Let x(a) be the first derivative of 97 + a**3 - 15/2*a**2 - 18*a. Factor x(i).
3*(i - 6)*(i + 1)
Let t = -92815 + 92815. Factor 5/6*u**2 + u + t - 1/6*u**3.
-u*(u - 6)*(u + 1)/6
Let d(i) = i**3 + 7*i**2 + 4*i + 31. Let z be d(-7). Find o, given that 3*o**2 - 24*o + 4*o**2 - 44*o**3 - z*o**4 + 5*o**2 + 50*o**3 = 0.
-2, 0, 2
Factor -1/7*q**3 + 0*q + 1/7*q**2 + 0.
-q**2*(q - 1)/7
Let m(i) be the first derivative of i**6/1080 - 7*i**5/90 + 49*i**4/18 - 20*i**3/3 - 59. Let g(v) be the third derivative of m(v). Factor g(n).
(n - 14)**2/3
Let z(x) be the first derivative of -5*x**4 + 535*x**3/3 + 695*x**2/2 + 140*x + 3247. Factor z(j).
-5*(j - 28)*(j + 1)*(4*j + 1)
Let o(u) = -21*u**4 + 92*u**3 - 71*u**2 + 6*u - 6. Let t(b) = b**4 - 3*b**3 + 3*b**2 - 1. Let w(v) = -5*o(v) + 30*t(v). Suppose w(d) = 0. Calculate d.
0, 2/27, 1, 3
Determine o so that -2444/5*o + 2/5*o**2 + 746642/5 = 0.
611
Factor 41/2*h**2 + 4 - 83*h.
(h - 4)*(41*h - 2)/2
Let 1/11*b**3 + 6084/11*b + 0 + 156/11*b**2 = 0. Calculate b.
-78, 0
Let s be (230/(-10) + 19)/(1/125). Let c = 500 + s. Suppose 15/2*g**3 + 0 + c*g + 15/2*g**4 + 5/2*g**5 + 5/2*g**2 = 0. Calculate g.
-1, 0
Let w be 1*(-10)/((-280)/6). Let q = w - -19/42. Find j, given that -1/3 - 1/3*j**2 + q*j = 0.
1
Let b(c) be the third derivative of -c**6/24 - 7*c**5/12 - 5*c**4/4 + c**2 + 2*c - 521. Factor b(f).
-5*f*(f + 1)*(f + 6)
Factor -t**3 - 6*t**2 - 27/4 - 45/4*t.
-(t + 3)*(2*t + 3)**2/4
Let i(j) = j + 43. Let k be i(-39). Find n, given that 9*n**3 - 8*n**2 + 10 - 10 + k*n - 5*n**3 = 0.
0, 1
Let t be (-2610)/(-14) + 2 + (-4)/(-7). Let r be t/294 + (-3)/6. Factor -2/7*x**2 + 0 + 1/7*x**3 + r*x.
x*(x - 1)**2/7
Let w(p) be the first derivative of p**5 - 65*p**4/4 - 145*p**3 - 315*p**2/2 + 810*p + 2448. Factor w(t).
5*(t - 18)*(t - 1)*(t + 3)**2
Let m(j) = 13*j**2 - 21*j + 12. Let o be m(1). Let a(k) be the first derivative of -4/7*k**3 + 14 + 0*k**o - 8/7*k**2 + 2/35*k**5 - 6/7*k. Factor a(p).
2*(p - 3)*(p + 1)**3/7
Let f be ((-1772)/10)/(4/(-5)). Let o = 222 - f. Solve o*a**5 - 1/2*a**3 - a**4 + 0 + 0*a + a**2 = 0.
-1, 0, 1, 2
Suppose -19/4*m - 5/4*m**3 + 0 + 24*m**2 = 0. Calculate m.
0, 1/5, 19
Factor -1852*y + 1108296*y**2 - 1107376*y**2 + 928 + 7*y**3 - y**3 - 2*y**3.
4*(y - 1)**2*(y + 232)
Let p = 410 - 339. Determine i so that -4*i**3 + 33*i + 26*i - 36*i**2 - 208 + 87*i - 25*i + p*i = 0.
-13, 2
Let a(g) be the second derivative of -g**7/378 + 14*g**6/45 - 41*g**5/90 - 7*g**4/9 + 83*g**3/54 - 2995*g. Let a(x) = 0. Calculate x.
-1, 0, 1, 83
Let q(z) be the third derivative of -z**7/42 - z**6/8 + z**5/3 + 853*z**2. Factor q(y).
-5*y**2*(y - 1)*(y + 4)
Suppose -859*g + 1665*g - 2418 = 0. Let 0 + 38/7*v**4 - 8/7*v**2 - 16/7*v**g + 0*v - 2*v**5 = 0. Calculate v.
