 be the first derivative of -v**4/11 + 106*v**3/33 - 76*v**2/11 + 50*v/11 + 54. Determine g, given that m(g) = 0.
1/2, 1, 25
Factor -189/8*x - 3/8 + 24*x**2.
3*(x - 1)*(64*x + 1)/8
Suppose 2*y + 7 = 5*h, 4*h - 3*h + 5 = 2*y. Solve -m**2 - h*m**4 + 5*m**2 - 30*m - 2*m**5 + 32*m - m**4 = 0 for m.
-1, 0, 1
Let c(d) be the second derivative of 1/4*d**4 + 0 + 27/2*d**2 - 3*d**3 + 13*d. Suppose c(z) = 0. What is z?
3
Let x = 114 + -227/2. Let v(k) be the second derivative of 3/20*k**5 + 2*k + 0*k**2 + x*k**3 + 0 + 1/2*k**4. What is p in v(p) = 0?
-1, 0
Let d(i) = i**4 + i**3 + 1. Let h(u) = 8*u**4 + 8*u**3 - 12*u**2 - 4*u + 12. Let p(j) = 4*d(j) - h(j). Solve p(v) = 0.
-2, -1, 1
Let d(n) be the second derivative of n**6/45 - 4*n**5/5 + 83*n**4/9 - 88*n**3/3 + 121*n**2/3 - 94*n. Factor d(h).
2*(h - 11)**2*(h - 1)**2/3
Factor 1/2*g**3 + 147/2 + 7/2*g - 11/2*g**2.
(g - 7)**2*(g + 3)/2
Let t = -2233 - -2233. Factor -n + 0 + t*n**2 + 49/4*n**3.
n*(7*n - 2)*(7*n + 2)/4
Suppose 5*m + 7 - 27 = -3*l, 0 = -2*l + m - 4. Factor l*u + 0 + 0*u**2 + 0*u**3 + 0*u**4 + 6/7*u**5.
6*u**5/7
Let g(i) be the second derivative of i**4/3 + 74*i**3/3 - 523*i. Factor g(t).
4*t*(t + 37)
Let u = -1429 - -1431. Suppose 10/11*g**3 + 32/11*g**u - 14/11*g**4 + 0 + 8/11*g = 0. Calculate g.
-1, -2/7, 0, 2
Suppose 0 = -3*y + 2*y + 10. Factor y*k**3 - 15*k + 25 + k**5 - 27*k**2 + 5*k**2 - 12*k**2 + 4*k**3 + 9*k**4.
(k - 1)**2*(k + 1)*(k + 5)**2
Let r(k) = -3*k + 5. Let n be r(3). Let v be n - ((-1018)/210 + (-26)/(-195)). Factor v*u + 3/7 - 1/7*u**3 + 1/7*u**2.
-(u - 3)*(u + 1)**2/7
Suppose 2*d + 1 = 4*v - 3, -v + 1 = 5*d. Let s(f) be the second derivative of d*f**2 + 3*f + 0*f**3 + 1/90*f**5 + 0 + 1/54*f**4. Let s(n) = 0. Calculate n.
-1, 0
Let f = -238217/5 - -47647. Suppose -48/5*w**2 - f*w**3 - 8*w + 0 - 2/5*w**4 = 0. What is w?
-5, -2, 0
Find a, given that 241*a**4 - 2409*a**2 + 14726*a**3 + 4*a**4 - 1660 + 13260*a + 5224*a**3 - 9557*a**2 - 19829*a**2 = 0.
-83, 2/7, 1
Let g(a) be the first derivative of -5*a**4/12 - 10*a**3/3 + 25*a**2/2 + a - 3. Let r(w) be the first derivative of g(w). Factor r(s).
-5*(s - 1)*(s + 5)
Suppose 2/3*s**5 + 24*s + 40*s**2 + 0 + 20/3*s**4 + 74/3*s**3 = 0. What is s?
-3, -2, 0
Let s(h) be the second derivative of -h**8/5880 + h**6/315 - 4*h**3/3 - 25*h. Let i(p) be the second derivative of s(p). Find b, given that i(b) = 0.
-2, 0, 2
Suppose -4*p = -h - 14, 5*h - 10 = -3*p + 6*h. Let a(k) be the first derivative of -2/3*k - 8 + 1/4*k**p - 13/18*k**3 - 1/30*k**5 + k**2. Factor a(t).
-(t - 2)**2*(t - 1)**2/6
Suppose -3*m = -3*d + 12, -11 = d + 2*m - 3. Let k(t) be the first derivative of 0*t**2 + 0*t + 2/5*t**5 + d*t**3 + t**4 - 4. Suppose k(y) = 0. What is y?
