n that p(q) = 0.
18
Let r(y) be the second derivative of -2 + 11/24*y**4 + 0*y**2 - y**3 + 20*y + 1/40*y**5. Factor r(a).
a*(a - 1)*(a + 12)/2
Factor 43680*l + 48*l**4 + 2321 + 744*l**3 - 30*l**4 - 12330*l**2 - 8266*l**2 - 25*l**4 - 13137.
-(l - 52)**2*(l - 2)*(7*l - 2)
Let v(g) be the first derivative of -13 - 150*g - 5/3*g**3 + 55/2*g**2. Factor v(l).
-5*(l - 6)*(l - 5)
Let r(f) be the second derivative of 5/42*f**7 - 63*f + 0*f**5 + 5/3*f**4 + 0 + 0*f**2 - 1/2*f**6 + 0*f**3. Factor r(a).
5*a**2*(a - 2)**2*(a + 1)
Let g(z) = z**2 - 21*z + 102. Let c be g(7). Let v be c/10 - (65/(-25) - 2). Find l such that -11/4*l**3 + 7/4*l**4 + 9/4*l**v + 1/2*l + 0 - 7/4*l**2 = 0.
-1, 0, 2/9, 1
Determine f, given that 39*f**2 - 28*f + 4 - 7*f**4 - 76 - 2*f**3 + 4*f**4 + 8*f**3 - 14*f = 0.
-3, -1, 2, 4
Let b(a) be the first derivative of 0*a**3 + 2/75*a**6 - 2/15*a**4 - 1/25*a**5 + 0*a**2 + 15 - 13*a. Let q(r) be the first derivative of b(r). Factor q(s).
4*s**2*(s - 2)*(s + 1)/5
Suppose -3*q + 3*v + 6 = 0, -11*q = -6*q - 4*v - 10. Suppose -36*b**3 + 36*b + 1696*b**4 - 324 + 323*b**q - 3399*b**4 + 1704*b**4 = 0. Calculate b.
-1, 1, 18
Factor 10/3*z**2 + 0 - 4*z - 2/3*z**3.
-2*z*(z - 3)*(z - 2)/3
Let u(z) be the first derivative of 2*z**5/15 + 16*z**4/3 + 52*z**3 - 1352*z**2/3 - 30758*z/3 - 3515. Determine r so that u(r) = 0.
-13, 7
Let w(k) be the first derivative of 9/2*k**4 + 0*k - 11*k**3 + 27 + 9*k**2 - 3/5*k**5. Factor w(z).
-3*z*(z - 3)*(z - 2)*(z - 1)
Let r(y) = -33*y - 9. Let f be r(-2). Let p = f + -52. Suppose -48*c**3 - 2*c**5 - p*c**4 + 10*c**4 - c**5 + 36*c**2 + 16*c**4 = 0. Calculate c.
0, 2, 3
Suppose -29*f = -28*f - 1. Let h(m) = -m**4 - m**3 + m + 1. Let t(q) = -7*q**4 + 7*q**3 + 5*q + 5. Let d(n) = f*t(n) - 5*h(n). Solve d(k) = 0 for k.
0, 6
Let o(w) = 10*w**2 + 130*w + 5. Let z(t) = -2*t**2 + t - 5. Let x be z(0). Let b(p) = 5*p**2 + 64*p + 3. Let q(n) = x*b(n) + 3*o(n). Factor q(j).
5*j*(j + 14)
Suppose 36*v = 47*v + 166*v + 69*v. Factor v - 1/3*j**2 - 8/3*j.
-j*(j + 8)/3
Suppose 5*p - 49 = -3*t, -71 = -4*t - 7*p - 7. Let d(o) be the third derivative of -1/24*o**6 - t*o**2 + 0 + 0*o**4 + 1/4*o**5 + 0*o + 0*o**3. Factor d(f).
-5*f**2*(f - 3)
Let y(n) be the second derivative of 0 + 1/3*n**3 + 1/60*n**5 + 0*n**2 - 5/36*n**4 + 54*n. Suppose y(q) = 0. Calculate q.
0, 2, 3
Let q(b) = 3*b**3 - 24*b**2 + 51*b - 28. Let c(k) = 20*k**3 - 165*k**2 + 355*k - 195. Let f(o) = 2*c(o) - 15*q(o). Factor f(j).
-5*(j - 3)*(j - 2)*(j - 1)
Let w be 15/60 + 35/4. Suppose -17*z = -24*z + 14. Factor -96*x**2 - w*x - 99*x**2 + 193*x**z + 12 - x.
-2*(x - 1)*(x + 6)
Let v be 1*12/(-48) - (-18)/8. Factor 6*d - d**v + 11*d + 5*d - 17*d + 2*d**2.
d*(d + 5)
Let t(d) be the second derivative of d**5/4 + 40*d**4/3 - 170*d**3/3 - 1032*d. Factor t(l).
