8254. Let j = -1 + 5. Factor -1/6*u**5 - 5/3*u**3 + 1/6 + 5/6*u**j + 5/3*u**b - 5/6*u.
-(u - 1)**5/6
Let f(m) be the first derivative of m**4/6 + 11*m**3/12 + 3*m**2/2 - 124*m - 99. Let o(r) be the first derivative of f(r). Find z, given that o(z) = 0.
-2, -3/4
Let r(b) be the first derivative of 28*b**3/9 + 78*b**2 - 136*b/3 - 813. Factor r(h).
4*(h + 17)*(7*h - 2)/3
Let w(r) be the first derivative of -3*r**4/28 + 61*r**3/7 - 348*r**2/7 + 684*r/7 + 1224. Factor w(o).
-3*(o - 57)*(o - 2)**2/7
Let r(z) = -3*z**3 + 13*z**2 - 8*z. Let o(g) = 611 - 611 + 10*g**3 - 40*g**2 + 23*g. Let b(n) = 6*o(n) + 21*r(n). Factor b(c).
-3*c*(c - 10)*(c - 1)
Let j(c) = 15 - 13*c**3 + 8*c**3 + 6*c**3 - 11*c**2 - 11*c. Let m be j(12). Let -4 + 4*h**2 - m*h + 13*h - 2*h**3 + 16*h = 0. What is h?
-1, 1, 2
Factor 318*n**3 - 3*n**4 - 5009 + 61029*n - 9867*n**2 - 126052 - 41739 + 15291*n.
-3*(n - 48)**2*(n - 5)**2
Factor -3*k**5 - 3*k**4 - 6*k**4 - 32*k**2 - 9*k - 7*k + k**4 - 24*k**3 + 2*k**5.
-k*(k + 2)**4
Let i(j) = -9*j**2 + 290*j - 4209. Let w(r) be the first derivative of 26*r**3/3 - 435*r**2 + 12626*r + 102. Let q(o) = -11*i(o) - 4*w(o). Factor q(c).
-5*(c - 29)**2
Let p(l) be the first derivative of -l**5/50 + 7*l**4/30 + l**3/3 + 5*l**2/2 - 21*l - 233. Let r(b) be the second derivative of p(b). Factor r(g).
-2*(g - 5)*(3*g + 1)/5
Factor 4/3*n**2 + 4/3*n - 320.
4*(n - 15)*(n + 16)/3
Let d = -9510697/5 + 1902140. Factor 1/10*w**4 + 3/10*w**2 + w - d*w**3 + 0.
w*(w - 5)*(w - 2)*(w + 1)/10
Let j(m) = -2*m**2 + m - 1. Let w(b) = -b**3 + b**2 + 2. Suppose 4*g + 4 = 2*g. Let y(h) = g*j(h) - 2*w(h). Solve y(v) = 0.
-1, 1
Let o = 433583 - 433578. Let -o - 20/3*t**3 + 5*t**2 + 20/3*t = 0. Calculate t.
-1, 3/4, 1
Suppose -26 = -25*o + 74. Let i be 27/36*(o + -4 + 4). Find b such that 1/5*b**2 - 1/5*b + 1/5*b**i - 1/5 = 0.
-1, 1
Let a(r) = 143*r + 2154. Let k be a(-15). Let h = 469/4 + -117. Solve k + h*p**2 - 3*p = 0.
6
Let a(k) be the third derivative of 0*k - 1/1176*k**8 - 11/210*k**5 + 3/140*k**6 - 1/735*k**7 + 35*k**2 + 0*k**3 + 2 + 1/21*k**4. Factor a(w).
-2*w*(w - 1)**3*(w + 4)/7
Let g(m) be the third derivative of m**7/245 - m**6/35 - 31*m**5/70 - m**4/2 + 48*m**3/7 - 5*m**2 + 5*m - 5. Solve g(o) = 0.
-3, -2, 1, 8
Let c(x) be the second derivative of x**6/135 + x**5/5 - 5*x**4/6 - 94*x**3/27 + 40*x**2/3 - x. Suppose c(v) = 0. Calculate v.
-20, -2, 1, 3
Let q(x) = -x**2 + 15*x - 27. Let o be q(11). Suppose -3*w - 13 = -3*z + 2, -3*w = -4*z + o. Factor -3/4*r**4 + 0 + 1/2*r**3 + 1/4*r**5 + 0*r**z + 0*r.
r**3*(r - 2)*(r - 1)/4
Let o(c) be the third derivative of c**5/75 + 274*c**4/15 + 150152*c**3/15 + 347*c**2. Solve o(j) = 0 for j.
-274
Let d(p) = 2*p**2 - 16*p + 65. Let l be d(10). Suppose 158*w + 0*w**3 - 110*w + 3*w**3 - l*w + 54*w**2 = 0. Calculate w.
