 such that s(a) = 0.
-17, -1, 0
Let j(d) be the first derivative of d**4/3 + 4*d**3/3 + 2*d**2 + 7*d - 8. Let m(b) be the first derivative of j(b). Solve m(i) = 0 for i.
-1
Let y(u) be the first derivative of -3/2*u**2 + 0*u - 15/4*u**4 - 22 + 4*u**3 + 6/5*u**5. Factor y(j).
3*j*(j - 1)**2*(2*j - 1)
Let h = 81621/5 + -16321. What is z in 96/5 - h*z + 2/15*z**2 = 0?
12
Let k(y) be the first derivative of 1/12*y**4 - 17 + 4/9*y**3 + 0*y + 2/3*y**2. Factor k(p).
p*(p + 2)**2/3
Let k(c) = -5*c**4 - 18*c**3 - 17*c**2 + 140*c - 180. Let s(v) = -2*v**4 - 6*v**3 - 6*v**2 + 46*v - 60. Let r(l) = -3*k(l) + 8*s(l). Factor r(p).
-(p - 5)*(p - 2)**2*(p + 3)
Let v(b) be the second derivative of -b**8/560 + b**7/56 - 7*b**6/120 + 3*b**5/40 + 5*b**3/6 + 21*b. Let j(r) be the second derivative of v(r). Factor j(z).
-3*z*(z - 3)*(z - 1)**2
Let n(f) be the second derivative of -1/50*f**6 - 1/10*f**3 + 0 + 1/20*f**4 + 0*f**2 + 22*f + 3/100*f**5. Factor n(s).
-3*s*(s - 1)**2*(s + 1)/5
Let p(r) be the second derivative of r**8/560 + r**7/140 + r**6/120 + r**3 + 5*r. Let l(k) be the second derivative of p(k). Solve l(y) = 0 for y.
-1, 0
Factor 0 + g - 7/2*g**2 - g**3 + 7/2*g**4.
g*(g - 1)*(g + 1)*(7*g - 2)/2
Let k(a) be the third derivative of -a**6/300 + a**5/50 + a**4/15 - 4*a**3/5 - 84*a**2. Let k(h) = 0. Calculate h.
-2, 2, 3
Suppose 5*s = 5*z - 35, 3*z + 5*s = -21 + 10. Factor 0 - t**2 + t**z + 1/3*t - 1/3*t**4.
-t*(t - 1)**3/3
Let o(q) be the first derivative of -5*q**4/6 + 11*q**3/3 - 2*q**2 - 43*q + 39. Let j(k) be the first derivative of o(k). Factor j(d).
-2*(d - 2)*(5*d - 1)
Let t(l) be the second derivative of 7*l**4/66 + 58*l**3/33 + 16*l**2/11 - 55*l. Factor t(b).
2*(b + 8)*(7*b + 2)/11
Factor -6*r**4 + 832*r**3 - 3*r**5 - 1650*r**3 + 827*r**3.
-3*r**3*(r - 1)*(r + 3)
Let v be 23/(-5) - (15 - -10)*7/(-35). Suppose 2/5*h**3 - 6/5*h**2 + 6/5*h - v = 0. Calculate h.
1
Let i be (-1 - (-1)/(-5))*370/(-222). Solve -6/5*n + 4/5 + 2/5*n**i = 0 for n.
1, 2
Let g(v) = -6*v**2 + 10. Let u(a) = 2*a**2 - a + 1. Let r(f) = g(f) + 2*u(f). Factor r(s).
-2*(s - 2)*(s + 3)
Let m(q) be the first derivative of q**4/6 - 2*q**3/3 + q**2 + 9*q - 7. Let u(z) be the first derivative of m(z). What is y in u(y) = 0?
1
Solve 18/7*l**2 + 8192/7 - 768/7*l = 0.
64/3
Let v(p) be the third derivative of p**8/112 - 2*p**7/105 - p**6/15 + p**5/10 + 5*p**4/24 - p**3/3 + 99*p**2. What is s in v(s) = 0?
-1, 1/3, 1, 2
Factor -2*f**3 + 1/3*f**4 + 0 + 5/3*f**2 + 0*f.
f**2*(f - 5)*(f - 1)/3
Let j(h) be the first derivative of -h**4 + 8*h**3/3 - 2*h**2 + 74. Solve j(n) = 0.
0, 1
Let o be (-2)/(-29) + (-874)/58 + 17. Determine h, given that 20*h**o - 55/3*h + 25/3*h**3 - 10 = 0.
-3, -2/5, 1
Let t(g) be the third derivative of -2/15*g**4 + 0 - 2/5*g**3 + 20*g**2 + 0*g - 1/75*g**5. Factor t(i).
