
Let q(a) be the second derivative of -a**5/30 - 3*a**4/2 - 206*a**3/9 - 160*a**2 + 5054*a. Let q(d) = 0. What is d?
-16, -6, -5
Let s(g) = -g**2 + g. Suppose -6 = -3*a - 0. Let b(v) = 16*v - 5*v + 2*v**a - 11*v**2 + 4*v**2. Let h(l) = -b(l) + 6*s(l). Factor h(z).
-z*(z + 5)
Let z(h) be the second derivative of -h**5/15 - 967*h**4/3 - 1870178*h**3/3 - 1808462126*h**2/3 + 43*h. Factor z(s).
-4*(s + 967)**3/3
Let h(y) be the second derivative of -y**4/24 - 73*y**3/6 + 1066*y + 3. Suppose h(p) = 0. Calculate p.
-146, 0
Factor -543186976/3 - 2056*d**2 - 1056784*d - 4/3*d**3.
-4*(d + 514)**3/3
Let a(r) be the second derivative of -3*r + 17/2*r**3 + 27*r**2 + r**4 - 27. Find m such that a(m) = 0.
-9/4, -2
Let d(h) = -5*h**2 - 2*h + 36. Let w be d(0). Factor -3*a**3 - w*a**2 + 1747*a - 24*a**2 - 1678*a + 126.
-3*(a - 2)*(a + 1)*(a + 21)
Let j = 3788 - 3759. Let t(h) be the second derivative of -5/3*h**3 + 0*h**4 + 0 - 5/2*h**2 + 1/6*h**6 + 1/2*h**5 - j*h. Factor t(z).
5*(z - 1)*(z + 1)**3
Let a(u) be the second derivative of -u**4/36 - 19*u**3/6 - 28*u**2/3 + 3182*u. Solve a(d) = 0.
-56, -1
Suppose -31 = -5*f - 3*a, 0*a + 5*a = 10. Let h be 52/f - 7 - (2 - -1). Suppose -2/5*d + h*d**2 + 2/15 - 2/15*d**3 = 0. What is d?
1
Let v(g) be the first derivative of -3*g**4/22 - 124*g**3/11 - 519*g**2/11 + 1416*g/11 + 708. Find f, given that v(f) = 0.
-59, -4, 1
Factor 26904969/5*r - 15506230467/5 + 3/5*r**3 - 15561/5*r**2.
3*(r - 1729)**3/5
Factor -1/9*c + 1/9*c**3 - 20/3*c**2 + 20/3.
(c - 60)*(c - 1)*(c + 1)/9
Let c(q) = q**3 + 5*q**2 + 5*q + 7. Let u be c(-4). Factor -28*y**u + 54*y**3 - 15*y**2 - 18*y - 29*y**3.
-3*y*(y + 2)*(y + 3)
Suppose 1218*c + 90 = 1263*c. Factor 0*q - 6/7*q**5 + 0 - 18/7*q**4 - 18/7*q**3 - 6/7*q**c.
-6*q**2*(q + 1)**3/7
Factor 0 + 3/5*c**4 + 0*c + 181548/5*c**2 - 1476/5*c**3.
3*c**2*(c - 246)**2/5
Suppose -32/5 - 22*a**2 + 34/5*a**4 - 116/5*a + 4/5*a**5 + 4/5*a**3 = 0. What is a?
-8, -1, -1/2, 2
Let k(h) be the first derivative of 32*h**2 + 0*h - 4/3*h**3 + 113. Factor k(q).
-4*q*(q - 16)
What is s in 2986/3*s - 2229049/3 - 1/3*s**2 = 0?
1493
Let q(l) be the first derivative of -l**3/15 - 11*l**2/5 + 408*l/5 + 542. Factor q(a).
-(a - 12)*(a + 34)/5
Let z = -94 - -97. Suppose z*d + 11 = 5, 4*h + d = 6. Factor -3*k**3 - 4*k**2 + 4*k**2 - 30*k**h - 105*k - 96 + 9*k.
-3*(k + 2)*(k + 4)**2
Let q be (5 - -2) + (-1398)/700 + -5. Let v(o) be the third derivative of 30*o**2 + 0 + 0*o**3 + 7/100*o**5 - 3/20*o**4 + 0*o**6 - q*o**7 + 0*o. Solve v(d) = 0.
-3, 0, 1, 2
Let k(o) be the third derivative of o**8/560 - o**7/70 - 7*o**6/50 + 8*o**5/25 - 4938*o**2. Let k(t) = 0. What is t?
-4, 0, 1, 8
Let q(i) be the first derivative of i**8/112 - 3*i**7/35 + 11*i**6/40 - 3*i**5/10 - 33*i**2 + i + 267. Let x(j) be the second derivative of q(j). Factor x(y).
