t o(w) be the second derivative of -w**8/336 + w**7/84 + w**6/72 - w**5/12 - 3*w**3/2 + 14*w. Let z(s) be the second derivative of o(s). Factor z(g).
-5*g*(g - 2)*(g - 1)*(g + 1)
Let 9 - 3/8*d**2 - 15/8*d = 0. Calculate d.
-8, 3
Factor 1/3*w**2 - 1 - 2/3*w.
(w - 3)*(w + 1)/3
Determine f so that -49*f - 147*f - 28 + 19*f**2 - 9*f**2 - 52 = 0.
-2/5, 20
Let m = 578 + -574. Let a(x) be the second derivative of 7/135*x**6 + 1/2*x**m + 3*x + 2/9*x**2 - 23/90*x**5 + 0 - 13/27*x**3. What is p in a(p) = 0?
2/7, 1
Let d = 18206 - 163844/9. Solve 20/9*l**3 - 20/9*l**2 - 2/9 + 2/9*l**5 - d*l**4 + 10/9*l = 0 for l.
1
Let c(p) be the first derivative of -p**7/2100 + p**6/150 - p**5/60 - 10*p**3/3 + 33. Let o(v) be the third derivative of c(v). Determine i so that o(i) = 0.
0, 1, 5
Let h(r) = 9*r**4 - 9*r**3 - 36*r**2 - 44*r - 11. Let u(n) = -90*n + 13*n**4 - 6*n**3 - 7*n**3 - 17 - 54*n**2 + 24*n. Let o(v) = 7*h(v) - 5*u(v). Factor o(g).
-2*(g - 4)*(g + 1)**3
Let j(v) be the second derivative of -v**6/75 - 8*v**5/25 - 16*v**4/5 - 256*v**3/15 - 256*v**2/5 - 2*v - 4. Factor j(y).
-2*(y + 4)**4/5
Let j(f) = 4*f**2 - 10*f + 16. Let m be j(8). Let 2*c**3 + 191 + c - m - 3*c**3 + c**2 = 0. What is c?
-1, 1
Factor 4*y**3 + 0 - 5/2*y**2 + 3/2*y**4 - 3*y.
y*(y - 1)*(y + 3)*(3*y + 2)/2
Let q = -7561 + 83189/11. Let -q*o**5 + 2*o**3 + 0 + 4/11*o - 30/11*o**4 + 2*o**2 = 0. Calculate o.
-2, -1/3, 0, 1
Suppose -125 - 110 = -5*b. Factor -50*q + 2 + b*q - 3*q**2 - 2 + 6.
-3*(q - 1)*(q + 2)
Find d, given that -2/3*d**2 - 1/9*d**4 + 0 - 5/9*d**3 + 0*d = 0.
-3, -2, 0
Suppose -17 = -27*n + 37. What is o in -2/3*o - 2/3*o**3 + 0 + 4/3*o**n = 0?
0, 1
Let j(x) be the first derivative of -2*x**3/51 - 11*x**2/17 - 56. Determine s, given that j(s) = 0.
-11, 0
Factor 112/13*s - 114/13 + 2/13*s**2.
2*(s - 1)*(s + 57)/13
Find o, given that o**2 - 2*o**2 + 6*o**2 - 6*o**2 - 26645 - 4*o**2 + 730*o = 0.
73
Let v = -10 - -16. Suppose -g - g + v = 0. Suppose -7*a**3 + 3*a**3 + 4*a**g + a**4 = 0. Calculate a.
0
Let s(n) = -2*n**2 - 3*n + 10. Suppose 0 = -c - 3*c. Let d be s(c). What is o in 25/3*o**2 + 3 - d*o = 0?
3/5
Let o = 15 - 10. Factor 2*m**2 + o + 2 + 4 - 8*m - 3.
2*(m - 2)**2
Let w = -2/115 + 119/230. Let i(p) be the second derivative of -4*p + 0 - 1/10*p**6 + 0*p**2 + w*p**3 + 9/20*p**5 - 3/4*p**4. Suppose i(j) = 0. What is j?
0, 1
Let u(l) = l**3 - 11*l**2 + 9*l - 97. Let c be u(11). Let w(q) be the second derivative of -4/3*q**c + 0 - 9*q + 4/9*q**3 - 1/18*q**4. Solve w(a) = 0 for a.
2
Factor 0*b**4 - 21*b**4 - 4*b**4 + 22*b + 46*b - 344*b**2 + 445*b**3.
-b*(b - 17)*(5*b - 2)**2
Let s(w) be the second derivative of -8*w**6/15 + w**5/5 + 4*w**4 - 22*w**3/3 + 4*w**2 - 193*w. Determine l so that s(l) = 0.
-2, 1/4, 1
Let k(i) be the second derivative of -27*i**5/100 - 11*i**4/20 - i**3/6 + i**2/10 + i - 1. Solve k(c) = 0 for c.
