ppose 34596 - 374*a**3 + 4544*a**2 + 18964*a**2 + 11833*a**2 + 29439*a**4 - 29438*a**4 - 69564*a = 0. Calculate a.
1, 186
Let y be 174/40 + (-271)/2710. Suppose -1/4*l + 1/4*l**3 + y - 17/4*l**2 = 0. Calculate l.
-1, 1, 17
Let n(r) be the third derivative of -r**8/10080 - r**7/1050 - r**6/450 - 13*r**5/12 - 11*r**2 - 3. Let j(p) be the third derivative of n(p). Factor j(d).
-2*(d + 2)*(5*d + 2)/5
Let j(g) be the second derivative of -g**7/105 + 56*g**6/75 + 23*g**5/10 + 29*g**4/15 - 1151*g - 1. Determine b, given that j(b) = 0.
-1, 0, 58
Let l(b) = b**3 - b**2 + b - 1. Let s(c) = 5*c**4 - 2*c**3 - 118*c**2 - 322*c - 238. Let p = -439 + 440. Let q(r) = p*s(r) + 2*l(r). Factor q(g).
5*(g - 6)*(g + 2)**3
Factor -78*k**3 + 132*k**3 + 356*k - 20*k**2 - 252 + 408*k - 66*k**3.
-4*(k - 7)*(k + 9)*(3*k - 1)
Let i(v) be the first derivative of 77 + 85/2*v**2 + 10/3*v**3 + 40*v. Factor i(c).
5*(c + 8)*(2*c + 1)
Let s(h) be the third derivative of -11*h**5/75 - 29*h**4/20 + 4*h**3/15 - 2*h**2 + 5397*h. Suppose s(f) = 0. Calculate f.
-4, 1/22
Let -2/7*j**2 + 362/7*j + 0 = 0. Calculate j.
0, 181
Determine j, given that -1/3*j**2 + 0 + 533/3*j = 0.
0, 533
Let p(a) be the first derivative of 4/3*a**3 + 34 - 36*a**2 + 324*a. Let p(x) = 0. What is x?
9
Let c be (2/(-2) + 1)/(-1). Factor 0*q**3 - 50*q**2 - 52*q - 10 - 8*q**3 + c.
-2*(q + 1)*(q + 5)*(4*q + 1)
Let u = -20/9 - -23/9. Let x be (-35152)/(-3380)*30/117. Let 2*w - u*w**2 - x = 0. Calculate w.
2, 4
Let y be (-132)/(-24) - (-3)/6. Factor 5*z + 11*z**2 + 21*z**2 - y - 33*z**2.
-(z - 3)*(z - 2)
Let h(s) = s + 21 - 5 - 4 + 18. Let a be h(-28). Determine v so that -3*v**2 + 18*v + 62*v**3 - 37*v**3 - 42*v**a - 10 - 5*v**4 + 17*v = 0.
1, 2
Let q(j) be the first derivative of -j**5/5 + 23*j**4 + 94*j**3 + 142*j**2 + 95*j - 1062. Solve q(c) = 0 for c.
-1, 95
Let t(s) be the first derivative of 0*s - 206 + 0*s**2 + 2/45*s**5 - 7/18*s**4 + 2/27*s**6 - 4/9*s**3. Determine d, given that t(d) = 0.
-3/2, -1, 0, 2
Let s be (4/16)/(900/120). Let h(b) be the first derivative of -s*b**4 + 2/15*b**3 + 5 - 1/5*b**2 + 2/15*b. Let h(d) = 0. What is d?
1
Let z(h) be the third derivative of -7*h**5/240 - 79*h**4/96 - 3*h**3 - 174*h**2 - h - 1. Factor z(p).
-(p + 1)*(7*p + 72)/4
Let 70 - 76/3*d**3 + 362/3*d - 2*d**4 + 2/3*d**5 + 28*d**2 = 0. Calculate d.
-5, -1, 3, 7
Let r(s) be the third derivative of 5*s**8/336 - 2*s**7 + 423*s**6/8 + 11045*s**5/6 - 2*s**2 - 2*s - 4162. Suppose r(w) = 0. Calculate w.
-10, 0, 47
Let o(z) be the first derivative of 4*z**3/21 - 160*z**2/7 + 528*z - 2884. Factor o(x).
4*(x - 66)*(x - 14)/7
Find f, given that 14/3*f**4 + 2*f**5 + 176/3*f + 0 - 542/3*f**3 + 346/3*f**2 = 0.
-11, -1/3, 0, 1, 8
Let f be (-908)/20 - 6/10. Let v = 55 + f. Factor -9*m**4 - 26*m**5 - m**2 - 2*m**2 + v*m**3 + 29*m**5.
