 2)**2
Let j = -328 + 324. Let h be -3 + 201/27 + j. Find l, given that 4/9*l**4 - h*l**2 - 2/9*l**3 + 0 + 2/9*l = 0.
-1, 0, 1/2, 1
Let w(u) be the second derivative of -11/18*u**3 - 1/90*u**6 + 1/12*u**4 + 1/20*u**5 - 60 + 2*u + u**2. Suppose w(p) = 0. Calculate p.
-2, 1, 3
Let i(a) be the second derivative of a**6/420 - a**4/84 + 21*a**2 + 38*a. Let n(f) be the first derivative of i(f). Solve n(o) = 0.
-1, 0, 1
Let k be ((228/8)/19)/((-5)/(-10)). Let o(u) be the third derivative of 17*u**2 + 0*u - 1/150*u**5 + 2/3*u**k + 0 - 3/20*u**4. Solve o(l) = 0 for l.
-10, 1
Let x(w) be the third derivative of 2*w**7/105 - 103*w**6/15 + 3536*w**5/5 + 103*w**4/3 - 21218*w**3/3 + 1089*w**2 - 3. Factor x(f).
4*(f - 103)**2*(f - 1)*(f + 1)
Let z(a) be the third derivative of 1/3*a**5 + 0*a**3 + 7 + 2*a**2 + 25/24*a**4 + 0*a - 1/24*a**6. Factor z(f).
-5*f*(f - 5)*(f + 1)
Let w = -409 + 1651/4. Let x = 7163/2 - 3579. Factor 5/4*r**2 - x*r - w.
5*(r - 3)*(r + 1)/4
Let p = -101181 - -101183. Factor 0 + 1/3*b**3 + 0*b + b**p.
b**2*(b + 3)/3
Suppose -54*q + 6 = -51*q. Suppose 4 = -5*x + 3*c - q, -x + 6 = 3*c. Find d, given that 2*d**5 - 10*d**2 + 0*d + x*d - 5*d + 3*d**5 + 10*d**4 = 0.
-1, 0, 1
Let k = 452 + -865. Let m = 415 + k. Factor 0 + 2/9*q**3 - 8/9*q - 2/3*q**m.
2*q*(q - 4)*(q + 1)/9
Let t = -42/2449 - -29598/12245. Factor 3/5*g**2 + 12/5*g + t.
3*(g + 2)**2/5
Let f = -1265 + 196. Let r = f - -5357/5. Factor 0 - r*p**4 - 12/5*p**3 - 4/5*p**2 - 4/5*p**5 + 0*p.
-4*p**2*(p + 1)**3/5
Let u = 744777 - 272588117/366. Let m = u + -7/122. Determine t so that 2/3*t**2 + 0*t - m = 0.
-1, 1
Let p(z) be the third derivative of -z**8/840 - z**7/420 - 71*z**3/6 + 43*z**2. Let u(x) be the first derivative of p(x). Factor u(y).
-2*y**3*(y + 1)
Factor 4 + 23 + 18 - 692*u + 27*u**2 + 284*u.
3*(u - 15)*(9*u - 1)
Let m(k) be the first derivative of -4*k**5/5 + 51*k**4 - 988*k**3 + 722*k**2 + 164616*k - 9447. Factor m(l).
-4*(l - 19)**3*(l + 6)
Find t, given that -57*t**2 + 11769*t**3 - 15*t**4 - 18*t - 11894*t**3 - 88*t**2 - 17*t = 0.
-7, -1, -1/3, 0
Suppose 0 = 77*g + 126*g - 431*g - 501*g + 8748. Solve -1/3*j**2 - g*j + 37/3 = 0.
-37, 1
Let q(w) = -84*w**3 + 28233*w**2 + 12560*w + 1399. Let v(f) = 83*f**3 - 28233*f**2 - 12560*f - 1398. Let c(l) = -2*q(l) - 3*v(l). Find o such that c(o) = 0.
-2/9, 349
Let 1/3*y**3 + 0*y + 0 - 265/3*y**2 = 0. Calculate y.
0, 265
Let t(u) = u**4 - u**3 + u - 1. Let h(o) = 7*o**4 - 19*o**3 + 45*o**2 + 31*o - 256. Let d = 10 - 16. Let m(j) = d*t(j) + h(j). Solve m(q) = 0 for q.
-2, 5
Let y(h) be the first derivative of -4*h**3/15 + 376*h**2 + 5325. Factor y(f).
-4*f*(f - 940)/5
Let z be 13 + 21042/(-910) + 11 - 9/117. Factor 1/5*v**3 + 3/5*v**2 + 0*v - z.
