)
Let i(t) be the second derivative of t**9/2016 - t**8/280 + 3*t**7/560 - t**3/3 + 17*t**2/2 + 106*t. Let u(q) be the second derivative of i(q). Factor u(a).
3*a**3*(a - 3)*(a - 1)/2
Let s(z) be the third derivative of -z**6/900 + 7*z**5/450 + 3*z**4/5 + 4*z**3 + z**2 + z + 1. Suppose s(r) = 0. What is r?
-6, -2, 15
Let t = -32 + 36. Suppose -t*n = -7*n + 36. Factor -n*y**4 - 22*y**2 + 193*y + 2*y**2 - 189*y + 28*y**3.
-4*y*(y - 1)**2*(3*y - 1)
Let q be (-4)/(-66) + 5900/660 + ((-1736)/20)/14. Let 2/5*w**4 + 2*w + 22/5*w**2 + 0 + q*w**3 = 0. Calculate w.
-5, -1, 0
Let z(m) be the second derivative of -m**5/10 - 17*m**4/2 - 95*m**3/3 + 147*m**2 + 2*m - 2509. Let z(g) = 0. What is g?
-49, -3, 1
Let v = -679 + 1055. Let t = -376 + v. Find u, given that 0*u**2 + 1/5*u + t - 1/5*u**3 = 0.
-1, 0, 1
Let h(u) = 13*u**3 - 10*u**2 - 11*u. Let q(r) be the third derivative of -r**6/5 + r**5/3 + 23*r**4/24 - 3*r**2. Let c(t) = -7*h(t) - 4*q(t). Factor c(x).
5*x*(x - 3)*(x + 1)
Let f be 36/(-24)*(-3)/6*(-1)/(-3). Let t(a) be the first derivative of 22 + 1/20*a**5 - 1/2*a**2 + 1/2*a**3 - 1/4*a**4 + f*a. Factor t(y).
(y - 1)**4/4
Let l(p) be the first derivative of 2 - 1/11*p**2 + 0*p + 0*p**3 + 1/11*p**4 - 1/33*p**6 + 0*p**5. What is x in l(x) = 0?
-1, 0, 1
Determine l, given that 37156*l**3 - 18573*l**3 - 28*l**2 - 18555*l**3 - 72*l + 12*l**4 - 32 - 4*l**5 = 0.
-1, 2, 4
Suppose 565 = -15*b + 595. Let r(f) be the second derivative of 3/8*f**b + 1/12*f**3 - 5/48*f**4 - 25*f + 0. What is n in r(n) = 0?
-3/5, 1
Let s(t) = 2*t - 1. Let l(b) = -3*b**3 - 11*b**2 - 22*b + 11. Let j(n) = -l(n) - 7*s(n). Factor j(i).
(i + 2)**2*(3*i - 1)
Determine p, given that 10*p - 18729323 - 10*p**5 + 6*p**2 + 18729308 + 44*p**2 - 35*p**4 = 0.
-3, -1, 1/2, 1
Suppose -47*b + 49*b - 8 = 0. Let t be b*(-6)/(-84) + 555/140. Let -8*y - 1 - 73/4*y**2 + 49/4*y**5 + 77/4*y**4 - t*y**3 = 0. Calculate y.
-1, -2/7, 1
Let v(t) be the first derivative of 2*t**5/35 + 169*t**4/14 - 692*t**3/7 + 2092*t**2/7 - 400*t + 6716. Factor v(w).
2*(w - 2)**3*(w + 175)/7
Let w(g) be the first derivative of -g**5/10 - 5*g**4/6 - 7*g**3/3 - 3*g**2 - 91*g + 221. Let r(d) be the first derivative of w(d). Factor r(a).
-2*(a + 1)**2*(a + 3)
Let c(n) be the second derivative of 75*n - 6*n**2 + 0 - 1/24*n**4 + 5/6*n**3. Factor c(w).
-(w - 6)*(w - 4)/2
Suppose -4*o + o - 2*o = 0. Suppose 3*f + 3 - 12 = o. Factor 2*m**3 + 0*m**3 - 4*m**3 + f*m**3.
m**3
Suppose 119*g - 3 + 111 = 173*g. Let i(p) be the third derivative of 3*p**g + 1/24*p**4 + 1/300*p**5 + 0*p + 0 + 1/5*p**3. Let i(h) = 0. What is h?
-3, -2
Let l(y) be the second derivative of y**5/170 - 359*y**4/102 - 721*y**3/51 - 361*y**2/17 + 1440*y. Factor l(m).
2*(m - 361)*(m + 1)**2/17
Let x = 18671 - 18671. Let b(u) be the third derivative of 0*u - 10/27*u**3 + 4*u**2 + 1/12*u**4 + x + 1/270*u**5. Factor b(g).