3*m**2*(m - 1)**3
Let s = -7471/6 + 3736/3. Factor -1/3*p - 1/6 - s*p**2.
-(p + 1)**2/6
Let o(s) = -s**3 - s**2 + 1. Let c(j) = 14*j**3 + 5*j**2 - 63*j + 11. Let i be (80/(-24))/(3 + (-7)/3). Let m(k) = i*c(k) - 35*o(k). Factor m(g).
-5*(g - 3)*(g + 3)*(7*g - 2)
Let h be 4/(-14) + (-2)/28*-4. Let q = -10/61 - -700/549. Suppose 2/9*a + h + q*a**2 + 8/9*a**3 = 0. What is a?
-1, -1/4, 0
Let l(d) be the second derivative of 6*d**5 - 126*d + d**2 - 49/6*d**4 + 0 - 4*d**3. Let l(z) = 0. Calculate z.
-1/4, 1/15, 1
Let d(s) = -23*s - 19. Let y be d(-1). Let f(v) be the first derivative of 1 - y*v + 4/3*v**3 - v**4 + 2*v**2. Find g, given that f(g) = 0.
-1, 1
Let c be -3 + 1 + 3876/696 + 28/(-406). Solve c*g - 5 - 1/2*g**2 = 0.
2, 5
Factor 1/2*a**2 + 105/2*a + 52.
(a + 1)*(a + 104)/2
Let j = -44823 - -44823. Find v such that -43/5*v + 1/5*v**2 + j = 0.
0, 43
Let z(x) be the first derivative of 2*x**5/65 - 17*x**4/26 + 134*x**3/39 - 87*x**2/13 + 72*x/13 - 474. Suppose z(g) = 0. What is g?
1, 3, 12
Let k(q) = q**3 + 4*q**2 - 9*q + 4. Let j be k(-5). Solve 3381*v - 2997*v + 4*v**4 - v**4 - 768 - j*v**3 = 0.
-4, 4
Suppose -560 = -7*g - g. Let 18*q**2 + 0*q**4 + 355*q + g*q**2 - 7*q**4 + 20*q**3 - 291*q + 3*q**4 = 0. Calculate q.
-2, -1, 0, 8
Determine n, given that 104/7*n**2 - 4/7*n**3 - 200/7 - 92/7*n = 0.
-1, 2, 25
Suppose 4*s = -r + 3 - 13, -3*r + 4*s + 18 = 0. Find w such that -10*w + 329*w**2 - 40 - 162*w**r - 162*w**2 = 0.
-2, 4
Let o be 4/(-10) + (-384)/(-160). Suppose 4*s**3 + 382 - 382 + 4*s**o + s**4 = 0. What is s?
-2, 0
Let r be ((-2)/7)/(11/(-154)). Factor 11 + 6*p + 3*p**3 - p - 38 + 15*p**2 + r*p.
3*(p - 1)*(p + 3)**2
Suppose -30*k = -6*k - 120. Let u be (-66)/(-55)*k/8. Find r, given that -u*r**3 + 15*r + 3*r**4 - 3/4*r**5 - 6 - 21/2*r**2 = 0.
-2, 1, 2
Let g(o) be the second derivative of -7*o**4/12 - 328*o**3/3 + 94*o**2 - 4096*o. Solve g(h) = 0 for h.
-94, 2/7
Let m(v) be the third derivative of -v**6/1260 + 11*v**5/140 + 17*v**4/42 - 85*v**3/3 - 83*v**2. Let s(u) be the first derivative of m(u). Solve s(q) = 0.
-1, 34
Let l(x) be the first derivative of 72 + 1/3*x**3 + 5/2*x**2 + 0*x. Factor l(b).
b*(b + 5)
Find z, given that -982/9*z + 256/3*z**2 - 172/9*z**3 - 4/3*z**4 + 44 + 2/9*z**5 = 0.
-9, 1, 2, 11
Factor 9/7*r**3 + 40*r - 92/7 - 219/7*r**2.
(r - 23)*(3*r - 2)**2/7
Let q(s) = s**4 + 16*s**3 + 26*s**2 - 22*s - 27. Let z(w) = -15*w**3 - 27*w**2 + 24*w + 27. Let h(g) = -3*q(g) - 2*z(g). Factor h(k).
-3*(k - 1)*(k + 1)*(k + 3)**2
Let i be 1633/71 - (1 + 22). Let v(o) be the first derivative of 1/6*o**4 - 1/3*o**2 + 1/3*o**3 + 18 + i*o. Factor v(b).
b*(b + 2)*(2*b - 1)/3
Let p be (30 + (-1568)/48)/(7/(-9)). Factor -2/7*i**3 - 38/7*i + 16/7*i**2 + p.
