073/3 - -215401/15. Factor n*h**2 + 0 - 3/5*h - 9/5*h**3.
-3*h*(h - 1)*(3*h - 1)/5
Let c(z) be the second derivative of 729*z**5/70 + 279*z**4/7 + 64*z**3/3 + 32*z**2/7 + 111*z + 1. Factor c(g).
2*(g + 2)*(27*g + 4)**2/7
Factor 328683/5 - 1986/5*l + 3/5*l**2.
3*(l - 331)**2/5
Factor -265*v - 14045 - 5/4*v**2.
-5*(v + 106)**2/4
Let r be -2*((-1)/2)/((-2)/(-4)). Suppose -2*n + 2 = -r. Determine k so that 4*k**4 - 6*k**4 + 10*k**n + 48*k - 12*k**2 - 32 - 12*k**3 = 0.
-4, 1
Let s(v) be the second derivative of v**4/42 - 2*v**3/7 + 5*v**2/7 - 5*v - 51. Determine u, given that s(u) = 0.
1, 5
Let l(j) be the third derivative of 119*j**6/600 - 79*j**5/25 + 78*j**4/5 + 32*j**3/15 - 2*j**2 + 2062*j. Factor l(v).
(v - 4)**2*(119*v + 4)/5
Let h(n) be the second derivative of 6*n**2 + 58*n + 1/10*n**5 - 2/3*n**4 + 0 + 1/3*n**3. Factor h(g).
2*(g - 3)*(g - 2)*(g + 1)
Let q = -543326 - -543328. Factor 0*l - 2/13 + 2/13*l**q.
2*(l - 1)*(l + 1)/13
Let v(p) be the second derivative of 106*p + 0 - 3/2*p**2 + 1/6*p**3 + 1/4*p**4 - 1/20*p**5. Suppose v(h) = 0. Calculate h.
-1, 1, 3
Let c(m) be the first derivative of 15*m**3 + 6*m + 99/2*m**2 - 12*m**4 - 102. Factor c(f).
-3*(f - 2)*(f + 1)*(16*f + 1)
Let q = 868961/3 - 289651. Suppose 0 + 1/3*v**5 - 5*v**3 + 0*v - q*v**2 - 2*v**4 = 0. Calculate v.
-1, 0, 8
Let a be (-226)/(-113) - (-1118)/(-4)*-16. Factor a*v + 3*v**4 + 7*v**3 + 6*v**2 + 2*v**3 - 4474*v.
3*v**2*(v + 1)*(v + 2)
Let b(c) be the second derivative of -9*c**2 - 1/4*c**4 - 63*c + 0 - 7/2*c**3. Factor b(r).
-3*(r + 1)*(r + 6)
Let r(s) = 172*s**2 - 1504*s - 1501. Let j(d) = 275*d**2 - 2256*d - 2251. Let n(x) = 5*j(x) - 8*r(x). What is g in n(g) = 0?
-1, 753
Let i = 71404/7 - 10168. Factor i*c - 60/7 - 57/7*c**2 - 3*c**3.
-3*(c - 2)*(c + 5)*(7*c - 2)/7
Let c(o) = -27*o**3 + 3*o**2 + 2*o. Let u be c(-1). Factor -u*s**2 + 311 - 2*s**3 - 54*s**2 + 571 - 798*s.
-2*(s - 1)*(s + 21)**2
Let t(m) be the first derivative of -20*m**2 + 64*m - 29 + 4/3*m**3. Factor t(j).
4*(j - 8)*(j - 2)
Let t = 64 + 924. Let y = t - 4916/5. Factor 48/5 + y*z + 3/5*z**2.
3*(z + 4)**2/5
Let j(d) be the second derivative of -7/20*d**5 + 1/4*d**4 + 0*d**3 + 1/15*d**6 + 0*d**2 + 4*d + 2. Factor j(i).
i**2*(i - 3)*(2*i - 1)
Let p be 161/23 - (-1104)/(-192). Suppose p*x**4 + 2*x - 1/4*x**2 - 1 - 7/4*x**3 - 1/4*x**5 = 0. Calculate x.
-1, 1, 2
Factor -266/3*p - 2/3*p**2 - 344.
-2*(p + 4)*(p + 129)/3
Let m(y) be the first derivative of 1/51*y**6 - 244 + 10/51*y**3 + 14/85*y**5 + 11/34*y**4 + 0*y**2 + 0*y. Factor m(j).
2*j**2*(j + 1)**2*(j + 5)/17
Let p = 457 - 410. Suppose p = -49*c + 194. Suppose -2/5*t**5 + 0 + 0*t - 8/5*t**2 + 2/5*t**4 + 8/5*t**c = 0. Calculate t.
