he third derivative of -v**8/672 - v**7/315 - v**6/1440 + v**5/240 - 14*v**4/3 - 289*v**2. Let f(g) be the second derivative of n(g). Factor f(t).
-(2*t + 1)**2*(5*t - 1)/2
Let r(b) be the first derivative of -b**4/2 + 4*b**3 + 27*b**2 + 2002. Factor r(c).
-2*c*(c - 9)*(c + 3)
Let l(n) = -5*n**2 + 15*n. Let z(g) = -6*g**2 - 2*g + 3. Let o be z(1). Let f(v) = -5*v**2 + 13*v. Let k(y) = o*f(y) + 4*l(y). Factor k(w).
5*w*(w - 1)
What is c in -300/7*c**2 - 60*c + 3*c**4 + 15/7*c**3 + 144/7 = 0?
-3, -2, 2/7, 4
Suppose 71 = 12*w + 11. Factor 37*n**2 + w*n**3 - 8*n**3 - 129*n**2 - 56*n - 9*n**3.
-4*n*(n + 7)*(3*n + 2)
Let z be (-8)/(-28) - (-232)/(-840). Let y(r) be the third derivative of 0*r**6 + 1/6*r**4 + 0 + 0*r**3 + 1/10*r**5 + 0*r + 10*r**2 - z*r**7. Factor y(i).
-2*i*(i - 2)*(i + 1)**2
Factor -369*s**3 + 229*s**3 - 1004 + 504*s**2 + 498*s + 142*s**3.
2*(s - 1)*(s + 2)*(s + 251)
Factor 400 - 201*s + 1/2*s**2.
(s - 400)*(s - 2)/2
Let w(f) = -f. Let a be w(-5). Let x be (-3)/27 - ((-24)/(-9))/(780/(-130)). Suppose -a*z**2 - 7/3*z - 3*z**3 - x = 0. What is z?
-1, -1/3
Let g(x) be the second derivative of -x**7/280 - 7*x**6/120 - 3*x**5/8 - 9*x**4/8 + 61*x**3/6 - 11*x. Let k(v) be the second derivative of g(v). Factor k(i).
-3*(i + 1)*(i + 3)**2
Suppose 0 = -12*q + 9 + 15. Suppose -q*y = -20*y + 72. Solve -12/5*a**y + 12/5*a + 0 - 9/5*a**3 - 3/5*a**5 + 12/5*a**2 = 0.
-2, -1, 0, 1
Let h = 5029 + -5025. Let f(t) be the third derivative of 0 + 1/12*t**5 + 0*t + 25/24*t**h - 41*t**2 + 10/3*t**3. Let f(z) = 0. What is z?
-4, -1
Let u(t) = -3*t**4 - 544*t**3 - 2104*t**2 + 32*t. Let a(x) = x**4 + 181*x**3 + 699*x**2 - 12*x. Let m(o) = 8*a(o) + 3*u(o). Factor m(q).
-q**2*(q + 4)*(q + 180)
Let i be (7571/339 - 17)/((-8)/(-3)). Factor 0 - 1/4*d**i - 3/4*d**4 + d**3 + 0*d.
-d**2*(d - 1)*(3*d - 1)/4
Let w be ((-70)/(-28))/5 - 1/4. Let d(u) be the first derivative of -3/10*u**5 + 0*u**2 + 14 + 1/2*u**3 - w*u**6 + 0*u + 3/8*u**4. Determine t so that d(t) = 0.
-1, 0, 1
Let k(b) = -4*b**3 + 427*b**2 + 72*b + 3748. Let v be k(107). Factor 0 + 3/5*r + 0*r**2 - 3/5*r**v.
-3*r*(r - 1)*(r + 1)/5
Suppose 0 = -y + 7*y - 30. Let a(x) be the second derivative of 8*x**3 + 4/5*x**5 + 9*x**2 + 11/3*x**4 - y*x + 1/15*x**6 + 0. Factor a(t).
2*(t + 1)**2*(t + 3)**2
Let z(l) be the third derivative of l**7/2415 - l**6/276 - l**5/230 + 13*l**4/276 + 10*l**3/69 + l**2 + 49. Let z(g) = 0. Calculate g.
-1, 2, 5
What is m in 246/5*m - 1032/5 + 3/5*m**2 = 0?
-86, 4
Let a = -7865 + 7865. Let w(t) be the second derivative of 2*t + 0 + 39/20*t**5 + 1/5*t**6 - 7/2*t**3 - 2*t**4 + a*t**2. Solve w(p) = 0 for p.
