et h(c) be the second derivative of c**5/5 - c**4 - 24*c**3 - 64*c**2 - 503*c. Factor h(s).
4*(s - 8)*(s + 1)*(s + 4)
Let d(w) = 15*w**3 - 250*w**2 + 110*w + 130. Let c(y) = -8*y**3 + 125*y**2 - 55*y - 64. Let s(k) = 5*c(k) + 2*d(k). Suppose s(f) = 0. Calculate f.
-1/2, 1, 12
Let h = 2600571/11 - 237110. Let t = h + 695. Factor -t*d**2 + 2/11*d**3 + 0 + 4/11*d.
2*d*(d - 2)*(d - 1)/11
Let t(h) = -2*h**3 - 32*h**2 - 5*h + 13. Let f(k) = k**3 + 15*k**2 + 2*k - 6. Let j(l) = -13*f(l) - 6*t(l). Find u such that j(u) = 0.
-4, 0, 1
Let f(p) be the first derivative of -2 + 1/36*p**4 - p**2 + 0*p**3 + 1/30*p**5 + 0*p. Let u(a) be the second derivative of f(a). Solve u(h) = 0.
-1/3, 0
Let j(a) be the third derivative of 0*a**3 + 0 + 0*a**4 - 1/2520*a**8 - 1/225*a**5 + 2/1575*a**7 + 2*a**2 + 0*a + 1/900*a**6. Let j(b) = 0. What is b?
-1, 0, 1, 2
Let n = 327 + -325. Let p(l) be the first derivative of -1/3*l - 1 + 5/6*l**4 - 7/18*l**3 - 11/12*l**n. Let p(v) = 0. Calculate v.
-2/5, -1/4, 1
Let b(p) be the second derivative of -p**6/10 + 3*p**5/5 - 3*p**4/4 - 2*p**3 + 6*p**2 - 88*p. Factor b(x).
-3*(x - 2)**2*(x - 1)*(x + 1)
Let -108/7*s**2 + 36/7 + 6/7*s + 48/7*s**3 = 0. Calculate s.
-1/2, 3/4, 2
Let s = 16 - 14. Factor -9*j**3 - 48*j**s - 3*j**4 + 12*j + 48*j**2.
-3*j*(j - 1)*(j + 2)**2
Let o(u) be the third derivative of -u**6/24 + u**5/6 + 5*u**4/24 - 5*u**3/3 + 48*u**2. Solve o(p) = 0.
-1, 1, 2
Let o = 10 + -6. Suppose -6 = o*t - 6*t. Factor 6*g**t - 9 - 3*g**3 + 9 - 3*g.
3*g*(g - 1)*(g + 1)
Let u = 9 - 5. Solve -u*q**3 - 3*q**4 + 4*q + 0*q + 17*q**4 - 2*q**4 - 12*q**2 = 0.
-1, 0, 1/3, 1
Let z be ((-28)/(-12) - 3) + 380/(-3). Let l = -122 - z. Determine u, given that 1/3*u**2 - 8/3*u + l = 0.
4
Let p be (336/63)/((-22)/(-6)). Let i = p - 58/55. Factor -2/5*w - 4/5*w**2 + 0 - i*w**3.
-2*w*(w + 1)**2/5
Suppose 4*y = -2*h + y - 15, -3 = 3*y. Let p = h + 12. Factor 3*u**2 + 4 - 2*u**5 + 22*u**3 - 14*u**3 - p*u - 7*u**2.
-2*(u - 1)**3*(u + 1)*(u + 2)
Let t(u) be the third derivative of u**8/5040 - u**7/630 - u**5/15 + 8*u**2. Let x(w) be the third derivative of t(w). Factor x(h).
4*h*(h - 2)
Let n = -1448 + 53579/37. Let i = 90/259 + n. Factor 0 + 3/7*g**4 - 3/7*g**2 + 3/7*g**3 - i*g.
3*g*(g - 1)*(g + 1)**2/7
Let h(p) = 3*p**3 - p**2 - 6*p + 6. Let l(c) = -25*c**3 + 7*c**2 + 48*c - 47. Let o(t) = -51*h(t) - 6*l(t). Solve o(k) = 0.
-2, 1, 4
Let p(o) be the second derivative of 11/60*o**4 - 5*o + 7/30*o**3 + 1/20*o**5 + 1/10*o**2 + 0. Factor p(z).
(z + 1)**2*(5*z + 1)/5
Let x(y) = 64*y**5 - 180*y**4 + 204*y**3 - 76*y**2 - 12*y + 16. Let m(k) = -k**5 - k**3 + k**2 - 1. Let h(r) = 8*m(r) + x(r). Let h(t) = 0. What is t?