-1, -1/3, 1/9
Let u(g) be the third derivative of 1/84*g**8 + 0*g**4 + 0*g - 1/30*g**6 - 2/15*g**5 + 4/105*g**7 + 0*g**3 + 0 - 11*g**2. Factor u(n).
4*n**2*(n - 1)*(n + 1)*(n + 2)
Let r = 837 - 5853/7. Factor r*c**2 + 0*c - 3/7*c**3 + 0.
-3*c**2*(c - 2)/7
Let t(r) be the third derivative of r**5/36 + 265*r**4/72 + 130*r**3/9 + 211*r**2. Factor t(c).
5*(c + 1)*(c + 52)/3
Let z(s) = 0*s**2 - 4*s**2 - 51*s + 11*s. Let a be z(-10). Suppose 0*l + a + 2/5*l**3 - 2/5*l**2 = 0. Calculate l.
0, 1
Let z(g) be the second derivative of 0*g**2 + 0 - 1/12*g**3 - 1/48*g**4 + 16*g. Factor z(x).
-x*(x + 2)/4
Let r(t) = 9*t**3 + 240*t**2 - 318*t. Let g(d) = -d**3 - 30*d**2 + 40*d. Let m(q) = -33*g(q) - 4*r(q). Factor m(s).
-3*s*(s - 8)*(s - 2)
Let b be (-16*7/252*9)/((-30)/9). Factor -b*k**2 + 0 + 6/5*k.
-6*k*(k - 1)/5
Let m = 53 + -56. Let k be (6/27 - 184/180)*m. Factor 12/5*a + 3/5*a**3 - k*a**2 + 0.
3*a*(a - 2)**2/5
Let z(n) be the second derivative of -3*n**5/160 + 11*n**4/32 - n**3/2 - 15*n**2/4 - 349*n + 1. Factor z(r).
-3*(r - 10)*(r - 2)*(r + 1)/8
Let q be (-32)/(-10) + (-13)/65. Solve -30*d**4 - 7*d + 23*d**3 - 38*d**2 - 87*d**3 + q*d = 0 for d.
-1, -2/15, 0
Let w(g) be the third derivative of 25/168*g**4 + 0*g + 1/2352*g**8 + 4/735*g**7 - 25*g**2 + 0*g**3 - 2/21*g**5 + 1/140*g**6 + 0. Factor w(b).
b*(b - 1)**2*(b + 5)**2/7
Let f(s) be the third derivative of -s**5/24 + 535*s**4/24 - 57245*s**3/12 - 11*s**2 + 15*s. What is o in f(o) = 0?
107
Let w(x) be the first derivative of -11 + 7/8*x**4 - 2*x**2 + 2*x + 1/12*x**6 - 1/2*x**5 + 1/6*x**3. Let w(i) = 0. Calculate i.
-1, 1, 2
Factor 58*m - 2*m + 10*m**2 - 128 - 6*m**2.
4*(m - 2)*(m + 16)
Let d(u) = u**2 - 16*u + 8. Let g be d(14). Let j be (-4)/(-10) + (-92)/g. What is m in 118*m - 114*m + m**2 - j*m**2 = 0?
0, 1
Let l(h) be the first derivative of -h**4 - 4*h**3 + 8*h**2 - 51. What is s in l(s) = 0?
-4, 0, 1
Let z(t) be the first derivative of -t**4/8 - 13*t**3/6 + t**2/4 + 13*t/2 - 198. Factor z(d).
-(d - 1)*(d + 1)*(d + 13)/2
Suppose -j = 35*j + 7*j. Factor j*q**2 - 1/6*q**3 + 1/2*q - 1/3.
-(q - 1)**2*(q + 2)/6
Let r = 30/457 - -1251/1828. Factor r*m**2 - 3/2*m - 9/4.
3*(m - 3)*(m + 1)/4
Let v(j) = -j**4 - j**3 + j - 1. Let x(h) = 4*h**4 + h**2 + 5. Let a(r) = 15*v(r) + 3*x(r). Factor a(f).
-3*f*(f - 1)*(f + 1)*(f + 5)
Let j be 0/(-3) - 1 - -7. Factor j - 4*q**2 - 15 - 3 - 16*q.
-4*(q + 1)*(q + 3)
Suppose -19 = -z - 4*j, -3*z - 4*j + 1 = -24. Factor -3*i**2 + i**3 - 12*i + 11*i**z + 3*i**4 - 4*i**2 + 4*i**2.
3*i*(i - 1)*(i + 1)*(i + 4)
Suppose 0*u - u**4 + 1/4*u**3 + u**2 - 1/4*u**5 + 0 = 0. What is u?
-4, -1, 0, 1
What is u in 108*u + 3/5*u**2 - 543/5 = 0?