-7, -1/2, 0, 1
Factor 48*f**2 - 369*f + 3*f**3 - 2*f**3 + 58*f**2 + 37*f**2 - 23*f**2.
f*(f - 3)*(f + 123)
Let p(i) be the third derivative of 0*i + 1/240*i**6 + 0*i**3 + 0 + 0*i**5 - 13/840*i**7 - 143*i**2 + 0*i**4. Factor p(o).
-o**3*(13*o - 2)/4
Let o(u) be the first derivative of -u**5/5 - 107*u**4/4 - 895*u**3 + 10175*u**2/2 + 30250*u - 2315. Factor o(g).
-(g - 5)*(g + 2)*(g + 55)**2
Let p = -1555 + 2729. Let o = 1176 - p. Find u, given that 2/9*u + 2/9*u**o + 0 = 0.
-1, 0
Factor 76*o**3 - 156 + 8 - 193 - o**4 + 4*o + 25 + 237*o**2.
-(o - 79)*(o - 1)*(o + 2)**2
Let v(a) be the third derivative of 0 + 7/60*a**5 + 0*a + 8*a**3 - 71*a**2 + 1/240*a**6 + 4/3*a**4. Factor v(o).
(o + 4)**2*(o + 6)/2
Let s(l) be the first derivative of -5*l**3/3 + 35*l**2/2 - 50*l + 1687. Find g such that s(g) = 0.
2, 5
Let j(m) = 2*m - 10. Suppose 2*i + 4 = u - 0, 25 = 4*u + i. Let t be j(u). Determine v so that t + 1 - 9 - 26*v - 26*v**2 - 6*v**3 = 0.
-3, -1, -1/3
Let f(q) be the first derivative of 0*q + 1/120*q**5 + 0*q**3 - 1/16*q**4 - 12 - 16*q**2. Let u(r) be the second derivative of f(r). Factor u(o).
o*(o - 3)/2
Let l be (2/3 + 0)/((-68)/(-1836)). Factor 25*t + l - 10*t + 16*t**2 + 12*t**2 - 31*t**2.
-3*(t - 6)*(t + 1)
Let 940*t**3 - 1282*t**3 + 390921*t**2 - 3849*t + 564*t**4 - 3*t**5 - 385959*t**2 - 2430*t**3 + 1098 = 0. What is t?
1, 2, 183
Let k be ((-12)/8)/((-40)/(-16)*1/(-5)). Solve 40/3*v - 25/3*v**2 - 16/3 + 1/3*v**5 - 5/3*v**k + 5/3*v**4 = 0 for v.
-4, 1
Factor 661*r**3 + 53*r**2 - 51*r - 5*r**2 - 658*r**3.
3*r*(r - 1)*(r + 17)
Let d(b) = b**2 - 13*b + 20. Let m be d(12). Suppose 0 = 11*c - m - 14. Factor 0 + 3/4*k**c - 3/4*k**3 + 0*k.
-3*k**2*(k - 1)/4
Let o be ((-1086)/(-180) - 6)/(1 - 0). Let v(s) be the second derivative of -5/36*s**4 - o*s**5 - 1/6*s**2 + 19*s + 0 - 2/9*s**3. Factor v(t).
-(t + 1)**2*(2*t + 1)/3
Let x = 424011/282670 + -3/141335. Factor -3/2*f**2 - 1/4*f + x + 1/4*f**3.
(f - 6)*(f - 1)*(f + 1)/4
Determine j so that -730*j**2 + 120*j**2 - 9804*j + 5*j**3 + 6649*j - 2540 = 0.
-4, -1, 127
Let a(c) = 7*c**3 - 334*c**2 + 938*c - 671. Let v(w) = 2*w**3 - 84*w**2 + 234*w - 168. Let u(y) = -4*a(y) + 15*v(y). Let u(d) = 0. What is d?
-41, 1, 2
Let b(t) be the first derivative of t**4 + 0*t + 0*t**2 - 51 + 2/5*t**5 + 8/9*t**3 + 1/18*t**6. Let b(o) = 0. Calculate o.
-2, 0
Let c(u) be the first derivative of u**5/5 + 29*u**4/2 - 4*u**3/3 - 116*u**2 + 655. Factor c(j).
j*(j - 2)*(j + 2)*(j + 58)
Factor -144/19 + 312/19*k + 10/19*k**3 + 116/19*k**2.
2*(k + 6)**2*(5*k - 2)/19
Suppose 19 = -5*q + 109. Let u = q - 16. Factor -9*k**u - 6*k**2 + 30*k**4 - 25*k**4 + 10*k**3.
5*k**2*(k - 1)*(k + 3)
Find k, given that 30/7*k**5 + 426/7*k**3 - 8 - 218/7*k**2 + 274/7*k**4 - 456/7*k = 0.
-7, -2, -1, -2/15, 1
Let f(l) be the first derivative of -2/3*l**3 + 6/5*l - 77 + 14/5*l**2. Solve f(o) = 0 for o.