-2/7, 1/2, 1
Let r be (-4 + 3/2)*6. Let i(j) = 2*j + 30. Let s be i(r). Factor 1/5*z + s*z**2 + 1/5*z**5 + 0*z**4 + 0 - 2/5*z**3.
z*(z - 1)**2*(z + 1)**2/5
Let t be (-1)/2 - 35/10. Let n be 8/(-6)*6/t. Factor -4*o**2 - 2 - 5*o - 6*o**2 - 5*o**3 + n.
-5*o*(o + 1)**2
Determine s so that 140/9*s + 2/9*s**2 + 2450/9 = 0.
-35
Factor 1/3*r**3 - 31/3*r**2 + 0 + 0*r.
r**2*(r - 31)/3
Let m(n) = 8*n**3 - 2*n**2 - 5*n + 5. Let s(z) = 4*z**3 + z**2 + 3*z**3 - 6*z**3. Let a(t) = -m(t) + 3*s(t). Let a(w) = 0. What is w?
-1, 1
Let v(k) = -k - 5. Let d(f) = 2. Let z(y) = 5*d(y) + 2*v(y). Let s be z(-1). Factor -6*t**s - 10*t**3 - 3*t**5 + 3*t**2 - 9*t**4 + t**3.
-3*t**2*(t + 1)**3
Let l(c) = 20*c**3 - 4*c + 8. Let v(p) = -2*p**3 - p. Let f(n) = l(n) + 8*v(n). Find s, given that f(s) = 0.
-2, 1
Let q(a) be the second derivative of a**4/96 - 49*a**3/6 + 2401*a**2 + 5*a - 8. Factor q(c).
(c - 196)**2/8
Let k = 1213 + -1207. Let y(f) be the first derivative of 1/6*f**k + 1/3*f**3 + 3/4*f**4 + 3/5*f**5 + 0*f**2 + 1 + 0*f. Factor y(z).
z**2*(z + 1)**3
Let w be (9/(-6) - -2) + 14/(-4). Let r be (w + -1)*(-12)/168. Find u such that -6/7*u**3 + 0*u + 0 + 6/7*u**4 - r*u**5 + 2/7*u**2 = 0.
0, 1
Let w(f) be the second derivative of -13*f + 1/150*f**5 + 0*f**4 + 0 + 2/15*f**2 - 1/15*f**3. Find d, given that w(d) = 0.
-2, 1
Let t(q) = -q**3 + q. Let v(p) be the third derivative of -3*p**6/40 - p**5/5 - 3*p**4/8 - p**3 - 4*p**2. Let o(z) = -6*t(z) + v(z). Find a such that o(a) = 0.
-2, -1
Factor 15*l**2 - 23*l**2 + 11*l**2 - 173*l + 47*l + 1323.
3*(l - 21)**2
Let h(t) = -t**5 + t**4 + t. Let b(m) = 16*m**4 + 32*m**3 + 16*m**2 - 30*m - 32. Let j(x) = -2*b(x) + 4*h(x). Factor j(w).
-4*(w - 1)*(w + 2)**4
Factor -468512/15 + 85184/15*b - 2/15*b**4 - 1936/5*b**2 + 176/15*b**3.
-2*(b - 22)**4/15
Let t be (9/10 + -1)*(-530)/212. Factor t*b**2 - 1/4 - 1/8*b + 1/8*b**3.
(b - 1)*(b + 1)*(b + 2)/8
Suppose 0 = 8913*k - 9021*k. Factor -1/4*a**2 + 1/2*a + k.
-a*(a - 2)/4
Let d(v) = -36*v**3 - 220*v**2 - 144*v + 400. Let y(b) = 7*b**3 + 44*b**2 + 29*b - 80. Let f(w) = 3*d(w) + 16*y(w). Solve f(x) = 0 for x.
-10, -2, 1
Let c be 8/(-18)*(6 + (-8 - 4)). Let j(v) be the second derivative of 0 - 5/6*v**4 - 4*v + 1/10*v**5 - 4*v**2 + c*v**3. Determine i, given that j(i) = 0.
1, 2
Find c, given that -6*c**2 + 188 + 18*c**2 + 8*c - 188 = 0.
-2/3, 0
Let r = 761/42 + -107/6. Let u(h) be the first derivative of 2/21*h**3 + 0*h - r*h**2 + 12. Factor u(j).
2*j*(j - 2)/7
Suppose 0 = -l - 4, x - 13 = 3*l + 2. Let -61*r**2 - 5 + 72*r - 12*r**4 + 2 - 50*r**2 - 9 + 63*r**x = 0. What is r?
1/4, 1, 2
Suppose -5*k + 9 = 4*t, 0 = -283*k + 282*k - t + 1. Let 0 - 2*x**3 + 1/3*x**4 + 1/2*x**k - 4/3*x**2 + 0*x = 0. Calculate x.