-181, 1
Find r, given that -96/11*r + 2/11*r**2 + 1152/11 = 0.
24
Let q = -1355 + 1360. Let b(k) be the first derivative of -4/3*k**3 + 4/3*k**2 - 2/15*k**q - 2/3*k - 7 + 2/3*k**4. Factor b(d).
-2*(d - 1)**4/3
Let c = -188142 + 35558948/189. Let d = -8/27 + c. Solve 2/7*f**2 - d + 0*f = 0.
-1, 1
Let n(o) = 17*o**3 + 3*o**2 - 18*o + 13. Let k(c) = -10*c**3 - 2*c**2 + 9*c - 6. Let t(x) = 5*k(x) + 3*n(x). Find s, given that t(s) = 0.
-3, 1, 3
Factor -15*c**2 + 6*c - 2*c**3 + 0*c**4 - 4*c - 7*c**2 + 14*c**4 + 8*c**4.
2*c*(c - 1)*(c + 1)*(11*c - 1)
Suppose -5*b + 7*b - 10 = 0. Suppose -5*h = 3*u - 10, b*u - 2 = -h + 2*u. Determine d so that d**5 - d - d**h + d**4 + 3*d - 12*d**3 + 9*d**3 = 0.
-2, -1, 0, 1
Let g(y) be the second derivative of y**7/21 + 11*y**6/15 + 17*y**5/5 + 4*y**4 + 8*y - 8. Factor g(o).
2*o**2*(o + 1)*(o + 4)*(o + 6)
Determine g so that -128/3 - 16/3*g - 1/6*g**2 = 0.
-16
Factor -2/3*s**2 - 4/3 - 2*s.
-2*(s + 1)*(s + 2)/3
Let m(q) be the first derivative of q**6/780 - q**5/78 + 2*q**4/39 - 4*q**3/39 - 16*q**2 - 31. Let a(x) be the second derivative of m(x). Factor a(r).
2*(r - 2)**2*(r - 1)/13
Let v(t) be the first derivative of -t**6/160 + t**4/32 + 9*t**2/2 - 26. Let f(k) be the second derivative of v(k). Factor f(p).
-3*p*(p - 1)*(p + 1)/4
Let x = 44 - 50. Let n(g) = -3*g - 18. Let l be n(x). Factor 1/3 + l*o - 1/3*o**2.
-(o - 1)*(o + 1)/3
Suppose -574 = -6*w - 220. What is k in 0*k - k + 57 - 2*k - w + k**3 = 0?
-1, 2
Let i = 81 - 88. Let v be ((-7)/(-18))/i*-6. Find r, given that 1/6*r**4 - v*r - 1/6*r**2 + 0 + 1/3*r**3 = 0.
-2, -1, 0, 1
Let a(c) be the second derivative of 1/5*c**5 + 14/3*c**3 + 0 + 6*c**2 + 7*c + 5/3*c**4. Determine u, given that a(u) = 0.
-3, -1
Let n = -5683177 + 1756104274/309. Let h = -2/103 + n. Factor -5*k - h*k**2 - 2/3.
-(5*k + 1)*(5*k + 2)/3
Let b(v) = -4*v + 15. Let c be b(3). Factor 0*n**4 + 38*n**c - 58*n**3 + 0*n**2 + 5*n**4 + 15*n**2.
5*n**2*(n - 3)*(n - 1)
Suppose 3*u + f = 5, 6*u - 2*f = u + 12. Let -4 - 2*z**u + 8*z**3 - 3*z**3 + 4 = 0. What is z?
0, 2/5
What is h in 14/3*h**4 + 0 + 10/3*h**5 - 4/3*h - 2*h**3 - 14/3*h**2 = 0?
-1, -2/5, 0, 1
Let o = -2609/6 - -871/2. Factor 2/3 + o*h**4 - 2/3*h - 2/3*h**5 + 4/3*h**3 - 4/3*h**2.
-2*(h - 1)**3*(h + 1)**2/3
Suppose -o + 6 + 8 = 2*c, 0 = 5*o - 10. Let k = 8 - c. Let -9*m**3 + 10*m - 8*m**k + 21*m**4 - 13*m**2 - 16*m + 15*m**5 = 0. What is m?
-1, -2/5, 0, 1
Suppose -5*b + 106 = 4*t, -b = -3*b + 3*t + 24. Factor 1 - b*l**2 + 17*l**2 - l - 1.
-l*(l + 1)
Let c(i) be the third derivative of -37*i**2 - 1/18*i**5 + 1/315*i**7 + 1/60*i**6 + 0 + 0*i + 1/18*i**4 + 0*i**3 - 1/504*i**8. Solve c(r) = 0 for r.
-2, 0, 1
Let t = 1969/3 - 655. Suppose 2/3*r**2 + 2/3 - t*r = 