-4*(i + 1)*(i + 3)/5
Let g(j) be the first derivative of 0*j**3 + 6 + 3/8*j**2 - 1/16*j**4 + 3*j. Let r(b) be the first derivative of g(b). Factor r(c).
-3*(c - 1)*(c + 1)/4
Let h = -5 - -9. Suppose -d + 8 = x, -2*x = -0*d + h*d - 22. Solve 7*f**d + 3*f**5 - 3*f**4 - 7*f**3 + 3*f**2 - 3*f**3 = 0 for f.
-1, 0, 1
Let z(p) = -2*p**2 + 24*p - 61. Let k be z(8). Factor -4/7*l**k + 8/7 + 12/7*l + 0*l**2.
-4*(l - 2)*(l + 1)**2/7
Let b(q) = 2*q**2 + 19*q - 13. Let z(m) = 4*m**2 + 40*m - 26. Let p(c) = -9*b(c) + 4*z(c). Factor p(h).
-(h - 1)*(2*h + 13)
Let j(u) be the second derivative of 7*u + 0*u**3 + 0 + 1/21*u**4 - 2/147*u**7 + 2/35*u**6 - 3/35*u**5 + 0*u**2. Factor j(k).
-4*k**2*(k - 1)**3/7
Let y(n) be the third derivative of n**8/2184 - 2*n**7/1365 - n**6/260 + 2*n**5/195 + n**4/39 + n**2 - 40. Factor y(l).
2*l*(l - 2)**2*(l + 1)**2/13
Factor 36*s - 1/4*s**5 + 3*s**4 - 8*s**3 - 32 - 4*s**2.
-(s - 8)*(s - 2)**3*(s + 2)/4
Let s be (7 - -1)/16*(0 + 0). Suppose s = -q + 4*x + 8, -2*q + 0 = -x - 2. Factor 0*v - 1/3*v**5 - 8/3*v**3 - 4/3*v**2 - 5/3*v**4 + q.
-v**2*(v + 1)*(v + 2)**2/3
Factor 2*z**2 + 10*z - 4 + 12*z - 21*z + 7*z + 10.
2*(z + 1)*(z + 3)
Let o(l) be the third derivative of 0*l**5 + 0*l**3 - 1/72*l**4 + 1/360*l**6 + 0*l - l**2 + 17. Factor o(k).
k*(k - 1)*(k + 1)/3
Let n(r) be the second derivative of r**4/3 + 10*r**3/3 + 8*r**2 + 3*r - 8. Factor n(t).
4*(t + 1)*(t + 4)
Let k(r) be the second derivative of 7*r**6/60 + 9*r**5/40 + r**4/12 + 2*r + 56. Find c such that k(c) = 0.
-1, -2/7, 0
Let w(l) = -15*l**3 + 31*l**2 - 17*l - 3. Let h(g) = 61*g**3 - 123*g**2 + 67*g + 13. Let u(a) = 6*h(a) + 26*w(a). Factor u(d).
-4*d*(d - 2)*(6*d - 5)
Let t be (-1)/6 - (6 + (-830)/120). Factor t*f - 1/4*f**2 - 1/2.
-(f - 2)*(f - 1)/4
Suppose y + 25 = 2*y. Let a = y + -23. Factor -2*p - a*p + 0*p - 3*p**2 + p.
-3*p*(p + 1)
Let u(m) = m**2 + 5*m - 2. Let z(o) = -2*o**2 - 2*o + 36. Let h(r) = 4*u(r) + z(r). Suppose h(b) = 0. Calculate b.
-7, -2
Let g(v) be the third derivative of 0*v - 1/120*v**6 + 0*v**3 + 0 + 0*v**4 - 14*v**2 - 1/30*v**5. Solve g(a) = 0 for a.
-2, 0
Determine j so that 7*j**3 - 142*j**4 + 143*j**4 + 17*j**2 + 8*j + 3*j**3 = 0.
-8, -1, 0
Suppose 13*l - 22 = 2*l. Let q(f) = 7*f**2 - 59*f + 199. Let y(d) = -6*d**2 + 58*d - 198. Let p(s) = l*q(s) + 3*y(s). Suppose p(a) = 0. What is a?
7
Let v(g) be the third derivative of g**6/180 + 2*g**5/15 + g**4 + 32*g**3/9 - 111*g**2. Factor v(p).
2*(p + 2)**2*(p + 8)/3
Suppose -19*v**4 + 2*v**5 - 3*v**3 + 8*v**4 + 10*v**4 = 0. What is v?
-1, 0, 3/2
Let a(h) be the first derivative of 1/9*h**3 + 0*h**5 - 1/360*h**6 + 7 + 1/24*h**4 + 7/2*h**2 + 0*h. Let v(l) be the second derivative of a(l). Solve v(j) = 0.