-2, 0, 1, 2
Let z(m) be the first derivative of -4*m - 8 - 26*m**2 - 2 - m**3 + 8 + 22*m**2. Find p such that z(p) = 0.
-2, -2/3
Suppose -h = 5*l + 5, 11*l - 6*l + 16*l + 21 = 0. Find w such that 2/9*w**5 + h*w - 2/9*w**3 + 0 + 10/9*w**4 - 10/9*w**2 = 0.
-5, -1, 0, 1
Let q(c) = 3*c**3 - 2*c**2 - c + 15. Let v be q(0). Suppose -4*k + 15 = -5*r, 4*k + 6 = 3*r + v. Factor -2/7*t**4 + k + 2/7*t**2 + 2/7*t**3 - 2/7*t.
-2*t*(t - 1)**2*(t + 1)/7
Let p = 2124 - 6362/3. Factor -5*a**2 - 19/3*a + p.
-(3*a + 5)*(5*a - 2)/3
Factor 15*r**2 + 12*r**2 - 5*r**2 + 216*r - 440 - 20*r**2.
2*(r - 2)*(r + 110)
Let w(p) be the third derivative of p**7/168 - 53*p**6/72 + 13*p**5/6 + 13*p**3 + 79*p**2. Let d(o) be the first derivative of w(o). Factor d(l).
5*l*(l - 52)*(l - 1)
Let l = 499/36 - -1283/36. Factor 1/2*u**3 - 21/2*u**2 + l*u + 121/2.
(u - 11)**2*(u + 1)/2
Let q(h) be the first derivative of -h**4/54 - h**3/27 + 4*h**2/3 - 3*h + 21. Let k(o) be the first derivative of q(o). Factor k(g).
-2*(g - 3)*(g + 4)/9
Solve 6883*c**2 + 2964*c - 6089*c**2 - 6686*c**2 - 9 = 0 for c.
3/982, 1/2
Let h(j) be the third derivative of -j**7/455 - 5*j**6/156 - 7*j**5/65 + j**4/39 + 8*j**3/13 + 5*j**2 - 139*j. Let h(q) = 0. What is q?
-6, -2, -1, 2/3
Let a(t) = 0*t**2 - 8*t + 10*t + t**2 - t. Let j(h) = -2*h**2 - 50*h - 48. Let o(m) = 6*a(m) + j(m). Solve o(u) = 0.
-1, 12
Let t(b) be the third derivative of b**5/20 - 7*b**4/8 - 15*b**3 + 9582*b**2. Determine k, given that t(k) = 0.
-3, 10
Let l(i) = -28*i + 5. Let o be l(-1). Let -o*r + 35 - 3*r**2 + 34 - 30 + 39 = 0. Calculate r.
-13, 2
Let 2/7*y**3 - 18/7*y + 0 + 0*y**2 = 0. Calculate y.
-3, 0, 3
Let t(q) = q**2. Let d(p) be the third derivative of -p**5/4 - 129*p**4/8 - 16*p**3 + 63*p**2 + p. Let h(f) = d(f) + 3*t(f). Suppose h(z) = 0. What is z?
-32, -1/4
Let j = 6073 - 6020. Let p be ((-54)/(-8))/(1/4). Solve p*y**2 + 729 - 139*y + j*y - y**3 - 157*y = 0 for y.
9
Let t(j) be the first derivative of j**4/4 - j**3 + j**2 + 109. Let d be t(2). Determine q, given that d - 24/5*q + 28/5*q**2 + 12/5*q**3 = 0.
-3, 0, 2/3
Let m(s) be the second derivative of -s**5/20 + 73*s**4/3 + 587*s**3/6 + 147*s**2 + 5*s - 9. Determine a, given that m(a) = 0.
-1, 294
Factor -3/4*f**2 - 15/2*f - 6 + 3/4*f**3.
3*(f - 4)*(f + 1)*(f + 2)/4
Let x(n) = -n**3 - 15*n**2 - 24*n + 30. Let z be x(-13). Let 3*o**2 + z*o - 16 + 4*o**3 + 5*o**2 - 16 + 32 = 0. What is o?
-1, 0
Solve -1/7*b**5 - 363/7 + 365/7*b**4 + 727/7*b - 726/7*b**3 - 2/7*b**2 = 0 for b.
-1, 1, 363
Let h(v) be the third derivative of -2*v**7/315 + v**5/15 - v**4/9 - 1074*v**2. Let h(n) = 0. What is n?
-2, 0, 1
Let h(k) be the second derivative of 0*k**3 + 0*k**2 - 1/40*k**5 + 11/12*k**4 - 17*k + 0. Factor h(c).
