3. Suppose 1/3 - 1/3*p - f*p**2 + 1/3*p**4 - 1/3*p**5 + 2/3*p**3 = 0. What is p?
-1, 1
Solve 0 - 4/7*h**2 - 4/7*h = 0.
-1, 0
Let h(k) be the second derivative of -k**4/12 + k**3/3 - k**2/2 - k. Let h(p) = 0. What is p?
1
Suppose 4*c = -5*r + 2*c, -5 = c. Suppose -y + 2 + r = 2*h, -4*y = -3*h - 16. Factor -4*v**2 + 2*v**3 + h*v**4 + 2*v**2 - 2*v + 2*v**4.
2*v*(v - 1)*(v + 1)**2
Let w be (-19)/38*(-188)/10 - 7. Determine z, given that 8/5*z**2 + 0 + 8/5*z - w*z**4 + 18/5*z**5 - 22/5*z**3 = 0.
-2/3, 0, 1
Let -6*y**3 - 8*y**2 - 8*y + 2*y**4 - y + 9*y = 0. Calculate y.
-1, 0, 4
Suppose 0 = k - 3 + 19. Let v = 18 + k. Factor 0*h + 0 - 2/9*h**v - 2/9*h**3.
-2*h**2*(h + 1)/9
Let o(c) = -c**3 + 2*c**2 - c. Let b be o(-3). Suppose 0 = 4*f - 5 - 3. Solve -47*t**f - 32*t**5 - 1 + b*t**4 - 19*t**3 + 12*t - 32*t**5 + 71*t**3 + 0 = 0.
-1, 1/4, 1
Let i(x) be the second derivative of -2*x**6/135 + x**4/27 + 3*x. Factor i(z).
-4*z**2*(z - 1)*(z + 1)/9
Let i = 18 + -17. Let b(u) be the first derivative of -2/5*u**3 + 3/5*u**2 + 1/10*u**4 - i - 2/5*u. Factor b(h).
2*(h - 1)**3/5
Let d(p) be the first derivative of -1/2*p + 9/8*p**2 - 1/4*p**4 - 1/4*p**3 + 4. Factor d(c).
-(c - 1)*(c + 2)*(4*c - 1)/4
Let k(q) be the first derivative of -q**4/60 - q**3/15 - 2*q + 5. Let g(z) be the first derivative of k(z). Factor g(u).
-u*(u + 2)/5
Let j(o) be the third derivative of 5*o**8/84 - 8*o**7/35 + 3*o**6/10 - 2*o**5/15 - o**2. Let j(h) = 0. What is h?
0, 2/5, 1
Suppose -5*z + 3*z + 4*y = -4, -3*y = -z + 1. Let k(t) = -t**2 + 6*t - 6. Let m be k(4). Solve 4*p**z - 2*p**m + 2 - 1 - 3*p**4 = 0.
-1, 1
Let m(f) be the first derivative of -9/28*f**4 - 2 + 3/7*f**2 - 5/7*f**3 + 0*f. Find z such that m(z) = 0.
-2, 0, 1/3
Factor 2*p**5 + 5/2*p**4 + 1/2*p**3 + 0*p**2 + 0*p + 0.
p**3*(p + 1)*(4*p + 1)/2
Factor 90 - 15*v - 20*v**2 - 17*v**3 + 37*v**3 - 15*v**3.
5*(v - 3)**2*(v + 2)
Factor -9/4*a**3 + 27/4 - 51/4*a**2 - 63/4*a.
-3*(a + 3)**2*(3*a - 1)/4
Let p = -1/3 + 5/12. Let q(l) be the second derivative of 0 - 1/84*l**7 - l - p*l**3 + 0*l**4 + 0*l**6 + 1/20*l**5 + 0*l**2. Factor q(j).
-j*(j - 1)**2*(j + 1)**2/2
Let r(q) = -3*q - 3. Let c be r(1). Let l be (-1)/(-2) - 9/c. Factor 0 - 2/5*z**l + 1/5*z**3 + 1/5*z.
z*(z - 1)**2/5
Let f(j) be the second derivative of j**6/45 + j**5/30 - j**4/18 - j**3/9 - 5*j. Determine o so that f(o) = 0.
-1, 0, 1
Factor b + 1/4*b**2 + 0.
b*(b + 4)/4
Suppose 5*y - 3 = 12. Factor 2*s + s - y*s + 2*s**2.
2*s**2
Let r be 1 + 2 + (-2 - -1). Let -2*v - v**r + 0 - 2 + v + 4*v = 0. What is v?
1, 2
Let m(n) = -6*n**3 + 378*n**2 - 7925*n + 55553. Let f(h) = 3*h**3 - 189*h**2 + 3963*h - 27777. Let z(r) = -13*f(r) - 6*m(r). Factor z(w).
-3*(w - 21)**3
Let f(s) = -4*s**5 + 4*s**4 + 8*s**3 + 4*s**2. Let v(t) = -4*t**5 + 3*t**4 + 8*t**3 + 3*t**2 - t. Let y(m) = 3*f(m) - 4*v(m). Factor y(w).
4*w*(w - 1)**2*(w + 1)**2
Suppose -2*o + 18 = 2*o + y, -o + 4*y = 4. Let q = o + -18/5. Factor -q*b**5 + 0 + 0*b**2 + 0*b + 4/5*b**4 - 2/5*b**3.
-2*b**3*(b - 1)**2/5
Let k = 52 + -52. Factor -d**4 + 0 + 2/3*d**5 + k*d**3 + 1/3*d**2 + 0*d.
d**2*(d - 1)**2*(2*d + 1)/3
Let g = -1 - -5. Let u(y) be the second derivative of 1/50*y**5 + 0 + 0*y**2 + 1/15*y**3 - 2*y - 1/15*y**g. Solve u(h) = 0.