-19, 0, 1
Let m(y) = -3*y**2 + 8*y - 5. Let g be m(7). Let u = 100 + g. Factor 51*h**4 - 108*h**5 + 68*h**2 + 180*h**3 + 44*h**u + 41*h**4 - 28*h**4 + 8*h.
-4*h*(h - 2)*(3*h + 1)**3
Suppose 4*j = 4*r + r - 30, 5*j = 5*r - 35. Factor -24 + 12*h - 249*h**r - 3*h**3 + 0*h**3 + 124*h**2 + 131*h**2.
-3*(h - 2)**2*(h + 2)
Let m(c) be the second derivative of c**4/6 + 120*c**3 + 716*c**2 + 1814*c. Suppose m(n) = 0. What is n?
-358, -2
Let a(v) be the third derivative of v**8/504 - 11*v**7/63 + 208*v**6/45 - 1012*v**5/45 - 52*v**4/9 + 2704*v**3/9 - v**2 + 11. Solve a(g) = 0 for g.
-1, 2, 26
Let q(r) be the third derivative of r**6/420 + 13*r**5/35 + 629*r**4/84 + 184*r**3/7 - 7*r**2 + 129*r. Solve q(z) = 0.
-69, -8, -1
Let d = 312 - 309. Suppose 8*r**2 - 1083 - d*r**2 - 8*r**2 + 114*r = 0. What is r?
19
Let d(q) be the second derivative of -q**4/30 - 8*q**3/15 + 48*q**2/5 + 1144*q. Find m, given that d(m) = 0.
-12, 4
Let m = -14473917/19 - -761791. Factor -2/19*u**5 + 22/19*u**4 + 32/19 - 86/19*u**3 - m*u + 146/19*u**2.
-2*(u - 4)**2*(u - 1)**3/19
Solve -387/2*h - 1/2*h**2 + 782 = 0.
-391, 4
Let b = -393 + 395. Let x = -1462/5 - -293. Find j, given that 3/5*j**b + 0 - x*j = 0.
0, 1
Let u be (4/2)/(11/98) - (-226)/1243. Solve u + 27/2*b**2 - 69/2*b - 3/2*b**4 + 9/2*b**3 = 0.
-3, 1, 4
Let o(s) be the first derivative of -3*s**5/35 + 3*s**4 - 171*s**3/7 + 3181. Factor o(f).
-3*f**2*(f - 19)*(f - 9)/7
Let t(s) be the third derivative of -s**6/160 + 19*s**5/10 - 447*s**4/32 - 3527*s**2. Factor t(g).
-3*g*(g - 149)*(g - 3)/4
Let c be 420*((-24242)/(-621) + -39). Factor -c*l**2 - 4/9*l**4 + 100/9*l + 0 + 44/9*l**3.
-4*l*(l - 5)**2*(l - 1)/9
Let x(l) be the second derivative of l**6/1620 - 7*l**5/540 + 5*l**4/54 - 14*l**3/3 - 55*l. Let g(k) be the second derivative of x(k). Factor g(q).
2*(q - 5)*(q - 2)/9
Let h be (25/((-20)/4))/(-1). Factor 0*l - 59*l**h - 2*l**2 + 2*l**4 + 60*l**5 - l.
l*(l - 1)*(l + 1)**3
Let v(k) be the first derivative of -7*k**4/34 - 76*k**3/17 + 2908*k**2/17 + 1680*k/17 + 7044. Suppose v(a) = 0. Calculate a.
-30, -2/7, 14
Let f = 5416067/5 + -1083211. Solve 33/5*s - 3/5*s**3 + 18/5 + f*s**2 = 0 for s.
-1, 6
Suppose 0 = -396*d + 431 - 271 + 632. Suppose -74/9*w + 8 + 2/9*w**d = 0. Calculate w.
1, 36
Let x(z) be the third derivative of -z**5/72 - 265*z**4/144 + 95*z**3/3 + 19*z**2 - 6*z - 3. Solve x(q) = 0 for q.
-57, 4
Let s(r) be the first derivative of -16/9*r**3 - 24*r - 107 + 146/3*r**2. Solve s(c) = 0.
1/4, 18
Factor -95/3*q**2 - 1/6*q**3 - 4606/3*q - 8836/3.
-(q + 2)*(q + 94)**2/6
Let p be ((-32396)/260 - -125)/(7/5). Suppose 18 = 5*d + j, 3*d + 4*j = -0*d + 21. Factor -8/7 + 16/7*x - 6/7*x**2 - 4/7*x**d + p*x**4.
