rd derivative of -l**5/20 - 3*l**4/8 + 9*l**3 + 7*l**2 - 2. Factor d(f).
-3*(f - 3)*(f + 6)
Let v(z) = -48*z**4 - 112*z**3 + 344*z**2 + 1100*z - 1324. Let x(s) = 7*s**4 + 16*s**3 - 49*s**2 - 157*s + 189. Let a(p) = 3*v(p) + 20*x(p). Factor a(k).
-4*(k - 3)*(k - 1)*(k + 4)**2
Let g(d) be the second derivative of d**4/120 + 2*d**3/3 + 20*d**2 - 26*d. What is t in g(t) = 0?
-20
Let l(f) be the first derivative of -f**5/20 + f**4 - 8*f**3 + 32*f**2 - 64*f - 223. Solve l(w) = 0 for w.
4
Suppose 5*h + 8 = 9*h. Let r be h/(-14) - 4/(-28). Determine o, given that 3/4*o + 3/4*o**2 + r = 0.
-1, 0
Let h be 0/1 + (-27)/(-54). Factor h*z**2 + 18 - 6*z.
(z - 6)**2/2
Suppose -2/3*m**3 - 40/21 + 128/21*m + 46/21*m**2 = 0. What is m?
-2, 2/7, 5
Factor 252 + 14*b + 238 - 482 + 4*b**2 - 2*b**3.
-2*(b - 4)*(b + 1)**2
Let -2/3*p - 2/3*p**2 + 4/3 = 0. Calculate p.
-2, 1
Let q(s) be the first derivative of -s**3/3 + 3*s**2/2 + 8. Factor q(a).
-a*(a - 3)
Let p(n) be the first derivative of n**3/18 + n**2/4 - 150. Find t such that p(t) = 0.
-3, 0
Let 0*f - 24/5*f**2 + 6/5*f**4 - 12/5*f**3 + 3/5*f**5 + 0 = 0. Calculate f.
-2, 0, 2
Let g = 137 - 85. Let h = -152/3 + g. Let 0 - 2/3*v**2 + 2/3*v**3 - h*v = 0. What is v?
-1, 0, 2
Let g = 13 - 12. Let l(m) = -3*m**3 + m + 2. Let o(j) be the third derivative of -j**6/120 + j**3/6 + 5*j**2. Let p(q) = g*l(q) - 2*o(q). Factor p(x).
-x*(x - 1)*(x + 1)
Let u(q) be the third derivative of q**7/525 + 47*q**6/300 + 221*q**5/50 + 289*q**4/12 - 19652*q**3/15 - 307*q**2. Factor u(d).
2*(d - 4)*(d + 17)**3/5
Let v(g) be the first derivative of -27 - 25/9*g**3 + 5/12*g**4 - 20/3*g + 20/3*g**2. Let v(n) = 0. What is n?
1, 2
Let j(q) = -8*q**5 + 14*q**3 + 14*q**2 - 30*q + 10. Let p(l) = l**5 - l**4 - l + 1. Let r(z) = -j(z) - 6*p(z). Factor r(w).
2*(w - 1)**3*(w + 2)*(w + 4)
Let o(z) = 9*z**2 + 2*z. Suppose 0 = -b - 4*b - 10. Let f be o(b). Find u, given that 2*u**2 + f - 9*u - 2*u - 5*u + 0*u = 0.
4
Let n(v) be the first derivative of 3*v**5 - 6 + 40*v - 55/3*v**3 + 25*v**2 - 25/2*v**4. Let n(k) = 0. Calculate k.
-1, -2/3, 1, 4
Let w be 2/(96/(-240)) + (-1 + 3 - -7). Find c, given that 7/10*c**5 + 4/5*c**2 + 0 - 21/10*c**3 + 1/5*c**w + 2/5*c = 0.
-2, -2/7, 0, 1
Let r(p) = -p**2 - 11*p - 7. Let v be r(-8). Let d = -14 + v. Factor -3*l - 3 + 3*l**d + 3 - 9 + 9*l**2.
3*(l - 1)*(l + 1)*(l + 3)
Let -20/7*l + 0 + 4/7*l**2 - 4/7*l**4 + 20/7*l**3 = 0. What is l?
-1, 0, 1, 5
Factor 57/5*d + 54/5*d**2 - 3/5*d**3 + 0.
-3*d*(d - 19)*(d + 1)/5
Let t(v) be the second derivative of 25*v - 1/3*v**4 - 4/3*v**3 + 0 + 6*v**2. Let t(q) = 0. What is q?
-3, 1
Let s(g) be the second derivative of g**5/120 - 5*g**4/48 - g**3/2 - 6*g**2 - 32*g. Let n(q) be the first derivative of s(q). Factor n(y).
