et m(o) be the second derivative of o**8/336 + o**7/210 - o**6/120 - o**5/60 + 2*o**2 - 5*o. Let f(h) be the first derivative of m(h). Let f(k) = 0. What is k?
-1, 0, 1
What is t in -3*t - 11/3*t**2 + 2/3 = 0?
-1, 2/11
Let s(o) = o**3 + 9*o**2 + 7*o - 2. Let c be s(-8). Find y such that -2 - 6 - c*y**3 - 6*y**2 + 7*y**3 + 12*y = 0.
2
Let s = -312/35 - -47/7. Let t = 43/15 + s. Find a, given that 0*a - t + 2/3*a**2 = 0.
-1, 1
Let q(a) be the second derivative of -a**4/15 + a**3/3 - 2*a**2/5 + 7*a. Factor q(h).
-2*(h - 2)*(2*h - 1)/5
Let y be 114/(-95)*(-20)/12. Determine n so that -1/6 + 0*n + 1/6*n**y = 0.
-1, 1
Let l(r) be the third derivative of -r**6/1620 + r**5/540 + 5*r**3/3 + 9*r**2. Let u(q) be the first derivative of l(q). Factor u(c).
-2*c*(c - 1)/9
Let o(u) be the third derivative of 2/45*u**6 + 0*u + 1/90*u**5 + 1/63*u**7 - 1/18*u**4 + 0 + 3*u**2 + 0*u**3. Find z, given that o(z) = 0.
-1, 0, 2/5
Let g be 10/(-6) - 8/24. Let b(q) = 18*q**5 - 42*q**4 + 32*q**3 - 10*q**2 + 6. Let o(h) = h**4 + h**3 - h**2 + 1. Let a(k) = g*b(k) + 12*o(k). Factor a(v).
-4*v**2*(v - 2)*(3*v - 1)**2
Let v be ((-4)/(-18))/((-6)/(-9)). Let h(j) be the first derivative of 1/5*j**5 + 1/2*j**2 + 1 + 0*j - 1/4*j**4 - v*j**3. Factor h(f).
f*(f - 1)**2*(f + 1)
Let 4/15 - 2/5*q**2 + 2/15*q + 2/15*q**4 - 2/15*q**3 = 0. Calculate q.
-1, 1, 2
Let -2/11*a + 10/11*a**5 + 20/11*a**2 - 8/11*a**3 - 16/11*a**4 - 4/11 = 0. What is a?
-1, -2/5, 1
Let z = 56 - 54. Factor 6*v + 2 - 7/2*v**z.
-(v - 2)*(7*v + 2)/2
Let 2*w**4 - 8/3*w**3 + 2/9*w**2 + 0 + 4/9*w = 0. What is w?
-1/3, 0, 2/3, 1
Let d be (12/(-9))/(6/(-9)). Let n(v) be the third derivative of 0*v**3 + 1/48*v**4 + v**d - 1/240*v**6 + 0 + 0*v + 0*v**5. Factor n(j).
-j*(j - 1)*(j + 1)/2
Let j(x) be the first derivative of x**4/32 - 7*x**3/24 - x**2/16 + 7*x/8 + 49. Factor j(s).
(s - 7)*(s - 1)*(s + 1)/8
Suppose -2*i + 11 + 63 = 0. Let k = i - 110/3. Factor 0 + 2/3*x**3 + 0*x - k*x**4 - 1/3*x**2.
-x**2*(x - 1)**2/3
Let b(x) be the second derivative of x**7/350 - x**6/50 + x**5/20 - x**4/20 - x**2 + x. Let o(d) be the first derivative of b(d). Factor o(i).
3*i*(i - 2)*(i - 1)**2/5
Let p(n) be the first derivative of -4*n**3/3 - 12*n**2 - 36*n + 4. Find r such that p(r) = 0.
-3
Suppose 3*b + 4 = -2. Let y be (12 + -10)*(-2)/b. Factor 0*h**4 - 1/4*h + 0*h**y + 1/2*h**3 + 0 - 1/4*h**5.
-h*(h - 1)**2*(h + 1)**2/4
Let a = -23 - -27. Let b(k) be the second derivative of 1/45*k**6 + 0*k**3 + 1/18*k**a + 0*k**2 + 2*k - 1/15*k**5 + 0. Factor b(z).
2*z**2*(z - 1)**2/3
Let v(j) be the second derivative of -j**4/12 + 2*j**3/3 - 2*j**2 + 29*j. Factor v(l).
-(l - 2)**2
Let r(w) be the first derivative of 2*w**6/45 + 2*w**5/15 + w**4/9 - 8*w - 3. Let h(v) be the first derivative of r(v). Find z, given that h(z) = 0.