0, 1
Find s such that 1/2 - 1/4*s**2 - 1/4*s = 0.
-2, 1
Let w be (-186)/(-45) - 6/45. Let i(o) be the second derivative of 1/40*o**5 + 2*o + 0*o**2 + 0*o**w + 0*o**3 + 0. Factor i(y).
y**3/2
Let l(o) be the second derivative of o**7/189 + o**6/135 - o**5/45 - o. Factor l(k).
2*k**3*(k - 1)*(k + 2)/9
Let n(d) be the third derivative of d**11/498960 - d**10/226800 + d**5/15 + 3*d**2. Let g(p) be the third derivative of n(p). Suppose g(c) = 0. What is c?
0, 1
Let v be 7 - 2 - (-1)/1. Let b(a) be the third derivative of 0*a + 1/6*a**4 + a**2 + 1/3*a**3 + 1/24*a**5 + 1/240*a**v + 0. Determine p, given that b(p) = 0.
-2, -1
Let y(v) = -3*v**2 - 15*v - 3. Let w(u) = -u**3 - u**2 - u - 1. Let x(t) = -3*w(t) + y(t). Determine p so that x(p) = 0.
-2, 0, 2
Suppose 4*q = 5*q + 11. Let m(i) = i**2 + 12*i + 16. Let s be m(q). Factor 0 + 0*z + 1/3*z**s - 2/3*z**4 + 1/3*z**3 + 0*z**2.
z**3*(z - 1)**2/3
Let j(z) be the second derivative of -z**6/70 - 9*z**5/35 - 27*z**4/14 - 54*z**3/7 - 243*z**2/14 - 11*z. Factor j(p).
-3*(p + 3)**4/7
Let f = 25/3 - 8. Let m(s) be the first derivative of -f*s + 0*s**3 - 2 + 1/2*s**2 - 1/3*s**4. Let m(k) = 0. Calculate k.
-1, 1/2
Suppose 0 = -81*x + 84*x - 6. Let 0 - z + 1/2*z**x = 0. What is z?
0, 2
Let o = 14 + -10. Let u(i) be the third derivative of 0*i**3 - 1/240*i**6 + 1/120*i**5 + 0*i**o + 0*i - 3*i**2 + 0. Solve u(y) = 0 for y.
0, 1
Let s(z) = z**3 + 4*z**2 - 5*z + 2. Let p(u) = u**2 + 5*u - 1. Let h be p(-4). Let a be s(h). Factor -1 - 4*m**a - 2*m + 7*m - m.
-(2*m - 1)**2
Let f be (2/(-24))/(17/(-68)). Factor -2/3*s + f*s**2 + 0.
s*(s - 2)/3
Suppose -1 - 2 = -j. Suppose 0 = -8*s + 9*s - j. Factor -1/2*p - 1/2*p**2 + 1/2 + 1/2*p**s.
(p - 1)**2*(p + 1)/2
Let d(n) be the first derivative of 9*n**6/10 - 99*n**5/25 + 57*n**4/20 + 33*n**3/5 - 36*n**2/5 + 12*n/5 + 7. Find x such that d(x) = 0.
-1, 1/3, 2
Suppose -2*q + 0 - 2 = 0. Let a be -1*((-12)/3 - q). Determine s so that a*s**3 - 2*s**3 + s**2 + 3*s**3 - 6*s**3 + s**4 = 0.
0, 1
Let o(l) be the first derivative of -3*l**4/2 + 22*l**3/3 - 12*l**2 + 8*l + 2. Solve o(c) = 0.
2/3, 1, 2
Factor -8/9*p + 0 + 8/9*p**2 + 2/9*p**3 - 2/9*p**4.
-2*p*(p - 2)*(p - 1)*(p + 2)/9
Suppose l = 5*a - 5, -2*l = -a - 3*a - 2. Let s(g) be the second derivative of 0*g**a - 1/3*g**3 - 2*g + 1/6*g**4 + 0. Factor s(p).
2*p*(p - 1)
Let m(h) be the second derivative of 10*h**7/21 + 28*h**6/15 + 12*h**5/5 + 2*h**4/3 - 2*h**3/3 + 8*h. Suppose m(i) = 0. Calculate i.
-1, 0, 1/5
Factor 85/4*s + 5/4*s**3 + 10*s**2 + 25/2.
5*(s + 1)*(s + 2)*(s + 5)/4
Let c = 1/17 - -27/119. Factor -2/7*w**3 - 6/7*w**2 - 6/7*w - c.
-2*(w + 1)**3/7
Let q(z) be the first derivative of 2*z**4/7 - 2*z**3/21 - 16*z**2/7 + 8*z/7 - 2. Suppose q(f) = 0. Calculate f.
-2, 1/4, 2
Let y(l) be the second derivative of l**5/150 + l**4/90 - 2*l**3/45 - 23*l. Find c such that y(c) = 0.
-2, 0, 1
Let d = 5 + -6. Let h(m) = -m**3 - m + 1. Let g(f) = 2*f**2 - 2*f + 2. Suppose 0*i = -i + 2. Let r(b) = d*g(b) + i*h(b). Factor r(y).
-2*y**2*(y + 1)
Let b(h) = 4*h**2 - 19*h. Let i(r) = r**2 - 6*r. Let a(t) = 2*b(t) - 7*i(t). Factor a(l).
l*(l + 4)
Let d(x) be the second derivative of x**4/8 + x**3/4 + 6*x. Determine b, given that d(b) = 0.
-1, 0
Let p(y) be the second 