-1, 2
Let f(i) = -2*i**2 + 4*i + 4. Let k be 1 - 1 - (6 - 0). Let c(r) = 9 + 0*r**2 + 31*r - 4*r**2 - 23*r. Let q(d) = k*c(d) + 13*f(d). Factor q(y).
-2*(y - 1)**2
Let l(u) be the second derivative of 1/30*u**4 + 0 - 2/15*u**3 + 0*u**2 - 9*u. Find h, given that l(h) = 0.
0, 2
What is h in -8*h - 20/3*h**2 + 48 - 2/3*h**3 = 0?
-6, 2
Let w be (11/165)/(27/90). Let s(m) be the third derivative of 0*m + 0*m**4 - 1/180*m**5 - 11*m**2 + 0 + w*m**3. Solve s(g) = 0 for g.
-2, 2
Let r be 5 + -3 + (4 - 4). Suppose 2*i = -r*g + 4*i + 12, -5*g - 4*i = -12. Factor 1 + 0 + 3*d**2 - g*d**4 - 4*d**3 + 0*d**2 - d**3 + 5*d.
-(d - 1)*(d + 1)**2*(4*d + 1)
Let u(q) be the third derivative of q**7/350 - 3*q**6/100 - 3*q**5/20 - q**4/5 - 143*q**2. Determine k, given that u(k) = 0.
-1, 0, 8
Let f(m) be the first derivative of -16/3*m**3 + 6*m**2 - 3 + m**4 + 0*m. Factor f(o).
4*o*(o - 3)*(o - 1)
Let w be 1 - (-14*16/(-56))/(-2). Let y(o) = -o + 1. Let b be y(1). Factor 4/5*s**5 + b*s - 2/5*s**2 + 8/5*s**w - 2*s**4 + 0.
2*s**2*(s - 1)**2*(2*s - 1)/5
Find o such that 30*o**2 + 119 - 67*o**2 - 110*o - 43 + 31*o**2 = 0.
-19, 2/3
Let h be (-36)/(-30)*(-20)/(-6) + -1. Let 4 - 18*f**2 + 97*f**3 + 6*f + 6*f**4 - 184*f**3 + 89*f**h = 0. What is f?
-2, -1/3, 1
Let z = -3396 + 3402. What is i in -2/3*i**5 - z*i**3 + 0*i + 0 + 0*i**2 + 4*i**4 = 0?
0, 3
Suppose 5*o - 2*m = -10, 9*o - 8*o - 5 = -m. Let y(r) be the second derivative of 1/78*r**4 - 1/65*r**5 + 3*r + 1/195*r**6 + 0*r**3 + o + 0*r**2. Factor y(u).
2*u**2*(u - 1)**2/13
Factor -440*j - 9*j**4 - 60*j**3 - 128 + 3*j**4 - 112 + j**4 - 105*j**2 - 150*j**2.
-5*(j + 1)*(j + 3)*(j + 4)**2
Let j(c) be the third derivative of 1/12*c**4 + 0*c - 3*c**2 + 2/3*c**3 + 0 - 1/30*c**5. Suppose j(s) = 0. Calculate s.
-1, 2
Let y be 1/(3/(-6)*2) - -1. Let t(o) be the third derivative of 0*o**3 + y*o + 0*o**4 + 0 + 0*o**5 + 5*o**2 - 1/210*o**7 - 1/360*o**6 + 1/252*o**8. Factor t(h).
h**3*(h - 1)*(4*h + 1)/3
Let b = 599/70 - 117/14. Let 0*c**2 - 2/5*c**3 - 1/5*c**4 + b + 2/5*c = 0. What is c?
-1, 1
Let p = -10 - -11. Factor -4*g**2 + 1 + 1 + 15 - p.
-4*(g - 2)*(g + 2)
Let m(b) be the third derivative of 1/180*b**4 - 1/900*b**6 - 14*b**2 - 2/45*b**3 + 0*b + 1/225*b**5 + 0. Factor m(l).
-2*(l - 2)*(l - 1)*(l + 1)/15
Suppose 0 = -3*c + 6*c - 201. Factor -c*b**2 + 70*b**2 + b + 5*b + 3.
3*(b + 1)**2
Let r = 2703/4 + -2697/4. Let 0 + r*j**2 + 3/2*j**4 + 0*j - 3*j**3 = 0. What is j?
0, 1
Let v(n) be the third derivative of 0 + 0*n - 1/100*n**5 + 0*n**3 - 1/10*n**4 + 51*n**2. Let v(i) = 0. Calculate i.
-4, 0
Let g(z) = -16*z - 1260. Let c be g(-79). Factor -1/2*w + w**c + 0 - 3/4*w**3 - 9/4*w**2.
w*(w - 2)*(w + 1)*(4*w + 1)/4
Let a(q) be the third derivative of 1/8