-1, 0
Factor 0 - 2/19*f**3 + 0*f + 2/19*f**2.
-2*f**2*(f - 1)/19
Let v(d) be the third derivative of d**10/604800 - d**9/241920 + d**5/30 + 3*d**2. Let x(z) be the third derivative of v(z). Factor x(n).
n**3*(n - 1)/4
Suppose 4*d - 5*i = 129, 4*d - 9 = -2*i + 85. Let t be d/36 - 10/45. Factor -a + 1/2*a**2 + t.
(a - 1)**2/2
Solve 0 - 3/8*p**5 - 21/8*p**3 - 9/8*p**2 - 15/8*p**4 + 0*p = 0.
-3, -1, 0
Suppose 5*g + 1505 = -4*u - u, -3*u = -g + 899. Let s = 2708/9 + u. Determine q so that -2/9*q**2 - 8/9 + s*q = 0.
2
Let k be (-44)/(-84) + (-44)/(-14) + -3. Factor -1/2 - k*c**2 - 7/6*c.
-(c + 1)*(4*c + 3)/6
Let c(q) be the second derivative of 5/6*q**3 + 1/2*q**2 + 0 + 7*q + 1/3*q**4. Suppose c(x) = 0. What is x?
-1, -1/4
Let l = -291/2 - -146. Factor -j**2 + 1/2*j + l*j**3 + 0.
j*(j - 1)**2/2
Let o be (1/8)/((-3)/(-6)). Let p(a) be the first derivative of -1/12*a**3 - 1 + 1/8*a**2 - 1/16*a**4 + o*a. Solve p(y) = 0.
-1, 1
Let z(w) = -4*w**2 - 16*w - 28. Let t(b) = b**2 + 5*b + 9. Let r(a) = 16*t(a) + 5*z(a). Solve r(f) = 0.
-1, 1
Let i be 42/38 + (-2)/19. Let f(o) = o**3 - 3*o + 2. Let u be f(2). Solve -i - w**u + 5*w**2 - 3*w**2 + 0 = 0 for w.
-1, 1
Let q = -10/671 + 824729/4697. Let w = q - 175. Determine h, given that 0 - 2/7*h**3 - 2/7*h - w*h**2 = 0.
-1, 0
Let q(j) be the third derivative of j**8/336 - 13*j**7/630 + 67*j**6/1080 - 19*j**5/180 + j**4/9 - 2*j**3/27 - 13*j**2. Let q(z) = 0. Calculate z.
2/3, 1
Suppose 2*m + 0*q + 4*q - 18 = 0, 4*m - 27 = -5*q. Let l(s) be the third derivative of -s**2 + 1/60*s**6 + 0*s**4 + 0*s + 0*s**m - 1/30*s**5 + 0. Factor l(t).
2*t**2*(t - 1)
Suppose -11*u**3 + 12*u + 9 + 9*u**3 - 22*u**2 - 10*u**3 - 3*u**4 + 16*u**2 = 0. Calculate u.
-3, -1, 1
Let v be (12/(-10))/(-1*6/4). Factor 1/5*d + 1/5*d**5 - 4/5*d**4 - v*d**2 + 6/5*d**3 + 0.
d*(d - 1)**4/5
Let z be (-5)/20*((-13)/5 - -1). Let -10*v**2 - z + 4*v = 0. What is v?
1/5
Let u(a) be the second derivative of a**7/420 - a**5/120 + a**2/2 + 2*a. Let y(c) be the first derivative of u(c). Determine s, given that y(s) = 0.
-1, 0, 1
Let l(v) be the first derivative of 2*v**5/13 + 4*v**4/13 + 2*v**3/39 - 2*v**2/13 - 8. Suppose l(k) = 0. Calculate k.
-1, 0, 2/5
Let x(g) be the first derivative of -g**3/3 + g**2 - 6. Suppose x(c) = 0. Calculate c.
0, 2
Let s(t) be the second derivative of -t**6/540 + t**5/30 - t**4/4 - t**3 - 4*t. Let y(q) be the second derivative of s(q). Factor y(k).
-2*(k - 3)**2/3
Let u(k) = -2*k**5 - 2*k**4 - 5*k**3 + 7*k**2 + k - 5. Let z(i) = -i**5 - 2*i**4 - 4*i**3 + 6*i**2 + i - 4. Let b(v) = 2*u(v) - 3*z(v). Factor b(t).