-2, 0
Suppose 0 = -0*c + 2*c - 6. Factor 4*k**2 + k**c - k**2 - 2*k**2 - 2*k**3.
-k**2*(k - 1)
Let o(g) be the first derivative of 0*g - 1/360*g**5 - 1/3*g**3 + 0*g**2 - 5 + 0*g**4 + 1/1080*g**6. Let x(y) be the third derivative of o(y). Solve x(i) = 0.
0, 1
Let v be ((-198)/12)/(-11) - (-470)/(-340). Factor 0 - v*g**3 + 0*g**2 - 2/17*g**4 + 0*g.
-2*g**3*(g + 1)/17
Let d = -7 - -11. Suppose -4 - r**2 + d*r**2 - 2*r**2 + 0*r**2 = 0. Calculate r.
-2, 2
Factor 0 + 28*l**2 + 86/3*l - 2/3*l**3.
-2*l*(l - 43)*(l + 1)/3
Let j(b) be the second derivative of 0 + 32/105*b**6 + 80/7*b**3 + 32/7*b**2 - 24/7*b**5 - 10*b + 193/21*b**4. Let j(h) = 0. What is h?
-1/4, 4
Let q(j) be the second derivative of 0 - 12*j + 1/10*j**5 - 1/6*j**4 - 3*j**2 - 5/3*j**3. Factor q(n).
2*(n - 3)*(n + 1)**2
Let r(v) = -v**3 + 5*v**2 + 6*v + 3. Suppose -o = 5*a - 30, 0 = 3*a - 0*a - 2*o - 18. Let x be r(a). Factor -3*c**2 - 6*c**2 + 3*c + 3*c**3 + 6*c**3 - x*c**4.
-3*c*(c - 1)**3
Let p be (-138)/(-21) - 7 - (-41)/14. Suppose -1/2*n**5 + 4*n - 7/2*n**3 - 2 - 1/2*n**2 + p*n**4 = 0. What is n?
-1, 1, 2
Factor -1600 - 1/4*b**2 + 40*b.
-(b - 80)**2/4
Suppose 3*g = 7*g - 8. Factor 101*y**g + 79*y**2 + 33*y - 18*y + 45*y + 5.
5*(6*y + 1)**2
Let z(f) be the first derivative of 11*f**6/30 - f**5/5 + 7*f**2 + 28. Let n(p) be the second derivative of z(p). Determine k, given that n(k) = 0.
0, 3/11
Let f(d) be the second derivative of 0*d**2 - 1/450*d**6 + 0*d**4 + 0 + d + 1/3*d**3 - 1/75*d**5. Let r(i) be the second derivative of f(i). Solve r(h) = 0.
-2, 0
Factor 5*b**2 + b**2 + 179 - 209 - 3*b.
3*(b + 2)*(2*b - 5)
Let w(z) be the first derivative of -13*z**3/6 + z**2/4 + 167. Factor w(q).
-q*(13*q - 1)/2
Suppose -4*p - 40 = -13*x, 5*p + 0 - 7 = 2*x. Let y(o) be the second derivative of -1/60*o**x + 0 - 1/10*o**2 + 1/15*o**3 - 9*o. Suppose y(z) = 0. Calculate z.
1
Let r(s) = s**3 - 2*s**2 + s + 1. Let o be r(2). Factor -7*a**2 + 2*a**3 + 11*a**2 - 2*a**o - 4*a**4.
-4*a**2*(a - 1)*(a + 1)
Let r(j) be the first derivative of 2*j**6/15 - 2*j**4/3 + 2*j**2 - 18*j + 13. Let y(m) be the first derivative of r(m). What is h in y(h) = 0?
-1, 1
Let m = -51 - -99. Factor 10*p**2 + 4*p**2 - 40*p - 10*p**2 + 4*p**3 - 2*p**3 + m.
2*(p - 2)**2*(p + 6)
Let i be 1/(-2) - 258/24*-2. Suppose 0*c + 2*c = 6. Factor 243/4*z**4 + 189/2*z**3 + c + 39/4*z**2 - i*z.
3*(z + 1)**2*(9*z - 2)**2/4
Let m(k) be the first derivative of -2*k**6/15 + 44*k**5/25 - 7*k**4 + 20*k**3/3 + 51. Solve m(t) = 0 for t.
0, 1, 5
Suppose b + 2*h = 0, 3*b - 9 - 7 = 2*h. Let k = b - -2. Find l such that -3*l**4 - 2*l**3 - 6 - l**3 + 3*l + k + 3*l**2 = 0.
-1, 0, 1
Suppose -4*s = 4*v - 20, 0 = -2*v - 22*s + 21*s + 9. Factor -1/4*t**v - 3/4*t**2 + 0 + 1/4*t + 3/4*t**3.