2*(x - 2)*(x - 1)**2*(x + 2)/7
Let x = -20380 - -20383. Let q(j) be the second derivative of 5*j + 1/15*j**x + 2 - 1/90*j**4 + 0*j**2. Factor q(t).
-2*t*(t - 3)/15
Let q(o) be the second derivative of 1/3*o**3 + 123*o - 1/15*o**5 + 1/90*o**6 + 0*o**2 + 0 + 1/36*o**4. Find d, given that q(d) = 0.
-1, 0, 2, 3
Suppose 8 - 28 = -34*c + 24*c. Let d(m) be the second derivative of -3/50*m**5 + 4/15*m**3 + 1/75*m**6 + 19*m + 0*m**4 + 0 + 0*m**c. Solve d(g) = 0.
-1, 0, 2
Let k(m) be the second derivative of -m**5/100 + m**4/30 + m**3/30 - m**2/5 + 656*m. Factor k(a).
-(a - 2)*(a - 1)*(a + 1)/5
Let b(t) be the second derivative of 0 + 1/7*t**3 + 3*t + 4/7*t**2 + 1/84*t**4. Let b(z) = 0. Calculate z.
-4, -2
Let o(l) be the first derivative of -l**6/3 - 2*l**5/5 + 7*l**4 + 4*l**3 - 45*l**2 + 54*l + 540. Let o(a) = 0. Calculate a.
-3, 1, 3
Suppose -32*h + 8 + 56 = 0. Let -23*c**2 - 7396 - 45*c**2 - 344*c + 64*c**h = 0. Calculate c.
-43
Determine v, given that -6/7*v**4 + 864/7*v + 246/7*v**2 - 1080/7 - 24/7*v**3 = 0.
-6, -5, 1, 6
Suppose 3*a + 5*o - 86 = 0, -3*o + 56 = -1459*a + 1463*a. Factor -1/3*t**2 + 1/3*t + a.
-(t - 3)*(t + 2)/3
Let y be (5406/1908)/(17/14). Factor 0*t + 0 + 5/3*t**4 - 1/3*t**5 + 13/3*t**3 + y*t**2.
-t**2*(t - 7)*(t + 1)**2/3
Factor 8*a**2 - a**2 - 22*a**2 + 10*a**2 - 459045 + 3030*a.
-5*(a - 303)**2
Determine t, given that 204*t + 1/2*t**2 - 410 = 0.
-410, 2
Let p(l) = l**4 + 3*l**3 + l**2 - l + 2. Let m(z) = 4*z**4 - 22*z**3 + 80*z**2 + 26*z - 76. Let b(c) = 2*m(c) - 4*p(c). Determine y, given that b(y) = 0.
-1, 1, 4, 10
Let i = -366807/4 - -91702. Let -3/4 + n**2 + i*n = 0. What is n?
-1, 3/4
Let g be (42/(-35))/(2/10). Let w be (-10)/g + 12/9. What is u in 10*u**2 - 6*u**w - u + u + u**3 - 5*u = 0?
0, 1
Factor 0 - 745/3*j**4 + 83/3*j**5 - 729*j**2 + 741*j**3 - 18*j.
j*(j - 3)**3*(83*j + 2)/3
What is t in -2*t**4 - 2*t**5 + 23878*t + 2*t**2 - 47796*t + 23894*t + 26*t**3 = 0?
-4, -1, 0, 1, 3
Factor 2*o**2 + 41 + 22*o - 11*o - 209 - o.
2*(o - 7)*(o + 12)
Let b(o) be the second derivative of -o**6/135 + 31*o**5/30 + 97*o**4/9 + 1180*o**3/27 + 88*o**2 - 49*o + 2. Let b(y) = 0. Calculate y.
-2, 99
Let p(a) be the third derivative of 2*a**6/15 + 61*a**5/3 - 274*a**4/3 - 104*a**3 + 515*a**2. Factor p(n).
4*(n - 2)*(n + 78)*(4*n + 1)
Let z be 1*(-5 + (-518)/(-98))*7. Find c, given that 2/3 - 1/2*c**4 + 11/6*c**z - 1/6*c**5 + 1/6*c**3 + 2*c = 0.
-2, -1, 2
Let f be ((-1)/(5/(-100)))/((-35)/(-42)). Suppose 3*z = 2*w + 11, -2*z - 4 = 5*w - f. Factor 6/5*j**w + 2/5*j**3 - 2/5*j - 6/5.
2*(j - 1)*(j + 1)*(j + 3)/5
Let n(s) = -88*s**2 - 11*s + 25. Let m(o) = -30*o**2 - 4*o + 8. Let i(z) = 11*m(z) - 4*n(z). Let h be i(4). Factor 683*q + 4*q**2 - 351*q - h*q.
4*q*(q - 2)
Let r(o) be the sec