3*y**2*(y - 3)*(y - 2)*(y - 1)
Factor -4*g**2 + 21300 - 171*g + g**2 - 23190.
-3*(g + 15)*(g + 42)
Let f(l) be the first derivative of l**4/20 - 61*l**3/3 + 428. Factor f(a).
a**2*(a - 305)/5
Let s(m) be the second derivative of -m**6/70 + 33*m**5/28 + 113*m**4/28 + 57*m**3/14 + 36*m - 4. Factor s(l).
-3*l*(l - 57)*(l + 1)**2/7
Let s(w) = 2*w**2 + 1404*w + 246407. Let z(x) = -3*x**2 - 2106*x - 369611. Let p(v) = -8*s(v) - 5*z(v). Find q, given that p(q) = 0.
-351
Let m = -1899 - -1898. Let f be (m + 8/7)/((-120)/(-1680)). Factor -6/5 - 12*y**3 + 2*y + 4*y**f + 10*y**4 - 14/5*y**5.
-2*(y - 1)**4*(7*y + 3)/5
Let g(i) be the first derivative of i**3/15 + 7*i**2/2 + 66*i/5 - 944. Suppose g(p) = 0. Calculate p.
-33, -2
Let y(s) be the third derivative of -s**5/20 - 533*s**4/4 - 284089*s**3/2 - 6*s**2 + 51*s. Determine q, given that y(q) = 0.
-533
Let y(b) = b**3 - 27*b**2 + b - 11. Let r be y(27). Let w be -21 + r + (-129)/(-21). What is m in -2/7*m**2 - w*m + 0 = 0?
-4, 0
Let n(o) = 22*o + 5. Let p be n(1). Let a be (-6)/p*1 - 40/(-18). Factor -3/2*j**a - 2*j + 2.
-(j + 2)*(3*j - 2)/2
Let l(k) = -14425*k - 288497. Let s be l(-20). Determine d, given that 4/13*d + 0 + 10/13*d**5 + 6/13*d**4 - 6/13*d**2 - 14/13*d**s = 0.
-1, 0, 2/5, 1
Let w(s) be the third derivative of s**2 - 4541/60*s**5 - 6859/12*s**3 - 31*s + 1/672*s**8 - 59/420*s**7 + 14801/48*s**4 + 0 + 599/120*s**6. Factor w(d).
(d - 19)**3*(d - 1)**2/2
Suppose -15*x + 12*x = -129. Find y such that 135*y - 43*y + 30 - 5*y**2 - 24*y - x*y = 0.
-1, 6
Let f be 8/2 + 1 - 1. Let z be 3/(f + -5) + 5. Factor 0 - 1/2*h**4 - h**3 + 2*h**z + 4*h.
-h*(h - 2)*(h + 2)**2/2
Let k be (86/(-156) + 155/403)/((-3)/54). Factor 3/2*c**4 + 0 + 63/2*c**2 + 0*c - 15*c**k.
3*c**2*(c - 7)*(c - 3)/2
Let l(m) = -m**5 + 3*m**2 + 4. Let z(f) = 32*f**5 + 471*f**4 + 1325*f**3 + 270*f**2 - 512*f + 64. Let i(p) = 5*l(p) + z(p). Let i(d) = 0. What is d?
-14, -3, -1, 2/9, 1/3
Let k = 13994 + -5221. Factor 32 - 8754*m**2 + 50*m + k*m**2 - 3*m**3 + 4*m**3.
(m + 1)*(m + 2)*(m + 16)
Find a such that 12*a**2 + 168 + 542/3*a - 2/3*a**3 = 0.
-9, -1, 28
Let o(g) be the third derivative of -g**5/60 - 13*g**4/12 - 169*g**3/6 - 136*g**2 - g. Suppose o(n) = 0. What is n?
-13
Let w(c) = -8*c**4 - 1955*c**3 - 7749*c**2 - 7712*c + 20. Let h(l) = -12*l**4 - 2933*l**3 - 11623*l**2 - 11568*l + 28. Let u(o) = 5*h(o) - 7*w(o). Factor u(t).
-4*t*(t + 2)**2*(t + 241)
Find u, given that -10/3*u**2 - 1/6*u**3 + 16*u + 0 = 0.
-24, 0, 4
Let -388/15*c + 2/15*c**2 + 18818/15 = 0. What is c?
97
Let h(j) = -j**2 + 18*j + 90. Let x be h(22). Suppose 101 + p**3 - p - 7*p**x - 211 + 0*p + 117 = 0. Calculate p.