-2/7, 0, 1, 2
Let t(u) be the second derivative of u**5/15 + 191*u**4/54 - 100*u**3/27 - 97*u**2/9 + 42*u + 9. Solve t(c) = 0.
-97/3, -1/2, 1
Suppose 4*m - 2*r = 22, -6*r = -5*m - 9*r. Solve 4*i**2 + m*i - 105 + 0*i - 3*i**2 + 93 - 2*i = 0.
-4, 3
Let i(u) = -5*u**2 - 27*u + 8. Let z(y) = -2*y**2 - 9*y + 3. Let t(l) = 3*i(l) - 8*z(l). Solve t(q) = 0 for q.
0, 9
Let k(n) be the first derivative of n**4/18 + 140*n**3/27 - 608*n**2/9 + 832*n/3 - 9484. Factor k(i).
2*(i - 4)**2*(i + 78)/9
Suppose -6*m + 0 - 19/7*m**2 + 1/7*m**3 = 0. Calculate m.
-2, 0, 21
Let q be (-51)/(-4284)*-21 + 2/8. What is m in 32/3*m + 2/9*m**2 + q = 0?
-48, 0
What is z in 4/5*z**5 + 8/5 + 4*z**4 + 5*z**3 - 2*z**2 - 4*z = 0?
-2, 1/2
Let j(t) be the first derivative of -4*t**3/3 - 8*t**2 + 384*t - 1309. Suppose j(v) = 0. What is v?
-12, 8
Let t(s) = s**3 - 17*s**2 + 15*s + 5. Let n be t(13). Let d be (-17)/(n/(-48)) - -2. Let -4/7*l - 2/7 - d*l**2 = 0. What is l?
-1
Let t(l) be the second derivative of -3*l**7/112 + l**6/8 - 37*l**5/160 + 5*l**4/24 - l**3/12 + 19*l - 24. Solve t(v) = 0.
0, 2/3, 1
Suppose 0 = -107*u + 115*u - 3168. Let x be 4*-1 + (-12 - u/(-24)). Find l such that -1/2 + l**2 - x*l**4 + 1/2*l - l**3 + 1/2*l**5 = 0.
-1, 1
Let d be (954/371)/(6/1876 - 0). Let p = d + -800. Solve 0 + 0*y - 4/11*y**2 + 14/11*y**3 - 10/11*y**p = 0 for y.
0, 2/5, 1
Let c(o) = -780*o**2 + 20*o + 1150. Let a(v) = 71*v**2 - 2*v - 105. Let b(y) = -65*a(y) - 6*c(y). Let b(h) = 0. Calculate h.
-15/13, 1
Solve f**2 + 14*f - 55 + 13 - 30 = 0.
-18, 4
Suppose 4*u - 3420 = -4*h, 0 = -76*h + 71*h + 2*u + 4240. Let w = h - 2545/3. Factor w*y + 2 + 1/3*y**2.
(y + 2)*(y + 3)/3
Suppose -14/3*b**4 + 0 - 46/9*b**2 + 0*b + 2/9*b**5 - 10*b**3 = 0. Calculate b.
-1, 0, 23
Factor 61*i**2 + 224/11*i + 0 + 669/11*i**3 + 221/11*i**4 - 1/11*i**5.
-i*(i - 224)*(i + 1)**3/11
Suppose -4*h + 9*h = 220. Let s = h - 33. Factor 9*n + 0 - s*n + 2*n**2 - 2*n**3 + 4*n - 2.
-2*(n - 1)**2*(n + 1)
Factor -14 - 21*v**2 - 1/5*v**4 + 157/5*v + 19/5*v**3.
-(v - 10)*(v - 7)*(v - 1)**2/5
Let w(h) be the first derivative of -h**6/10 - 117*h**5/25 - 81*h**4/5 + 4*h**3/5 + 216*h**2/5 + 1993. Find y, given that w(y) = 0.
-36, -2, 0, 1
Suppose 464/3*l**4 - 10346/3*l**2 - 7280*l - 178/3*l**3 - 4056 - 32/3*l**5 = 0. What is l?
-2, -1, 39/4
Factor 2/7*g**2 + 223112/7 - 1336/7*g.
2*(g - 334)**2/7
Let g(y) = 104 - 3*y**2 - 29*y**2 + 76*y - 497*y**3 + 493*y**3 - 6. Let f(z) = 3*z**3 + 31*z**2 - 75*z - 98. Let m(x) = 6*f(x) + 5*g(x). What is k in m(k) = 0?
-1, 7
Let n be 18*(-6)/(-12) + -12. Let s be ((90/432)/(n/12))/(-1). Factor 0 + s*i**2 - 1/3*i.
i*(5*i - 2)/6
Let h(s) = s**3 + 20*s**2 + 97*s + 78. Let r be h(-13). Determine w, given that -4*w**3 + r + 4*w - 32/3*w**2 = 0.