-c**2*(c - 22)/2
Let q(b) = -60*b**4 - 36*b**3 + 38*b**2 - 14. Let v(j) = -20*j**4 - 12*j**3 + 13*j**2 - 5. Suppose 5*k = 18*k + 65. Let c(f) = k*q(f) + 14*v(f). Factor c(h).
4*h**2*(h + 1)*(5*h - 2)
Let l(n) be the first derivative of 1/9*n**3 + 131 - 4*n**2 + 0*n. Factor l(t).
t*(t - 24)/3
Let j(m) be the second derivative of 2*m**2 - 1/8*m**4 + 1/40*m**5 + 0 - 1/2*m**3 + 327*m. What is s in j(s) = 0?
-2, 1, 4
Let g(a) be the third derivative of -1/420*a**5 + 65*a**2 + 0 - 5/21*a**3 + 1/24*a**4 + 0*a. Suppose g(d) = 0. What is d?
2, 5
Let n be 8/6 - 24/(-36). Suppose f - 4 = n*z - 0, 4*f - 16 = -3*z. Let -1/2*k**5 + 5/2*k**f + 7/2*k**2 - 9/2*k**3 - k + 0 = 0. Calculate k.
0, 1, 2
Let g = 187 + -182. Find c such that c**g - 40 - 10*c**4 - 68*c**2 + 38*c**3 + 22 + 0*c**5 + 57*c = 0.
1, 2, 3
Let i(m) = -1958*m - 281947. Let t be i(-144). Find w, given that 1/5*w**4 - 6/5*w**3 + 2/5*w**2 - 3/5 + w + 1/5*w**t = 0.
-3, -1, 1
Factor 8/5 - 398/5*f**2 - 326/15*f.
-2*(3*f + 1)*(199*f - 12)/15
Let g = 96554 + -1062092/11. Factor -2/11*c**5 + 0*c + 0*c**2 + g*c**4 + 0 + 4/11*c**3.
-2*c**3*(c - 2)*(c + 1)/11
Solve -1790*i - 4*i**2 - 555815 - 245210 + 3*i**2 = 0.
-895
Let u(r) be the first derivative of -r**6/15 - r**5/15 - r**2 + 2*r + 75. Let c(m) be the second derivative of u(m). Let c(n) = 0. Calculate n.
-1/2, 0
Determine a so that 1584 - 409281*a + 204128*a + 204369*a - 4*a**2 = 0.
-198, 2
Let m(o) be the first derivative of o**3/3 - 8*o**2 + 15*o + 1183. Factor m(g).
(g - 15)*(g - 1)
Let t = -9124/14619 + 8/443. Let q = -3/11 - t. Factor 1/3*y**2 - 2/3*y + q.
(y - 1)**2/3
Let o(d) be the first derivative of d**6/10 + 37*d**5/60 + 49*d**4/36 + 23*d**3/18 + d**2/3 - 6*d - 56. Let q(m) be the first derivative of o(m). Factor q(g).
(g + 1)**2*(g + 2)*(9*g + 1)/3
Let p(f) be the first derivative of 0*f + 22/7*f**2 + 9/7*f**4 + 4*f**3 - 4/35*f**5 - 40. Factor p(s).
-4*s*(s - 11)*(s + 1)**2/7
Let b = 5029 + -5026. Let z(s) be the first derivative of 8*s + 3*s**2 + 16 - 2/3*s**b. What is w in z(w) = 0?
-1, 4
Let l = 284 - 277. Let r be l/(-21) + 3/18*2. Factor -1/5*k**5 - 2/5*k**4 + r + 0*k**2 - 1/5*k**3 + 0*k.
-k**3*(k + 1)**2/5
Let h(s) be the first derivative of s**5/150 + 6*s**4/5 + 432*s**3/5 - 11*s**2/2 - 5*s - 233. Let u(g) be the second derivative of h(g). Factor u(o).
2*(o + 36)**2/5
Let c(h) be the second derivative of h**7/23940 - h**6/6840 - h**4/2 + 3*h**2/2 + 4*h + 4. Let w(s) be the third derivative of c(s). Factor w(g).
2*g*(g - 1)/19
Let v(z) = -z**2 - 55*z - 694. Let j(s) = -s**3 + 7*s**2 + 2*s + 28. Let y be j(8). Let q be v(y). Factor 27 + q*g + 1/3*g**2.
(g + 9)**2/3
Let j(f) = -11*f**3 + 93*f**2 - 306*f + 7. Let q(s) = -3*s**3 + 31*s**2 - 102*s + 2. Let k(c) = 6*j(c) - 21*q(c). Determine i, given that k(i) = 0.
-34, 0, 3
Suppose 0 = -5*q + 4*k + 37, -