et y be a(14). Suppose 2*w + 4*j = -20, -5*w - 8*j + y*j = 25. Factor 0 + 0*d**2 + 1/2*d**3 + w*d.
d**3/2
Let n(h) be the third derivative of -4/3*h**3 + 0*h + 4/105*h**7 - 8/15*h**5 - 200*h**2 - 1/84*h**8 + 1/15*h**6 + 7/6*h**4 + 0. Let n(d) = 0. Calculate d.
-2, 1
Let k(p) be the second derivative of 5*p**3 + 225/2*p**2 + 9*p + 1/12*p**4 - 7. Find j, given that k(j) = 0.
-15
Let c be (-2 - (9 + -2))*(-78 + (-13048)/(-168)). Determine p so that p + 0 + 4/3*p**2 + 1/3*p**c = 0.
-3, -1, 0
Suppose -3*b = 2*b - 4*o - 31, -2*o - 17 = -3*b. Let d = -483/2095 - -8217/8380. Find c, given that -9/4 + 9/2*c**b - d*c**4 + 15/2*c - 9*c**2 = 0.
1, 3
Let s(i) be the second derivative of i**6/40 + 57*i**5/4 + 8637*i**4/4 - 36860*i**3 + 225816*i**2 - 6671*i. Let s(o) = 0. What is o?
-194, 4
Let u = -764900 + 17592714/23. Factor u*z**4 + 0*z - 2/23*z**3 - 6/23*z**2 + 0 + 10/23*z**5.
2*z**2*(z + 1)**2*(5*z - 3)/23
Factor 2/3*d + 1 - 1/3*d**2.
-(d - 3)*(d + 1)/3
Let x be (-4 - 1) + (-126)/3528*-176. Factor -x*j**4 + 0*j**3 + 0 + 0*j + 3/7*j**5 + 12/7*j**2.
3*j**2*(j - 2)**2*(j + 1)/7
Let g be ((-48)/40)/((-15)/(-500)*2). Let h be 24/g*(-90)/27. Solve 2/3*c**h + 0 + 18*c**2 - 6*c**3 - 18*c = 0.
0, 3
Let k(o) = 2*o**3 + 25*o**2 - 43*o - 12. Let n be k(-14). Factor -t**4 - 4 - n*t**3 - t**4 + 6*t**2 - 16183*t + 16185*t.
-2*(t - 1)**2*(t + 1)*(t + 2)
Let g(x) be the first derivative of -x**6/15 - 16*x**5/25 + x**4/5 + 48*x**3/5 + 63*x**2/5 - 929. Solve g(f) = 0.
-7, -3, -1, 0, 3
Let o(j) be the second derivative of 1/6*j**3 + 0 + 26*j - 1/2*j**2. Let s(t) = 2*t**2 + 7*t + 7. Let z(d) = -o(d) - s(d). What is n in z(n) = 0?
-3, -1
Let o(y) = -2*y**3 + 65*y**2 + 227*y + 84. Let c(h) = -h**3 + 33*h**2 + 114*h + 36. Let w(t) = 7*c(t) - 3*o(t). Factor w(a).
-a*(a - 39)*(a + 3)
Let j(q) be the first derivative of -q**4/10 + 502*q**3/15 + 101*q**2 + 506*q/5 - 1800. Find l such that j(l) = 0.
-1, 253
Let c(z) be the second derivative of -z**6/120 + 3*z**5/80 + 17*z**4/48 - 13*z**3/8 + 5*z**2/2 - 501*z. Factor c(t).
-(t - 5)*(t - 1)**2*(t + 4)/4
Let f be ((-2)/6)/(3/(-54)). Find j such that -2 - 103*j**3 + 101*j**3 + f*j**2 + 2*j**5 - 6*j**4 + 2 = 0.
-1, 0, 1, 3
Let y(h) be the third derivative of 1/15*h**5 + 10*h - 8/3*h**3 + 0 + 0*h**4 + h**2. Solve y(f) = 0.
-2, 2
Let a(y) = 3*y**3 - 39*y**2 - 3*y + 39. Let f be a(13). Let r be ((-1)/27)/(7/(-42)). What is j in 0*j + f - r*j**3 + 2/9*j**5 + 0*j**2 + 0*j**4 = 0?
-1, 0, 1
Find c such that -3/5*c**2 + 12/5 - 9/5*c = 0.
-4, 1
Let p(f) be the second derivative of 0 + 0*f**2 + 158*f + 1/210*f**7 + 0*f**3 - 2/75*f**6 + 1/20*f**5 - 1/30*f**4. Factor p(h).
h**2*(h - 2)*(h - 1)**2/5
Let y(h) be the third derivative of 4*h**7/105 + 13*h**6/30 + h**5 - h**4/6 - 10*h**3/3 - 3244*h**2. Suppose y(f) = 0. Calculate f.