-3, 0, 1/3
Let d = -243 - -871. Let n = -624 + d. What is y in -7/2*y**3 + 15*y**2 + n - 18*y = 0?
2/7, 2
Let i be 56/12 - (0 - -1*(-8 + 1)). Let y(w) be the second derivative of i*w**3 + 5/12*w**4 + 245/2*w**2 + 0 - 31*w. Determine l, given that y(l) = 0.
-7
Let u(n) be the first derivative of -n**4 - 56*n**3/3 - 114*n**2 - 288*n + 2529. Find i, given that u(i) = 0.
-8, -3
Let k(p) be the second derivative of -p**7/17640 - 5*p**6/1008 - p**5/35 - 67*p**4/12 - 35*p + 1. Let o(c) be the third derivative of k(c). Factor o(x).
-(x + 1)*(x + 24)/7
Let t(s) be the third derivative of 9*s**8/224 - 21*s**7/20 - 107*s**6/80 + 83*s**5/40 + 17*s**4/8 - 2268*s**2. Solve t(d) = 0 for d.
-1, -1/3, 0, 2/3, 17
Let c = 1502/4797 - 2/369. Let m(k) = 2*k**2 + 16*k - 16. Let z be m(-9). Factor 2/13*s**z - 16/13 - c*s.
2*(s - 4)*(s + 2)/13
Let m(r) be the second derivative of r**4/3 + 40*r**3/3 + 128*r**2 + 9479*r. Factor m(f).
4*(f + 4)*(f + 16)
Let t(c) = -9*c - 63. Let d be -8*2*9/18. Let o be t(d). Factor 34*i + i - 130*i**2 - 35*i**3 - 4*i + o*i.
-5*i*(i + 4)*(7*i - 2)
Let a = -10 + 4. Let o(m) = m**2 + 3*m - 14. Let s be o(a). Factor 3*q**4 - 5*q**s - 3*q**4 + 5*q**2.
-5*q**2*(q - 1)*(q + 1)
Let r = -476 + 477. Let d(v) = -6*v**2 + 4*v - 5. Let c(b) = b**3 - 6*b**2 + 6*b. Let p be c(5). Let k(z) = -z + 1. Let w(h) = p*k(h) + r*d(h). Factor w(i).
-i*(6*i + 1)
Let b(z) be the first derivative of -z**6/6 - 284*z**5/5 - 841*z**4/4 + 574*z**3/3 + 1690*z**2 + 2248*z + 11200. Solve b(d) = 0 for d.
-281, -2, -1, 2
Determine h so that -148*h + 419*h**2 + 1368 - 1258*h**2 + 423*h**2 + 420*h**2 = 0.
18, 19
Let s(w) be the second derivative of w**7/84 + 13*w**6/60 - 7*w**5/20 - 18*w + 6. Factor s(b).
b**3*(b - 1)*(b + 14)/2
Factor 114 - 234*w + 15/2*w**3 - 261/2*w**2.
3*(w - 19)*(w + 2)*(5*w - 2)/2
Determine w so that 114/11*w**3 + 540/11*w**2 + 984/11*w + 6/11*w**4 + 624/11 = 0.
-13, -2
Let z = -983906 + 983908. What is a in -14/5*a**z + 32/5 - 18/5*a**4 + 2/5*a**5 - 48/5*a + 46/5*a**3 = 0?
-1, 1, 4
Let b(w) = -385*w**2 + 810*w + 1245. Let p(f) = -43*f**2 + 90*f + 141. Let o(s) = 4*b(s) - 35*p(s). Factor o(l).
-5*(l - 3)*(7*l + 3)
Let j(h) be the second derivative of -h**4/4 + 215*h**3 - 138675*h**2/2 + 8*h + 84. Factor j(y).
-3*(y - 215)**2
Suppose -65*i + 112 = 2*k - 66*i, 0 = 3*k - i - 166. Solve -3/2*m**3 - 18*m**2 - k*m - 48 = 0 for m.
-8, -2
Let l = 4/129 + 357/43. Let r(a) be the second derivative of l*a**2 + 1/18*a**4 + 0 - 8*a - 10/9*a**3. Factor r(s).
2*(s - 5)**2/3
Factor 8/5 - 7/5*f**3 - 38/5*f + 37/5*f**2.
-(f - 4)*(f - 1)*(7*f - 2)/5
Let t(o) = 47*o**2 + 36*o**2 + 18*o**3 - 59*o - 27*o**2 + 11*o**2. Let x(l) = 4*l**3 + 17*l**2 - 15*l. Let h(b) = 6*t(b) - 26*x(b). What is a in h(a) = 0?
0, 1, 9
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