-t*(t - 1)**3/4
Let p(x) = -19*x + 1. Let b be p(-1). Let l = 163 + -160. Find n such that -5*n**3 + b*n**l + n**2 - 14*n**3 = 0.
-1, 0
Let n(i) = i**2 - 2*i + 2. Let m be n(0). Find k such that -7*k**3 - 10*k**4 + 4*k**4 + 4*k**2 + m*k**4 + 4*k + 3*k**3 = 0.
-1, 0, 1
What is z in 1031*z**5 - 3*z**4 + 15*z**2 - 12 - 15*z**3 + 1033*z**5 - 2061*z**5 + 12*z = 0?
-2, -1, 1, 2
Solve -6 - 11 + 6 + h**2 - 13 - 23*h = 0 for h.
-1, 24
Let t(l) be the first derivative of -l**3/5 + 108*l**2/5 - 3888*l/5 + 51. Let t(o) = 0. What is o?
36
Let q(o) = -4*o**2 + 16*o - 22. Let l(c) = 5*c**2 - 17*c + 22. Let r(t) = -3*l(t) - 4*q(t). Find g, given that r(g) = 0.
2, 11
Let q = -29344 + 29346. Determine g so that -g**q + 0*g + 0 - 1/2*g**3 = 0.
-2, 0
Let b(t) be the second derivative of -7/30*t**4 + 3/50*t**5 - 4/105*t**7 + 8/75*t**6 + 0 + 2/15*t**3 - 32*t + 0*t**2. Let b(l) = 0. Calculate l.
-1, 0, 1/2, 2
Let f(k) = -k**3 + k**2 - k - 1. Let i(p) = p**2 + 5*p + 4. Let g be i(-3). Let r(n) = n**3 - 5*n**2 + 6*n + 14. Let u(b) = g*f(b) - r(b). Factor u(h).
(h - 2)*(h + 2)*(h + 3)
Let z be (-11)/(-6) + 76/(-57). Solve z*c**3 - 1/2*c**5 - c**2 + 0 + c**4 + 0*c = 0.
-1, 0, 1, 2
Let z = 2482 + -2482. Let m(l) be the third derivative of -1/168*l**8 - 2/35*l**7 - 4/15*l**5 + 0*l + 4*l**2 + 0*l**4 + z*l**3 - 1/5*l**6 + 0. Factor m(p).
-2*p**2*(p + 2)**3
Let m(l) be the second derivative of 30*l - 16/15*l**2 + 7/150*l**5 - 8/45*l**3 + 23/90*l**4 - 7/225*l**6 + 0 + 1/315*l**7. What is f in m(f) = 0?
-1, 1, 4
Let s(d) = -2*d**2 + 42*d - 104. Let i be s(18). Let l(c) be the first derivative of 3*c**2 - 5/2*c**3 + 6*c - 9/8*c**i - 6. Solve l(b) = 0 for b.
-2, -2/3, 1
Let o(s) be the first derivative of 2/33*s**3 - 12/11*s - 7/11*s**2 + 1/11*s**4 + 44. Let o(r) = 0. Calculate r.
-3/2, -1, 2
Let j(l) be the first derivative of 2*l**3/15 + 64*l**2/5 + 43. Factor j(i).
2*i*(i + 64)/5
Let b = -49 + 53. Factor -b*a**2 - 12*a**3 - 1948 + 1948.
-4*a**2*(3*a + 1)
Let f be (-180)/(-100) - (-1)/5. Suppose -s + f*s - 9*s**2 + 8*s**2 + 4 - 2 = 0. Calculate s.
-1, 2
Let w(q) be the first derivative of -3/5*q**2 + 2 + 1/6*q**4 + 2/15*q**3 - 6*q. Let v(h) be the first derivative of w(h). Factor v(i).
2*(i + 1)*(5*i - 3)/5
Let l(a) be the third derivative of a**7/630 + a**6/90 + a**5/30 + 5*a**4/8 + 4*a**2. Let g(f) be the second derivative of l(f). Find d such that g(d) = 0.
-1
Let a(y) be the third derivative of -y**8/560 + 5*y**7/168 - y**6/40 + 5*y**4/8 - 18*y**2. Let l(w) be the second derivative of a(w). Let l(b) = 0. Calculate b.
0, 1/4, 6
Let q(d) be the first derivative of 2*d**5/25 + 3*d**4/5 + 2*d**3/3 + 538. Factor q(w).
2*w**2*(w + 1)*(w + 5)/5
Let z(g) be the first derivative of g**4/5 + 4*g**3/3 + 8*g**2/5 - 182. Find u, given that z(u) = 0.
-4, -1, 0
Let h