2*(g - 1)*(g + 10)/9
Let -9*f + 25/3*f**3 + 9/2 + 0*f**2 - 9/2*f**4 + 2/3*f**5 = 0. Calculate f.
-1, 3/4, 1, 3
Let m(s) be the third derivative of s**7/42 + 3*s**6/8 - s**5/2 - 145*s**4/6 + 140*s**3 + 729*s**2. Factor m(o).
5*(o - 2)**2*(o + 6)*(o + 7)
Let c(l) be the first derivative of 14 + l**2 - 7/4*l - 1/12*l**3. Factor c(o).
-(o - 7)*(o - 1)/4
Let u be 0/(3*70/(-15) - (-3 - 10)). Factor -2*q**2 + 4/5*q + u.
-2*q*(5*q - 2)/5
Let v(m) be the second derivative of m**4/102 - 341*m**3/51 + 3*m - 69. Suppose v(p) = 0. Calculate p.
0, 341
Suppose s - 6 = 4*s. Let h be (-1)/s + (-27)/(-18). Factor 0*q**2 - 4*q**h - 12*q**2 - 4*q**2 - 8 - 28*q.
-4*(q + 1)*(5*q + 2)
Let l be 5/(-1 - -10 - 8) - (-8)/16. Factor 1/2*w**4 - l*w**2 + 2*w**3 + 0 + 3*w.
w*(w - 1)**2*(w + 6)/2
Let s(t) = 2*t**2 - 3*t - 20. Let r be 3/(-15)*1 + 210/50. Let k be s(r). Solve -1/5*x**2 + 0 + k*x = 0.
0
Let q(x) be the second derivative of -2*x**6/15 + 4*x**5 - 6*x**4 - 40*x**3/3 + 38*x**2 - 270*x. Let q(c) = 0. Calculate c.
-1, 1, 19
Let t(s) be the third derivative of -11*s**7/945 - 34*s**6/27 + 766*s**5/135 - 64*s**4/27 + 8662*s**2. Suppose t(q) = 0. Calculate q.
-64, 0, 2/11, 2
Let f(y) be the second derivative of y**8/84 + 4*y**7/15 + 13*y**6/30 + 55*y**2/2 + 3*y. Let m(n) be the first derivative of f(n). Determine l so that m(l) = 0.
-13, -1, 0
Let q(v) be the third derivative of -232/135*v**5 + 2585/36*v**4 - 242/3*v**3 + 7/540*v**6 + 23 + v**2 + 0*v. Factor q(d).
2*(d - 33)**2*(7*d - 2)/9
Let l(v) be the second derivative of v**6/50 + 51*v**5/100 + 27*v**4/20 - 9*v**3/2 + 333*v + 3. Find g such that l(g) = 0.
-15, -3, 0, 1
Let v = 10220 - 6068. Factor 13*q - 73*q - 4117*q**2 + v*q**2.
5*q*(7*q - 12)
Let v(b) be the second derivative of b**7/42 - 7*b**6/30 + 9*b**5/20 + 9*b**4/4 - 9*b**3 + 1252*b + 1. Factor v(a).
a*(a - 3)**3*(a + 2)
Suppose 57*o + 2585039 = 2585153. Factor -2/7*l**o - 38/7 - 40/7*l.
-2*(l + 1)*(l + 19)/7
Let o(r) = r**3 + 4*r**2 - 6*r - 3. Let y be o(-5). Factor 46*w**2 - 124*w + 449*w - 41*w**y.
5*w*(w + 65)
Let x(r) be the third derivative of r**6/72 - r**5/6 - 3*r**3 - 88*r**2. Let w(u) be the first derivative of x(u). Let w(k) = 0. What is k?
0, 4
Let t(g) = -13*g**2 - g + 1. Let h(c) = 112*c**2 - 1906*c + 1911. Let a(o) = h(o) + 9*t(o). Suppose a(b) = 0. What is b?
-384, 1
Factor 1707/4*x + 213*x**2 + 427/2 - 1/4*x**3.
-(x - 854)*(x + 1)**2/4
Factor -1142761/3 - 2138/3*l - 1/3*l**2.
-(l + 1069)**2/3
Determine g, given that 848/5*g + 2588/5*g**3 - 2472/5*g**2 - 672/5*g**4 - 196/5*g**5 - 96/5 = 0.
-6, 2/7, 1
Suppose 2*c + 5*m - 133 = 0, 221 = 6*c - 2*c + m. Suppose -5*q**4 + 6*q**4 - 96*q + 3*q**4 - q**4 - c*q**2 - 30 - 15 = 0. What is q?