(y - 6)*(y + 1)/2
Let a(q) be the first derivative of -q**4/8 + q**3/6 + 5*q**2/4 + 3*q/2 - 24. Solve a(o) = 0 for o.
-1, 3
Let k = -269/2 - -135. Let h = -98/3 - -33. Let -k*d + h + 1/6*d**2 = 0. What is d?
1, 2
Let i be 9/12*228/(-171)*-1. Find k, given that 1/4*k**2 - 5/4*k + i = 0.
1, 4
Let w(s) be the first derivative of 1/6*s**3 - 3/20*s**5 + 3/8*s**2 + 1/4*s + 1 - 1/24*s**6 - 1/8*s**4. What is d in w(d) = 0?
-1, 1
Factor -4/9*f + 2/9 + 2/9*f**2.
2*(f - 1)**2/9
Let a(h) be the third derivative of -h**6/72 - 5*h**5/12 - 125*h**4/24 + 9*h**3/2 - 19*h**2. Let d(i) be the first derivative of a(i). Factor d(o).
-5*(o + 5)**2
Suppose 0 = 5*w + 11 - 21. Factor -33*j**3 - 2*j**w + 36*j**3 + 2*j**2 - 3*j.
3*j*(j - 1)*(j + 1)
Let b = -26 - -44. Suppose 6*y + 0*y - b = 0. Suppose -3*m**4 - 7*m**y - 54*m**2 - 14*m**3 + 250 - 274 - 60*m = 0. What is m?
-2, -1
Let d(w) = 21*w**4 + 60*w**3 + 75*w**2 + 42*w + 9. Let q(c) = c**5 - c**3 + 2*c + 1. Let p(y) = -d(y) - 3*q(y). Solve p(j) = 0 for j.
-2, -1
Let t(l) be the second derivative of 8/15*l**3 + 16/5*l**2 + 9*l + 0 + 1/30*l**4. Solve t(c) = 0.
-4
Let g(c) be the first derivative of -5/12*c**4 + 55/6*c**2 + 10*c + 15 + 20/9*c**3. Factor g(v).
-5*(v - 6)*(v + 1)**2/3
Let g(r) be the second derivative of 2*r**7/21 - 8*r**6/5 + 9*r**5 - 50*r**4/3 - 3*r + 99. Factor g(y).
4*y**2*(y - 5)**2*(y - 2)
Let i(p) = 1000*p**4 + 695*p**3 + 135*p**2 - 55*p - 55. Let h(o) = 37*o**4 + 26*o**3 + 5*o**2 - 2*o - 2. Let u(x) = -55*h(x) + 2*i(x). Let u(n) = 0. What is n?
-1, -1/7, 0
Suppose -4*m - 24 + 21 = s, -2*m + 2*s = -6. Let x(y) be the second derivative of 1/32*y**4 - 3/8*y**2 + 12*y + 1/16*y**3 + m. Find z such that x(z) = 0.
-2, 1
Let b(p) be the first derivative of 2*p**3/21 - 10*p**2/7 - 22*p/7 + 165. Factor b(y).
2*(y - 11)*(y + 1)/7
What is b in 39/2*b + 69/4*b**2 - 36 - 3/4*b**3 = 0?
-2, 1, 24
Let f be (-1711)/(-1947) - 2/6. Suppose -f*v**3 + 6/11*v**4 + 12/11 + 6/11*v - 18/11*v**2 = 0. Calculate v.
-1, 1, 2
Suppose -136 = -5*i + 4*m + 30, 146 = 5*i + m. Let a = i - 26. Factor -4/5*l**3 - 2/5*l**2 + 3/5*l**a - 1/5 + 4/5*l.
(l - 1)**2*(l + 1)*(3*l - 1)/5
Let b(h) = 11*h**4 - 26*h**3 + 24*h**2 - 26*h + 5. Let u(a) = 21*a**4 - 51*a**3 + 49*a**2 - 51*a + 10. Let t(m) = -11*b(m) + 6*u(m). Factor t(w).
5*(w - 1)**4
Let w(f) be the first derivative of -3*f**4/28 - 3*f**3 - 30*f**2/7 - 1097. Solve w(x) = 0.
-20, -1, 0
Let k(c) be the third derivative of -c**6/60 + 7*c**5/150 + 7*c**4/15 - 4*c**3/5 - 63*c**2. Determine z, given that k(z) = 0.
-2, 2/5, 3
Let v(w) be the first derivative of w**3/3 + 16*w**2 + 256*w - 42. Find p such that v(p) = 0.
-16
Let j(w) = 2*w**2 - 4*w - 1. Let c be j(3). Let q(p) = p**2 - 4*p - 3. Let v be q(c). Factor -13*f**v - 40*f**4 + 19*f**5 + 25*f**3 + f**5 + 8*f**2.