-5, -1, 1/2
Solve 2/5*i**4 - 16/5*i**2 - 36/5*i + 4/5*i**3 - 18/5 = 0 for i.
-3, -1, 3
Let o = 2217 - 4429/2. Let m be 0*(-1)/4*-4 + 3. Factor -o*x + 1/2*x**2 + 3/2 + 1/2*x**m.
(x - 1)**2*(x + 3)/2
Let 2*g + 2/9*g**2 + 40/9 = 0. Calculate g.
-5, -4
Suppose o - 36 = -2*o. Let p(m) = 3 + m**3 - 5*m**4 + 15*m - o*m - 24*m**3. Let y(c) = c**3 - c - 1. Let l(a) = -p(a) - 3*y(a). Let l(v) = 0. What is v?
-4, 0
Let m(v) = -3*v**2 - 454*v - 2. Let x(t) = -25*t**2 - 3646*t - 17. Let p(a) = 34*m(a) - 4*x(a). Find w, given that p(w) = 0.
-426, 0
Let n(k) be the second derivative of k**9/12096 - k**8/672 - 11*k**7/3360 + 127*k**3/3 - 3*k. Let p(v) be the second derivative of n(v). Factor p(l).
l**3*(l - 11)*(l + 1)/4
Let h(m) = 2 - 4 + m + 4. Let q be h(0). Find w such that 4*w + w**2 + 0*w**2 + 6*w**4 - 4*w**2 - q*w**3 - 3*w**2 - 2*w**5 = 0.
-1, 0, 1, 2
Let v(g) = 412*g - 507. Let u be v(6). Let m = u + -9821/5. Let -2/5*r**4 - 2/5 + 4/5*r**2 - m*r**3 + 2/5*r**5 + 2/5*r = 0. What is r?
-1, 1
Let w = -22 + 38. Suppose 5*v - w = h - 3*h, 3*v - 21 = -5*h. What is j in -4/7*j**3 - 8/7*j**v + 0 + 0*j = 0?
-2, 0
Let y(v) = -3*v + 34. Let x be y(6). Suppose -2*r = x*b - 19*b + 7, r - 1 = 0. Factor -1/4*t**2 - 1 + 3/8*t**b + 1/8*t**4 - 3/2*t.
(t - 2)*(t + 1)*(t + 2)**2/8
Let x(f) = f**3 - 4*f**2 + 5*f - 3. Let d be x(3). Let z be 4*d/6 + 0. Factor -7*b + 2*b + 0*b + 11*b + z*b**2.
2*b*(b + 3)
Let c be 2393/(-2100) - (966/98 + -11). Let r(h) be the third derivative of 0 - c*h**5 + 0*h + 4*h**2 - 7/60*h**4 - 49/30*h**3. Solve r(d) = 0 for d.
-7
Let s(t) be the third derivative of 9/20*t**6 + 0*t + 0 - 54*t**2 + 23/4*t**4 + 12/5*t**5 + 15/2*t**3 + 1/70*t**7. Factor s(y).
3*(y + 1)**3*(y + 15)
Suppose -84*m + 349 - 13 = 0. Let p(i) be the second derivative of 1/3*i**m - 6*i + 1/50*i**6 + 0 + 0*i**2 - 7/50*i**5 - 4/15*i**3. Factor p(r).
r*(r - 2)**2*(3*r - 2)/5
Suppose 2075*o + 1351*o - 7308 = 990*o. Factor 1/2*g**2 + 7*g - 12 - 1/2*g**o.
-(g - 3)*(g - 2)*(g + 4)/2
Factor -657/7*b + 324/7*b**2 + 3/7*b**3 + 330/7.
3*(b - 1)**2*(b + 110)/7
Let h(p) be the third derivative of 0 - 1/30*p**6 - 2*p**2 + 1/5*p**5 + 0*p**4 + 0*p**3 + 7*p - 2/35*p**7 + 1/84*p**8. Solve h(c) = 0.
-1, 0, 1, 3
Factor 43 - 20*m**3 - 258*m - 40 - 203*m**3 - 525*m**2 - 41*m**3.
-3*(m + 1)**2*(88*m - 1)
Let s = -77 + 233/3. Let p be 43/129 + 1/3. Let 1/3 - 1/3*q**4 - s*q + p*q**3 + 0*q**2 = 0. What is q?
-1, 1
Let v(x) = x**3 + 10*x**2 + 14. Let q(s) = s**2 + s - 1. Let y(i) = q(i) + v(i). Let h be y(-11). Factor 55*z**h + 75 - 60*z - 128 - 15*z**3 + 73.
-5*(z - 2)*(z - 1)*(3*z - 2)
Let 83640*j**2 - 1/9*j**5 - 24568/9*j**3 - 75600*j + 271/9*j**4 - 162000 = 0. Calculate j.