-1, 1, 7
Let t be (-8)/(-26)*2054/4740. Let r(d) be the third derivative of 2/105*d**7 + 1/10*d**6 + 0*d**4 - 22*d**2 + 0*d**3 + 0 + t*d**5 + 0*d. Solve r(y) = 0.
-2, -1, 0
Let l(g) be the third derivative of -g**7/16380 - 17*g**6/4680 + 19*g**5/390 + 85*g**4/24 - 51*g**2. Let m(a) be the second derivative of l(a). Factor m(r).
-2*(r - 2)*(r + 19)/13
Let c = -404831/6 - -67472. Find h such that -14/3*h + 11/6*h**3 - c*h**5 - 4 + h**2 + 0*h**4 = 0.
-2, -1, 2, 3
Let o(u) be the third derivative of -1/896*u**8 + 0*u**3 - 6*u**2 + 0*u**7 + 1/80*u**5 + 3/320*u**6 + 0*u + 0*u**4 + 0. Factor o(l).
-3*l**2*(l - 2)*(l + 1)**2/8
Let j be 165/(-30)*(-4 - (-4 - -2)). Factor -12*o + 24*o**3 + j*o**3 - 31*o**3 - 8*o**2.
4*o*(o - 3)*(o + 1)
Let t(k) = 4*k**2 + 3*k - 12. Let q be t(3). Let h be q/(-88) - (-35)/8. Solve -9*l**4 - h*l**2 + 25*l**4 - 12*l**4 + 0*l**2 = 0.
-1, 0, 1
Let a(t) be the third derivative of t**5/105 - 61*t**4/42 + 220*t**3/7 - 2*t**2 + 6904*t. Suppose a(z) = 0. Calculate z.
6, 55
Let t = 539 + -321. Let 42*z**3 + 4 + 58*z**4 + 8*z**2 + t*z**5 - 4 - 206*z**5 = 0. Calculate z.
-4, -1/2, -1/3, 0
Let v(j) be the third derivative of 0*j**3 + 0 - 3/4*j**5 + 25/24*j**4 + 127*j**2 + 61/480*j**6 + 1/1344*j**8 + 3/140*j**7 + 0*j. Factor v(c).
c*(c - 1)**2*(c + 10)**2/4
Suppose 0 = 45*g - 5550 + 5415. Factor -1/5*t**4 - 9/5*t**g + 0 + 0*t + 0*t**2.
-t**3*(t + 9)/5
Factor -517/7*k**2 - 1028/7 + 1544/7*k + 1/7*k**3.
(k - 514)*(k - 2)*(k - 1)/7
Let u(a) be the second derivative of -a**6/25 + 71*a**5/50 + 148*a**4/45 + 20*a**3/9 + 79*a + 13. Factor u(b).
-2*b*(b - 25)*(3*b + 2)**2/15
Let h be (-68)/(-14) + -5 - 255/(-63). Let x = h + -143/42. Factor -10*m**3 - 75*m**2 - x*m**4 - 250*m - 625/2.
-(m + 5)**4/2
Let x = -2051 - -1414. Let l = -634 - x. Factor -4/15*a**2 + 2/15 - 2/15*a - 2/15*a**5 + 2/15*a**4 + 4/15*a**l.
-2*(a - 1)**3*(a + 1)**2/15
Let o(v) be the first derivative of v**6/1800 + 19*v**5/600 + 3*v**4/20 - 51*v**3 + 167. Let k(h) be the third derivative of o(h). Suppose k(g) = 0. What is g?
-18, -1
Let l = -916 - -916. Suppose l = s + 5*k - 4, -4*k = 5*s - 6*k - 47. Factor 3/2*y**2 - s*y + 0.
3*y*(y - 6)/2
Let r = 429/10 - 1277/30. Let s(v) be the first derivative of 2/3*v**3 + r*v**4 + 1/3*v**2 + 0*v - 14. Let s(a) = 0. Calculate a.
-1, -1/2, 0
Suppose 7*w = 2*i + 2*w - 10, -w - 8 = -i. Suppose -i*l + 4 = -8*l. Factor -3/2*k**l - 2 + 1/4*k**3 + 3*k.
(k - 2)**3/4
Let q(n) be the third derivative of 0*n + 0*n**3 + 1/20*n**4 + 1/60*n**6 - 1/525*n**7 + 3 - 7/150*n**5 - 2*n**2. Find f such that q(f) = 0.
0, 1, 3
Let k(a) be the first derivative of a**7/120 + 13*a**6/180 - a**5/15 - 2*a**3/3 - 43*a**2/2 + 78. Let b(l) be the third derivative of k(l). Factor b(d).
d*(d + 4)*(7*d - 2)
Suppose -585*s + 583*s +