(v - 1)*(v + 2)**2/5
Let c be ((-665)/42)/19*-2. Let b be (-6)/36 - 73/(-6) - 8. Determine o, given that 20/3*o + 0 + 10*o**3 - 15*o**2 - c*o**b = 0.
0, 1, 4
Let o(f) = 87*f**3 + 1236*f**2 + 493*f - 701. Let k(t) = -48*t**3 - 618*t**2 - 246*t + 351. Let v(w) = -5*k(w) - 3*o(w). Factor v(n).
-3*(n + 1)*(n + 29)*(7*n - 4)
Let q(y) be the second derivative of -y**2 - 1 - 55*y - 1/9*y**3 - 1/90*y**5 + 5/54*y**4. Factor q(h).
-2*(h - 3)**2*(h + 1)/9
Let p(i) = -15191*i + 60824. Let j be p(4). Suppose -5/4*a**2 - j - 35/2*a = 0. What is a?
-8, -6
Let k be ((-50)/225)/((-10)/90) - ((-7)/6 + 2). Solve -k*m + 1/6*m**3 - 5/3 + 2/3*m**2 = 0.
-5, -1, 2
Let f(h) = -h**3 + 5*h**2 - 4*h - 1. Let d be f(3). Suppose 36*j - 33*j + 4*t = 22, j - t = 12. Factor -2*w**2 - 3 + d - j*w - 14.
-2*(w + 2)*(w + 3)
Let s(z) be the second derivative of -1/6*z**4 + 1/70*z**5 + 0*z**3 - 5*z + 1 + 0*z**2. Factor s(d).
2*d**2*(d - 7)/7
Factor -2004*j**3 - 2021*j**3 + 4193*j**3 + 2*j**4.
2*j**3*(j + 84)
Suppose 0*f**3 + 3*f**3 + 35565*f**2 - 35139*f**2 - f + f = 0. Calculate f.
-142, 0
Let h(l) be the second derivative of -l**4/20 + 453*l**3/10 - 1353*l**2/5 + 60*l + 16. Factor h(p).
-3*(p - 451)*(p - 2)/5
Let j(o) be the second derivative of 2*o**7/21 - 14*o**6/5 + 57*o**5/5 - 55*o**4/3 + 12*o**3 + 2*o + 812. Factor j(n).
4*n*(n - 18)*(n - 1)**3
Let z be 6 + 944292/(-102096) - -4. Let y = z - 2/2127. Find b, given that 3/4*b**3 + y*b**2 - 3/4*b + 0 - 3/4*b**4 = 0.
-1, 0, 1
Let p(a) be the second derivative of -2*a**4 - 1111*a**3/2 + 417*a**2/2 - 2*a + 12. Determine w so that p(w) = 0.
-139, 1/8
Let h(b) be the third derivative of -b**8/3360 + 7*b**6/720 - b**5/40 + 23*b**3/6 + 125*b**2. Let c(l) be the first derivative of h(l). Factor c(g).
-g*(g - 2)*(g - 1)*(g + 3)/2
Let y(r) = -2499*r**4 + 1485*r**3 - 60*r**2 - 60*r - 6. Let d(n) = -4999*n**4 + 2969*n**3 - 119*n**2 - 122*n - 14. Let c(v) = 3*d(v) - 7*y(v). Factor c(w).
3*w*(8*w - 3)**2*(13*w + 2)
Let k = 29871/275 - 2261/25. Let -3018/11*o**2 - k + 1480/11*o - 98/11*o**4 + 1036/11*o**3 = 0. What is o?
2/7, 5
Factor 6*h - 20/3 - 8/5*h**2 + 2/15*h**3.
2*(h - 5)**2*(h - 2)/15
Suppose 55331 - 110667 + 400*p + 2244*p**2 + 55352 = 0. Calculate p.
-2/17, -2/33
Let m be (-12)/(-48) - (-3)/((-24)/(-22)). Factor 3*k**4 + 0*k**2 - 2*k**3 + 15*k + 4*k**m - 9*k**2 - 5*k**3 - 6.
3*(k - 1)**3*(k + 2)
Let c(l) = 9*l**2 - 3616*l + 655236. Let h(j) = -8*j**2 + 3617*j - 655232. Let t(r) = -3*c(r) - 4*h(r). Factor t(u).
5*(u - 362)**2
Let j(a) be the first derivative of -a**5/15 + 2*a**4/3 + 8*a**3 - 71*a**2/2 - 97. Let p(c) be the second derivative of j(c). Suppose p(r) = 0. What is r?
-2, 6
Let j(g) be the third derivative of -g**6/24 - 65*g**5/4 - 15345*g**4/8 + 49005*g**3/2 - 4*g**2 + 94. Factor j(v).