5*l*(l - 2)*(l + 34)
Let f(c) be the third derivative of 5*c**8/84 - 97*c**7/42 + 107*c**6/3 - 820*c**5/3 + 3040*c**4/3 - 2560*c**3/3 + 580*c**2. Determine h, given that f(h) = 0.
1/4, 4, 8
Let s = -739/13260 + 16/221. Let i(o) be the second derivative of -3*o - s*o**5 - 1/90*o**6 + 1/18*o**4 + 0*o**3 + 0*o**2 + 0. Factor i(a).
-a**2*(a - 1)*(a + 2)/3
Let f(x) be the first derivative of x**4/2 + 2*x**3 + 3*x**2 + 2*x + 10835. Factor f(p).
2*(p + 1)**3
Suppose h = 2*g - 5, -4*h + 6 = 2. Factor 1629*r**4 - 18*r**g - 10 - 1609*r**4 - 2*r**3 - 5*r**5 - 10*r**2 + 25*r.
-5*(r - 2)*(r - 1)**3*(r + 1)
Let r(z) be the second derivative of z**5/20 - 4*z**4 - 34*z**3 + 11560*z**2 - 16*z + 6. Factor r(p).
(p - 34)**2*(p + 20)
Suppose -270*s**2 + 1983*s - 3954 - 265*s**2 - 265*s**2 + 797*s**2 = 0. Calculate s.
2, 659
Let f = 52945/42 + -17583/14. Solve -6*u**2 - 2/3*u**4 + 20/3 - f*u**3 + 14/3*u = 0.
-5, -2, -1, 1
Suppose 3*f = n + 2, -71*n = -76*n - 5*f + 50. Let r be (-9)/n + 369/123. Suppose -9/7 - r*a - 3/7*a**2 = 0. Calculate a.
-3, -1
Find r such that r**2 - 4*r**3 - 29*r**2 + 7*r**4 + 461*r**5 - 460*r**5 = 0.
-7, -2, 0, 2
Let p(b) be the second derivative of b**6/135 - b**5/5 - 4*b**4/9 + 98*b**3/27 - 19*b**2/3 + 813*b - 2. Determine i so that p(i) = 0.
-3, 1, 19
Let a(y) = y**5 + 2*y**4 + 7*y**3 - 6*y**2 - 2*y. Suppose 5*k = -o - 15 - 2, 5*o + 25 = -5*k. Let n(f) = f**5 + f**4 - f. Let j(b) = o*n(b) + a(b). Factor j(d).
-d**2*(d - 2)*(d - 1)*(d + 3)
Let n(k) = 10*k**3 + 273*k**2 + 642*k + 263. Let i(r) = -18*r**3 - 545*r**2 - 1288*r - 525. Let g(q) = -6*i(q) - 10*n(q). Suppose g(b) = 0. Calculate b.
-65, -2, -1/2
Let r(v) be the first derivative of 5/2*v**2 - 36 - 5/12*v**3 - 15/4*v. Determine p so that r(p) = 0.
1, 3
Solve 25*q**2 + 0 + 1/6*q**3 + 0*q = 0 for q.
-150, 0
Suppose -19 + 199 = 6*m. Let u be 9*(-12)/(-630)*m - 5. Factor 0 + 1/7*v**2 + u*v**3 - 1/7*v - 1/7*v**4.
-v*(v - 1)**2*(v + 1)/7
Let j(t) = -6*t**3 - 58*t**2 - 230*t - 284. Let o(n) = n**3 + n**2 + n - 2. Suppose 65*i - 74*i + 18 = 0. Let k(y) = i*o(y) + j(y). Find u such that k(u) = 0.
-8, -3
Suppose 592/7 - 156/7*s + 2/7*s**2 = 0. Calculate s.
4, 74
Let f = 71561/39870 + 41/7974. Find a such that -6/5*a + 1/5*a**2 + f = 0.
3
Let t(v) be the second derivative of v**5/4 - 35*v**4/12 - 5*v**3/6 + 35*v**2/2 - 1915*v. Factor t(g).
5*(g - 7)*(g - 1)*(g + 1)
Let l(t) = -t**3 - 70*t**2 - 57*t + 444. Let j(y) = 2*y**3 + 139*y**2 + 112*y - 887. Let x(v) = 6*j(v) + 13*l(v). Factor x(o).
-(o - 2)*(o + 3)*(o + 75)
Suppose -1 = 4*w - 2*r - 7, 0 = 4*r - 12. Let z(d) = 18*d**2 + 6*d + 9. Let p(m) = -35*m**2 - 11*m - 15. Let k(j) = w*p(j) + 5*z(j). Factor k(c).