-2, -2/3, 0, 2
Let q(j) be the second derivative of -j**5/20 + 7*j**4/72 + j**3/9 - 9*j**2/2 + 4*j. Let r(m) be the first derivative of q(m). Factor r(i).
-(i - 1)*(9*i + 2)/3
Let t = 788/43 - 7837/430. Factor -t*o**2 + 16/5*o - 128/5.
-(o - 16)**2/10
Let j(z) = z**3 - 35*z**2 + 125*z - 31. Let r be j(31). Factor -3*w + r + 9/2*w**2 - 3/2*w**3.
-3*w*(w - 2)*(w - 1)/2
Let u(t) be the first derivative of 3*t**5/5 - 9*t**4/4 + 13*t**3/4 - 9*t**2/4 + 3*t/4 + 71. Let u(c) = 0. What is c?
1/2, 1
Let a(w) be the second derivative of -1/40*w**6 - 19*w + 0 - 1/2*w**3 - 3/2*w**2 + 3/16*w**4 + 3/40*w**5. Solve a(j) = 0 for j.
-1, 2
Let l(k) = -k + 4. Let r be l(-10). Suppose 3*c + 2*w = r, -w = -0*c - 2*c + 7. Find f such that f**c - 2*f**4 - f**3 + 0*f**4 = 0.
-1, 0
Let x(t) be the third derivative of t**5/12 - 25*t**4/24 + 10*t**3/3 - 43*t**2 - t. Factor x(b).
5*(b - 4)*(b - 1)
Let k = 3326 - 3322. Let h = 523/6 - 87. Factor 0*g**2 - h*g**k + 0 + 0*g - 1/6*g**3.
-g**3*(g + 1)/6
Let y(g) be the first derivative of -g**3/9 - g**2/6 + 2*g - 63. Find q, given that y(q) = 0.
-3, 2
Let o be (549/(-48))/(7/(-28)). Let k = -45 + o. Solve -3/4*h - k*h**2 + 3/2 = 0.
-2, 1
Let o(k) be the second derivative of k**7/1890 - 43*k**4/12 + 5*k. Let h(b) be the third derivative of o(b). Suppose h(p) = 0. Calculate p.
0
Factor 356*c**2 - 189*c**2 - 223*c**2 + 4*c**3.
4*c**2*(c - 14)
Let j(q) be the second derivative of -q**5/180 - 11*q**4/108 - 4*q**3/9 + 130*q. Determine t, given that j(t) = 0.
-8, -3, 0
Let p be -2*(-6)/(-12)*(-2 + 14). Let g be (16/p)/(5 - 8). Factor g*h - 2/9*h**2 - 2/9.
-2*(h - 1)**2/9
Suppose 2/15*o**2 - 92/15*o + 1058/15 = 0. What is o?
23
Let a(c) = -37*c + 2. Let i be a(-1). Suppose 0 = 3*k + 3 - i. Factor -k*z**2 + 3*z**2 + 2*z**2 + 5*z**2 + 2.
-2*(z - 1)*(z + 1)
Let p(j) be the third derivative of -j**5/420 - 3*j**4/56 + 221*j**2. Suppose p(z) = 0. Calculate z.
-9, 0
Let x = 95 + -93. What is g in -1 + 7 - 466*g + 4*g**x + 10 + 450*g = 0?
2
Suppose 0 = -5*z - 2*l + 24, -4*z + l = -l - 12. Let v be (-3)/(20/((-16)/z)). What is o in -1/5*o**2 + 2/5*o + v = 0?
-1, 3
Let r(k) be the second derivative of -6*k - 1/6*k**3 - 1/60*k**5 + 5/2*k**2 + 0 - 1/12*k**4. Let n(v) be the first derivative of r(v). What is x in n(x) = 0?
-1
Factor -3/2*m**3 + 0 - 48*m - 18*m**2.
-3*m*(m + 4)*(m + 8)/2
Let n(y) be the second derivative of -1/96*y**4 + y**2 + 0 - 1/12*y**3 + 1/240*y**5 + 2*y. Let f(c) be the first derivative of n(c). Let f(t) = 0. Calculate t.
-1, 2
Let j(a) = 64*a + 6019. Let w be j(-94). Suppose -c + 1/4*c**4 - c**2 + 1/4*c**w + 0 = 0. What is c?
-2, -1, 0, 2
Let s(n) be the second derivative of 11*n**7/84 - 4*n**6/15 - 3*n**5/10 + 2*n - 3. Factor s(o).
o**3*(o - 2)*(11*o + 6)/2
Let v(p) be the second derivative of -p**5/12 - 11*p**4/36 + 13*p**3/18 + p**2/2 - p + 66. What is q in v(q) = 0?