-5*(v - 3)*(v + 99)**2
Let x(w) be the first derivative of 5*w**3/9 + 3025*w**2/6 + 2010*w - 402. Let x(m) = 0. What is m?
-603, -2
Let y(a) be the first derivative of -a**4 + 11*a**3 - 4*a**2 - 5565. Find f such that y(f) = 0.
0, 1/4, 8
Let q(k) = 3*k**3 + 13*k**2 - 7*k + 7. Let r(l) = l**3 + 9*l**2 - 3*l + 3. Let p(a) = -6*q(a) + 14*r(a). Factor p(t).
-4*t**2*(t - 12)
Let k be 3859/153 + 2/(-9). Suppose -v + 163 = 5*d, -4*v + k = -0*d + d. Factor -4*f**3 + 3*f**3 + 75 + d*f**2 + 0*f**3 + 4*f**3 + 105*f.
3*(f + 1)*(f + 5)**2
Solve -481*o + 19*o**2 - 2*o**2 + 75 + 19*o**2 + 686*o + 24*o**2 = 0 for o.
-3, -5/12
Let c = 313/182 - -1529/910. Determine s, given that 81/5 + 63/5*s + 1/5*s**3 - c*s**2 = 0.
-1, 9
Factor -13/4*v - 1/4*v**2 + 57/2.
-(v - 6)*(v + 19)/4
Let o be 32/24*45/(-6). Let w be 54/(-90) - 78*2/o. Solve w*h + 49 + 4*h + 14*h**3 - 26*h**2 - h**4 - h**5 - 54 = 0.
-5, 1
Let m(d) be the first derivative of 1/78*d**4 + 1/39*d**3 - 4*d - 2/13*d**2 - 6. Let v(z) be the first derivative of m(z). Let v(h) = 0. What is h?
-2, 1
Let n(r) be the first derivative of -r**3/12 + 73*r**2/4 + 147*r/4 - 84. Factor n(g).
-(g - 147)*(g + 1)/4
Let v(a) be the first derivative of -a**6/3 + 7*a**5/4 + 35*a**4/6 + 25*a**3/6 + 137*a - 187. Let b(p) be the first derivative of v(p). Factor b(w).
-5*w*(w - 5)*(w + 1)*(2*w + 1)
Factor -38/7*f**3 + 2/7*f - 36/7*f**2 + 0.
-2*f*(f + 1)*(19*f - 1)/7
Let j be 4/(-50) + (-7896)/(-10575). Let g(o) be the third derivative of 0*o - 2*o**2 - j*o**3 + 0 - 5/36*o**4 - 1/90*o**5. Determine s, given that g(s) = 0.
-3, -2
Let c(i) = i**3 + 12*i**2 - 52*i + 26. Let x be c(3). Let s be (-1 - -3)*(-6)/(-3). Factor -567*r + s*r**x - 8*r**2 + 567*r - 12*r**3 + 0*r**2.
4*r**2*(r - 2)*(r + 1)**2
Let b = 2951/45 + -10049/180. Let 1/2*a**3 - 10*a + 1/4*a**4 - b*a**2 + 100 = 0. Calculate a.
-5, 4
Let u be (101/(-4))/(7 + 385/(-56)). Let d be 2*4 + -1 + u/606. Let -2/3*g**5 - d*g**2 - 10/3*g**4 - 20/3*g**3 - 10/3*g - 2/3 = 0. Calculate g.
-1
Let k(h) = 8*h**4 - 491*h**3 + 1353*h**2 - 1328*h + 458. Let f(b) = -2*b**4 + 122*b**3 - 338*b**2 + 332*b - 114. Let o(t) = -18*f(t) - 4*k(t). Solve o(z) = 0.
1, 55
Let x(c) = -44*c**2 + 1543*c - 309. Let i(o) = -13*o**2 - o. Let s(q) = 6*i(q) - 2*x(q). Factor s(h).
2*(h - 309)*(5*h - 1)
Suppose 11 + 625*n**2 + 10 - 422*n - 11 - 18*n - 205*n**3 + 10 = 0. Calculate n.
2/41, 1, 2
Let p(z) = 2*z**4 + 3*z**3 + 42*z**2 + 38*z + 12. Let q(h) = 7*h**3 + 958 + 3*h**4 + 57*h - 940 - h**3 + 63*h**2. Let j(r) = -7*p(r) + 5*q(r). Factor j(o).
(o + 1)**3*(o + 6)
Suppose 4*z + 96 = 9*d, 132*d = 130*d - 3*z - 37. Find g, given that 6/5*g**5 - 68/3*g**3 + 144/5*g**2 + 28/15 - 206/15*g + 68/15*g**d = 0.
-7, 2/9, 1
Let m(w) be the first derivative of 1/1800