-3*c*(5*c + 1)
Let u(q) = 6*q**2 - 20*q + 12. Let g be u(4). Let a be ((21/g - 3) + 2)/(-1). Factor a*y + 1/4*y**2 - 1/2.
(y - 1)*(y + 2)/4
Let x(o) be the first derivative of 5*o**4/28 - 989*o**3/21 + 787*o**2/14 + 197*o/7 - 3806. Determine g so that x(g) = 0.
-1/5, 1, 197
Let l(q) be the second derivative of -3*q**7/14 + 11*q**6/10 + 103*q**5/10 - 137*q**4/2 + 475*q**3/6 - 75*q**2/2 - 4270*q. Determine c so that l(c) = 0.
-5, 1/3, 3, 5
Let k = 205190 - 205188. Solve -15/4*d - 5/4*d**3 - 15/4*d**k - 5/4 = 0 for d.
-1
Let k be (1 - 9) + -6 + 11. Let n(f) = 2*f**2 + 7*f + 6. Let i be n(k). What is l in 8 - 126*l + 134*l + 19*l**3 - 86*l**2 + 9*l**i + 24*l**2 = 0?
-2/7, 1/2, 2
Factor -506*j**3 - 285*j + 64008*j**2 - 35803 + 791*j + 1010 - 29216 + j**4.
(j - 253)**2*(j - 1)*(j + 1)
Let f(s) = -25*s + 533. Let r be f(16). Let j be (10/(-7))/((-76)/r). Suppose -j*y + 0 + 17/4*y**2 - 2*y**3 + 1/4*y**4 = 0. Calculate y.
0, 1, 2, 5
Let l(g) be the second derivative of -g**5/180 - 31*g**4/36 - 46*g**3/27 + 12558*g. Factor l(a).
-a*(a + 1)*(a + 92)/9
Let s(a) be the first derivative of a**5/10 - 5*a**4/4 + 23*a**3/6 - 7*a**2/2 - 2174. Suppose s(u) = 0. Calculate u.
0, 1, 2, 7
Let i = 20099 + -20099. Suppose -5*v = -3*u + 6 - 1, 0 = 4*v - u - 3. Factor 8/5*n - 4/5*n**v + i.
-4*n*(n - 2)/5
Let b(l) = -27*l**3 + 102*l**2 - 262*l + 61. Let d(v) = v**3 - 7. Let i(o) = -2*b(o) - 38*d(o). Suppose i(h) = 0. What is h?
-1/4, 4, 9
Let u = 7/14071 + 78065859/98497. Let w = u + -792. Suppose -3/7*o - w + 1/7*o**2 = 0. Calculate o.
-1, 4
Let i(w) be the third derivative of 2/15*w**5 - 1/6*w**4 - w**3 + 1/30*w**6 - 5 - 1/105*w**7 + 0*w - 5*w**2. Factor i(a).
-2*(a - 3)*(a - 1)*(a + 1)**2
Factor -2/13*r**2 - 2580992/13 + 4544/13*r.
-2*(r - 1136)**2/13
Suppose 3*k = 4*z + 25, z + z = -8. Factor 48*f - 30*f**2 + 3*f**k + 29*f**2 - 50*f**2.
3*f*(f - 16)*(f - 1)
Let t(l) be the second derivative of -l**7/1680 + 17*l**6/480 - l**4/6 - 83*l**2 - 157*l. Let f(z) be the third derivative of t(z). Suppose f(i) = 0. What is i?
0, 17
Let q(d) be the first derivative of 1/8*d**2 + 0*d + 1/6*d**3 + 1/16*d**4 + 198. Let q(j) = 0. What is j?
-1, 0
Let x(j) be the second derivative of 0 - 2/3*j**3 + 1/60*j**5 + 7*j**2 + 1/8*j**4 + 9*j. Let m(v) be the first derivative of x(v). Factor m(u).
(u - 1)*(u + 4)
Suppose 8*s + 5*i = 6*s, 3*i = 0. Let a(h) be the first derivative of 1/30*h**6 + 0*h**3 - 3/25*h**5 + 2 + 0*h**2 + s*h + 1/10*h**4. Factor a(m).
m**3*(m - 2)*(m - 1)/5
Suppose 3*c - 23 = -4*q, -c = 4*q + 4*c - 33. Factor -8 + 8 + 3 + 6*k + 3*k**q.
3*(k + 1)**2
Let z(q) be the first derivative of q**6/144 + q**5/48 - 5*q**4/24 - 65*q**3/3 - 29. Let s(o) be the third derivative of z(o). What is y in s(y) = 0?
-2, 1
Let p = -2507/173 - 3/346. Let w = -83/6 