-1, 2, 90
Let u(r) be the third derivative of -r**7/105 + r**6/80 + 31*r**5/120 - 7*r**4/8 - 49*r**2. Factor u(h).
-h*(h - 2)*(h + 3)*(4*h - 7)/2
Suppose 3*u - 5*q + 2 = 36, 3*q + 21 = 2*u. Factor 0*k**3 + 16*k + 2*k**u - 6*k**3 + 8*k**2 - 20*k.
-4*k*(k - 1)**2
Factor -76*y + 32 + 25/4*y**3 + 40*y**2.
(y + 8)*(5*y - 4)**2/4
Let q(o) = -o**2 - 5*o + 8. Let a be q(-6). Let 23*v**2 + 14*v**4 + 2*v**3 - 4*v + 10*v**5 - 37*v**a - 8*v**3 = 0. Calculate v.
-1, -2/5, 0, 1
Let l(m) be the second derivative of 121*m + 1/2*m**2 - 3/4*m**4 + 1/6*m**3 + 0 - 9/20*m**5. Factor l(v).
-(v + 1)*(3*v - 1)*(3*v + 1)
Determine o so that 15*o**2 - 25*o - 14*o - 5*o**4 + 29*o = 0.
-2, 0, 1
Let a(w) be the second derivative of -w**6/15 - 104*w**5/5 - 5408*w**4/3 + 560*w - 1. Factor a(j).
-2*j**2*(j + 104)**2
Determine z so that -12500*z**5 + 222*z - 415*z + 214*z + 7375*z**4 + 3560*z**2 + 23295*z**3 + 119*z = 0.
-1, -2/25, 0, 7/4
Let h(b) be the first derivative of -4*b**4 - 428*b**3/3 - 346*b**2 + 200*b - 1347. Factor h(p).
-4*(p + 2)*(p + 25)*(4*p - 1)
Let y = 1867218/13 - 143632. Factor y*t + 2/13*t**5 + 12/13*t**3 + 8/13*t**2 + 0 + 8/13*t**4.
2*t*(t + 1)**4/13
Let d = 74190 - 148377/2. What is k in -9/4*k + d - 9*k**2 - 21/4*k**3 = 0?
-1, 2/7
Factor -2/7*r**4 + 0 - 1628/7*r**3 + 0*r - 331298/7*r**2.
-2*r**2*(r + 407)**2/7
Suppose 0 = -h - 1, -4*l - 4*h + 14 = -2*l. Let w = l - 4. Factor -y - 2*y**3 - 31*y**w + 4*y**3 + 30*y**5 + 0*y.
-y*(y - 1)**2*(y + 1)**2
Let l(u) be the second derivative of u**5/80 + 1027*u**4/48 - 2057*u**3/24 + 1029*u**2/8 - 10650*u. Suppose l(p) = 0. Calculate p.
-1029, 1
Suppose 948 + 72 = 51*q. Suppose 5*m - q = 5*g, 2*g + g + 2 = -2*m. Determine w, given that w**3 - 7/2*w + 3/4 + 7/4*w**m = 0.
-3, 1/4, 1
Suppose 0 = 36*i - 38*i + 6. Let o be -4 - (6*(2 + -4) + i). Find a, given that 2/7*a**o + 0 - 2/7*a**2 + 4/7*a - 6/7*a**3 + 2/7*a**4 = 0.
-2, -1, 0, 1
Let r(g) = g**2 - 5*g - 16. Let o be r(-2). Let p be (55/(-66) - -4) + 1/o. Factor 0 - 4/3*i**5 - 5/3*i**3 + 1/3*i**2 + 0*i + p*i**4.
-i**2*(i - 1)*(2*i - 1)**2/3
Let x be ((-4)/((-24)/9))/(21/28). What is i in -i**2 - i**x + i**5 - i**4 + 3*i**2 - i**3 = 0?
-1, 0, 1
Suppose 3*a = 8*a - 100. Factor -8*p - 2*p**2 - a*p - 12*p - 5*p**4 + 32*p**2 + 15.
-5*(p - 1)**3*(p + 3)
Let n(q) = -30 - 71*q**2 - 4*q**3 - 49*q - 5*q**3 + 13 + 19. Let b(s) = 2*s**3 + 14*s**2 + 10*s. Let j(z) = 11*b(z) + 2*n(z). Factor j(c).
4*(c + 1)**3
Let v(u) be the first derivative of 19683/2*u + 27/2*u**3 - 1/8*u**4 - 85 - 2187/4*u**2. Factor v(f).
-(f - 27)**3/2
Suppose 27*n - 93*z - 32 = -91*z, -2*n - z = 16. Factor -9/2*y**3 - 3/4*y - 3*y**2 - 3/4*y**5 + n - 3*y**4.
-3*y*(y + 1)**4/4
Determine o so that -50*o + 254*o**2 + 685*o**5 - 1247*o**4 + 3181*o**2 - 295*o**3 + 1694*o**4