-1/5, 3
Suppose 370 = -50*n + 235*n. Determine f so that -40/3*f - 2/3*f**n - 38/3 = 0.
-19, -1
Let d(u) = -4*u**2 + 16*u - 9. Let y be d(3). Let 961 - 6*c**y - 608*c + 5*c**3 - 13*c - 402*c + 63*c**2 = 0. What is c?
1, 31
Determine j so that 1/4*j**2 - 3/2*j - 10 = 0.
-4, 10
Let w(y) = -y**2 - 6*y + 5. Let k be w(4). Let o = -33 - k. Factor 6 - 2*c**3 - 3*c + c**3 + 4*c**3 - 6*c**o.
3*(c - 2)*(c - 1)*(c + 1)
Let w(q) be the first derivative of q**4/18 - 2320*q**3/27 + 336400*q**2/9 - 2054. Determine o, given that w(o) = 0.
0, 580
Let w(o) = -9*o + 47. Let d = 32 - 27. Let j be w(d). Determine x so that 17 + x**2 + j*x + 2 - 7 + 6*x = 0.
-6, -2
Let g be (-244 + 241)/(36/(-45)). Factor 5 - 5/4*n**2 + g*n.
-5*(n - 4)*(n + 1)/4
Let j(o) = -o**3 + 2*o. Let v(a) = a**3 - 15*a**2 - 4*a + 46. Let t(d) = -2*j(d) - v(d). Let m(k) be the first derivative of t(k). Factor m(y).
3*y*(y + 10)
Let n(m) = 2*m**4 - m**3 + m**2 + 11*m. Let r(w) = -15*w**4 + 35*w**3 + 235*w**2 + 717*w + 588. Let i(a) = -8*n(a) - r(a). Determine y, given that i(y) = 0.
-12, -7, -1
Let w be (-91)/(-7)*(-2)/(-8) + 5215/(-4172). Suppose 16/3 + 10/3*a**3 - 8/3*a - 20/3*a**w + 4/3*a**4 - 2/3*a**5 = 0. Calculate a.
-2, -1, 1, 2
Suppose -139*x - 95*x + 702 = 0. Factor -56/3*h - 4*h**x + 92/3*h**2 + 0.
-4*h*(h - 7)*(3*h - 2)/3
Let v(i) be the third derivative of -i**8/420 + i**7/15 - 49*i**6/90 + 15*i**3 + 22*i**2. Let b(d) be the first derivative of v(d). Let b(t) = 0. What is t?
0, 7
Suppose -21*n + 16*n + 20 = 0. Let -4*a**3 + 24*a**2 + 112*a - 14*a**4 - 15*a**n + 25*a**4 + 96 - 8*a**3 = 0. What is a?
-2, 3
Let -68*k**4 - 536/5*k**3 + 0*k + 0 + 352/5*k**2 + 8/5*k**5 = 0. Calculate k.
-2, 0, 1/2, 44
Suppose 3 = -h, -5*b + 24*h - 27*h = -46. Let x(m) be the second derivative of 0 - 7/6*m**4 - 2/3*m**3 - 1/2*m**5 - b*m + 0*m**2. Find g, given that x(g) = 0.
-1, -2/5, 0
Let d(r) = 4*r**3 - 1735*r**2 - 331804*r - 21233636. Let f(b) = -5*b**3 + 1736*b**2 + 331808*b + 21233632. Let k(s) = 8*d(s) + 7*f(s). Factor k(q).
-3*(q + 192)**3
Let k(v) = 81*v**2 + 44*v + 60. Let q(s) = 162*s**2 + 86*s + 106. Let d(r) = -7*k(r) + 4*q(r). Find b such that d(b) = 0.
-2/9
Let y(j) be the first derivative of 5*j**4/4 + 790*j**3/3 + 1565*j**2/2 + 780*j + 3307. Factor y(d).
5*(d + 1)**2*(d + 156)
Suppose l - 77 = 4*v - 47, -2*l + v + 11 = 0. Solve -49/5 + 14/5*w - 1/5*w**l = 0 for w.
7
Let c(f) = 3*f**2 + 81*f - 171. Let r be c(-29). Let v(z) be the third derivative of 0*z**r + 0 - 1/75*z**5 + 1/30*z**4 + 0*z - z**2. Factor v(q).
-4*q*(q - 1)/5
Let c(a) be the first derivative of 1/28*a**4 - 136 + 43/7*a + 41/21*a**3 - 85/14*a**2. Suppose c(o) = 0. Calculate o.
-43, 1
Let h = -298 + 958. Factor -h*c**3 + 1 - 1 + 658*c**3 + 8*c**2.
-2*c**2*(c - 4)
Let 