5*f**2*(f - 1)*(2*f - 1)**2
Determine f, given that -1/4*f**2 + 3 - 17/4*f + 5/4*f**3 + 1/4*f**4 = 0.
-4, -3, 1
Let l(v) be the first derivative of 256/7*v + 32/7*v**2 + 4/21*v**3 + 19. Factor l(t).
4*(t + 8)**2/7
Let p(u) be the first derivative of -2*u**5/5 - u**4 + 40*u**3/3 - 24*u**2 + 64. Factor p(y).
-2*y*(y - 2)**2*(y + 6)
Let m be (9 + -7)*(-4)/(-3 + -1). Suppose j - 5 = -2*v, -7 = -m*v - 2*j - j. Factor -1/2 + 1/6*o**v - 1/3*o.
(o - 3)*(o + 1)/6
Factor 296/9*t + 2/9*t**2 + 10952/9.
2*(t + 74)**2/9
Let b = -10283 + 51428/5. Factor 3/5*v**2 - b*v + 4/5.
(v - 4)*(3*v - 1)/5
Let b(h) be the second derivative of -1/3*h**3 - 3/2*h**2 + 17*h + 0 + 1/12*h**4. Factor b(f).
(f - 3)*(f + 1)
Let y be (-3)/(-15) - (-8 + 164/20). Let x(z) be the second derivative of y + 6*z + 1/6*z**3 + 0*z**2 - 1/12*z**4. Factor x(j).
-j*(j - 1)
Let u = 92 + -32. Let o be (-36)/24 + 106/u. Factor o*v**2 + 8/15*v**4 + 0 + 2/15*v - 14/15*v**3.
2*v*(v - 1)**2*(4*v + 1)/15
Let -2/3*r**3 + 8/9*r - 2/9*r**4 + 0*r**2 + 0 = 0. Calculate r.
-2, 0, 1
Let h be -4*(0 + 1/(-1)). Let r be -1 - (-4 + h/(-4)). Factor 16*y**4 + 0*y**r - 12*y**5 - 5*y**3 - 8*y**2 + 9*y**3.
-4*y**2*(y - 1)**2*(3*y + 2)
Let a(m) be the first derivative of -20/3*m**3 - 16*m + 32*m**2 - 7*m**4 - 9. Factor a(t).
-4*(t - 1)*(t + 2)*(7*t - 2)
Let b = 21 - 24. Let z(s) = -3*s + 1. Let r be z(b). Factor 3 - 1 + r*p - 5*p**2 - 7.
-5*(p - 1)**2
Factor -z**2 + z**4 + 1/3*z**3 + 1/3*z**5 + 0 - 2/3*z.
z*(z - 1)*(z + 1)**2*(z + 2)/3
Let q(b) = -35*b**4 - 83*b**3 - 19*b**2 + 19*b + 5. Let p(l) = 53*l**4 + 125*l**3 + 28*l**2 - 28*l - 8. Let z(c) = 5*p(c) + 8*q(c). What is x in z(x) = 0?
-2, -1, 0, 2/5
Let l = -4/459851 - -5143893338/5978063. Let j = l - 860. Determine k, given that j*k**2 + 0 + 8/13*k**3 + 2/13*k**4 + 0*k = 0.
-3, -1, 0
Let t be (1 - 0)/((-7)/(-14)). Suppose -3*x + 2 + 4 = 0. Suppose -t*j**x + 2*j + 4*j + 0*j**2 + 5*j**2 = 0. What is j?
-2, 0
Let v(t) be the second derivative of t**6/135 + 2*t**5/9 + 13*t**4/9 - 220*t**3/27 + 121*t**2/9 - 2*t - 11. Let v(g) = 0. What is g?
-11, 1
Let x(n) be the third derivative of -n**5/12 + 55*n**4/6 - 1210*n**3/3 + 4*n**2 - 20. Find s, given that x(s) = 0.
22
Suppose -4*z = -12 + 4. Suppose -4 = -2*c + z. Factor 4*x**4 + 4*x**2 - 8 - 20*x + 4*x**c - 5*x**2 - 11*x**2.
4*(x - 2)*(x + 1)**3
Let d be -1 - (2 - 3) - (3 - 8). Let p(c) be the second derivative of 9*c - 1/15*c**6 - 1/12*c**4 + 0 - 1/8*c**d + 0*c**2 + 0*c**3 - 1/84*c**7. Factor p(j).
-j**2*(j + 1)**2*(j + 2)/2
Suppose -27 - 113 = -28*h. Let i(r) be the third derivative of 0*r**h - 5*r**2 + 1/600*r**6 + 0*r + 0*r**3 + 0 - 1/120*r**4. Let i(b) = 0. Calculate b.
-1, 0, 1
Let u be 2 - (4 - 3/1). Let f(i) = i**