-3, -1, 5
Suppose -h - 87*h**2 - 52*h**3 + 63*h + 2*h + 23*h**4 + 98*h**3 - 16 - 30*h**4 = 0. Calculate h.
4/7, 1, 4
Let w(o) = 3*o - 27. Let h be w(30). Factor -15*n**3 - 28*n**2 - 46*n**4 + h*n**3 + 26*n**4.
-4*n**2*(n - 1)*(5*n - 7)
Let j be 214/70 - 16/280. Suppose 4*f = -j*f + 14. What is o in 8/3*o - 4/3*o**4 + 4/3*o**f + 0 - 8/3*o**3 = 0?
-2, -1, 0, 1
Let u be (51*(-1)/(-5))/(3/15). Suppose -2 = -3*f - 11, -3*h = -4*f - u. Factor 0*g**2 + g**2 - h*g**2 + g - 4*g.
-3*g*(4*g + 1)
Factor 698/7*j + 860/7 - 2/7*j**3 - 164/7*j**2.
-2*(j - 5)*(j + 1)*(j + 86)/7
Let l(v) = v**4 - v**3 - 3*v**2. Let k(m) = -m**5 + 148*m**4 - 6221*m**3 + 90955*m**2 + 97336*m. Let p(h) = 4*k(h) - 44*l(h). Determine u so that p(u) = 0.
-1, 0, 46
Find j, given that 24*j**4 - 183 + 3868*j + 752*j**2 - 1842011*j**3 + 1837375*j**3 - 1361 = 0.
-1, 1/2, 2/3, 193
Factor 45*d - 197*d - 26 + 50079*d**2 - 50075*d**2 - 869 + 223.
4*(d - 42)*(d + 4)
Let s be 60/4 + 2 - (-6557)/(-395). Factor -4/5*z**3 - z**2 + 0 - 1/5*z**4 - s*z.
-z*(z + 1)**2*(z + 2)/5
Factor -4/7 - 6/7*n - 2/7*n**2.
-2*(n + 1)*(n + 2)/7
Factor -1182*g**4 + 76*g**3 + 1220*g - 492*g**2 + 541*g**4 + 637*g**4 - 800.
-4*(g - 8)*(g - 5)**2*(g - 1)
Let a(c) be the third derivative of -13*c**8/252 - c**7/63 + 7931*c**2. Suppose a(n) = 0. Calculate n.
-5/26, 0
Let q(o) = -o**4 - o**3 - 7*o**2 + 2*o. Let u(l) = 16*l**4 + 120*l**3 - 304*l**2 + 108*l + 32. Let b(y) = -4*q(y) + u(y). Solve b(z) = 0 for z.
-8, -1/5, 1
Suppose 3*g - 11 = -5*v, 3*g - g = 2*v - 14. Let i = 3132433 - 3132424. Solve 1/2*d**2 + 5/2*d**3 - i - 21/2*d + 1/2*d**v = 0.
-3, -1, 2
Let h(u) be the third derivative of -1/100*u**5 - 3 + 1/600*u**6 + 1/60*u**4 + 0*u + 0*u**3 - 25*u**2. Find l such that h(l) = 0.
0, 1, 2
Let s(n) = -31*n**2 + 200*n + 220. Let u(h) = -11*h**2 + 67*h + 74. Suppose -3*v + 21 = 9. Let b(z) = v*s(z) - 11*u(z). Factor b(g).
-3*(g - 22)*(g + 1)
Factor 20/7*u**2 - 9/7*u - 2 + 3/7*u**3.
(u - 1)*(u + 7)*(3*u + 2)/7
Let i(c) be the second derivative of 3*c**5/20 + 5*c**4/2 - 23*c**3/2 + 18*c**2 - 15*c. Find q such that i(q) = 0.
-12, 1
Suppose -24 = -4*k - 8. Suppose 20 = 4*v - k. Determine j, given that 2*j**3 - 19*j + 12*j**5 - 40*j**4 + 8 + 16*j**3 + 32*j**2 + v*j**3 - 17*j = 0.
-1, 1/3, 1, 2
Let i(q) be the first derivative of -33 + 10/21*q**3 - 4/7*q - 3/7*q**2. Suppose i(y) = 0. Calculate y.
-2/5, 1
Let p(z) be the third derivative of 0*z - 23/15*z**5 + 2/21*z**7 + 0*z**3 + 2/3*z**4 + 0 + 55*z**2 + 7/15*z**6. Suppose p(o) = 0. What is o?
-4, 0, 1/5, 1
Let n(v) be the second derivative of 8*v**3 - 14*v + 2 + 6*v**2 - 3/4*v**4 - 2/5*v**6 - 39/20*v**5. Solve n(h) = 0 for h.
-2, -1/4, 1
Let w(l) be the firs