-(t - 2)*(t - 1)**2*(t + 1)**2
Let h(g) = -g**5 - 3*g**3 + 2*g - 2. Let k(o) = -2*o**5 - 3*o**3 + o**2 + 3*o - 3. Let r(z) = 3*h(z) - 2*k(z). Factor r(a).
a**2*(a - 2)*(a + 1)**2
Let c(x) = -5*x**2 + 8*x + 1. Let y(d) = -3*d**2 + 4*d. Let r(o) = 4*c(o) - 7*y(o). Find s such that r(s) = 0.
-2
Let w(i) be the first derivative of i**7/70 + i**6/40 - 3*i**5/20 - i**4/8 + i**3 - 7*i**2/2 + 5. Let g(n) be the second derivative of w(n). Factor g(c).
3*(c - 1)**2*(c + 1)*(c + 2)
Suppose 5*x = -5*p - 15, 5 + 10 = -3*x. Let d(h) be the first derivative of 0*h**2 + 0*h + p - 1/3*h**3. Factor d(a).
-a**2
Suppose -3*r = -7*r + 32. Let v be r/12*12/14. Factor 2/7*f - 2/7*f**2 + 0 - v*f**3.
-2*f*(f + 1)*(2*f - 1)/7
Let d = -3/20 + 33/20. Factor d*n**4 - 3/2*n**3 - 3 + 15/2*n - 9/2*n**2.
3*(n - 1)**3*(n + 2)/2
Suppose 4*s - 825 = -s. Suppose s = 4*d + d. Determine v, given that 1 - v**3 - 34*v**2 + 0 + d*v**2 + v = 0.
-1, 1
Solve 0 - 2*a**4 + 5/2*a**3 - a**2 + 1/2*a**5 + 0*a = 0.
0, 1, 2
Let y = 8 + -6. Let b be (-16)/(-20) - -1*y. Factor -4/5*m**2 + 4/5 - b*m**3 + 14/5*m.
-2*(m - 1)*(m + 1)*(7*m + 2)/5
Suppose 7*h - 10 = 2*h. Find a such that -6*a**4 + 7*a - h*a + 8*a**3 - 5*a + 8*a**2 = 0.
-2/3, 0, 2
Let o(a) be the second derivative of 39/20*a**5 - 3/2*a**2 - 2/5*a**6 + 7/2*a**3 + 0 - 6*a - 15/4*a**4. Suppose o(i) = 0. What is i?
1/4, 1
Factor -4/7 - 2/7*p + 2/7*p**2.
2*(p - 2)*(p + 1)/7
Let d(w) be the third derivative of -w**6/120 - w**5/20 - w**4/24 - 2*w**2. Let r be d(-3). Factor 0*o**3 + 2*o**2 - o**2 - o**r.
-o**2*(o - 1)
Let o(z) be the third derivative of z**7/840 - z**6/120 - z**4/6 - 5*z**2. Let l(f) be the second derivative of o(f). Factor l(m).
3*m*(m - 2)
Determine d, given that -2*d**3 - 5*d**3 + 14*d**3 - 5*d**3 - 6*d**2 + 4*d = 0.
0, 1, 2
Let n = -54 + 54. Factor 0 + n*d - 1/5*d**5 + 0*d**2 - 1/5*d**3 - 2/5*d**4.
-d**3*(d + 1)**2/5
Let c(b) = 2*b**2 + 6*b + 7. Let h be c(-3). Let l be (-1 + h)*(-12)/(-24). Let -2/3*x**l + 0*x - 2/3*x**2 + 0 = 0. What is x?
-1, 0
Let b(r) be the second derivative of -r**7/28 - r**6/5 - 9*r**5/20 - r**4/2 - r**3/4 + 6*r. Find z, given that b(z) = 0.
-1, 0
Let p(n) be the second derivative of -n**7/21 - 6*n**6/35 - 6*n**5/35 + n**4/21 + n**3/7 - 20*n. Find v, given that p(v) = 0.
-1, 0, 3/7
Let l(y) be the third derivative of y**6/60 + y**5/6 + y**4/2 + 8*y**2. Suppose l(n) = 0. What is n?
-3, -2, 0
Let l(b) be the first derivative of 5*b**4/16 + 5*b**3/12 - 6. Let l(m) = 0. What is m?
-1, 0
Solve -33/7*f - 3/7*f**2 + 36/7 = 0 for f.
-12, 1
Let m(n) be the first derivative of -3 - 1/6*n**3 + 1/10*n**5 - 5/16*n**4 + 0*n + 0*n**2 + 5/24*n**6. Suppose m(r) = 0. What is r?
-1, -2/5, 0, 1
Let q(r) be the first derivative of r**8/1120 - r**7/140 + r**6/48 - r**5/40 - 7*r**3/3 - 5. Let b(c) be the third derivative of q(c). Solve b(i) = 0 for i.
0, 1, 2
Let j(i) be the third