-2*(i - 4)*(i - 3)*(i - 1)/7
Suppose 22*d - 19*d - 21 = 0. Suppose -2*g = 3*n + 4, 3*n + 0*n - 5*g - 31 = 0. Find p such that -n*p**2 + d*p - 12*p - 7 - 21 - 13*p = 0.
-7, -2
Let x be ((-108875)/30)/(-25) + (-2)/12. Let g be (-2 - -3)/(x/10 - 7). Find j, given that g*j**2 - 4/15*j + 2/15*j**4 + 0 + 4/5*j**3 - 4/15*j**5 = 0.
-1, 0, 1/2, 2
Let r be (-6)/4*166/(-3). Factor -47*o + r*o + 7*o**2 - 11*o**2 - 32.
-4*(o - 8)*(o - 1)
Let r(f) = f**2 - 6*f - 29. Let n be r(10). Let h(q) = -3*q + 38. Let p be h(n). Factor -p*z**2 - 4*z**3 - 4 - 4*z**3 - 4*z**3 - 8*z + 11*z**3.
-(z + 1)*(z + 2)**2
Let w(d) = 3*d**2 + 24*d - 19. Let a be w(-21). Solve 800 + 20*k**4 - 20*k**2 + 5*k**5 - a + 15*k**3 - 20*k = 0 for k.
-2, -1, 0, 1
Let h = -1528/305 + 330/61. Let g(o) be the first derivative of -32 + 0*o + 1/20*o**4 + h*o**2 - 4/15*o**3. Determine u so that g(u) = 0.
0, 2
Suppose 1842077 + 1439215 = 18*x. Factor -2*s**4 - x - 8748*s**2 - 216*s**3 - 157464*s - 128588 - 752000.
-2*(s + 27)**4
Let y be (-2)/(-1) - (-4)/12*-6. Let x = 5567/3 + -38957/21. Determine i so that -16/7*i**2 + 11/7*i**4 + 4/7*i + x*i**5 - 3/7*i**3 + y = 0.
-2, 0, 1/4, 1
Let y(d) be the third derivative of d**7/10 + d**6/20 - 7*d**5/5 - d**4 - 17*d**2 - 26. Solve y(l) = 0.
-2, -2/7, 0, 2
Let j be (-80)/90*((-174)/12 - -10). Let p(f) be the third derivative of f**j - 12*f**3 + 0 - 1/30*f**5 + 8*f**2 + 0*f. Solve p(q) = 0 for q.
6
Let w = -283 - -286. Solve 28 + 10*m - w*m + 9*m + 8*m - 4*m**2 = 0.
-1, 7
Determine r so that -992782*r + 381609*r**2 + 3928582*r + 1211*r**3 - 3*r**4 - 1855803*r**2 - 1465803 + 2989*r**3 = 0.
1, 699
Let j(y) = -12 - y + 21 + 10. Let f be j(4). Factor 24*d**2 - 144 + f*d**2 - 62*d**2 + 24*d + 22*d**2.
-(d - 12)**2
Let d(m) be the third derivative of -m**5/15 - 5*m**4/6 + 16*m**3 - 303*m**2 - 4*m. Factor d(c).
-4*(c - 3)*(c + 8)
Suppose 0 = 6*u - 49*u. Let g(c) be the second derivative of 4/15*c**5 - 1/9*c**6 + 1/63*c**7 + u*c**2 - 2/9*c**4 + 0 + 25*c + 0*c**3. Factor g(s).
2*s**2*(s - 2)**2*(s - 1)/3
Let y(z) be the third derivative of 5*z**8/24 + 41*z**7/315 - 139*z**6/90 + 62*z**5/45 + 2*z**4/9 + 69*z**2 - 2*z - 8. Let y(n) = 0. What is n?
-2, -2/35, 0, 2/3, 1
Let w(u) be the first derivative of -2*u**5/75 + 127*u**4/30 - 2644*u**3/15 - 4352*u**2/15 + 16384*u/15 + 301. What is n in w(n) = 0?
-2, 1, 64
Let g = -385 - -382. Let v(j) = -2*j**3 - 9*j**2 - 11*j - 4. Let l be v(g). Factor 18/11*k + 4/11*k**l - 10/11.
2*(k + 5)*(2*k - 1)/11
Suppose 0 = 23*a + 2632 + 5855. Let v = 372 + a. Factor -1/5*c**5 + 0*c + 0 - 3/5*c**v - c**4 + 9/5*c**2.
-c**2*(c - 1)*(c + 3)**2/5
Factor 1/4*q**5 - 73/2*q**2 - 23/2*q**4 - 36*q**3 + 0 - 49/4*q.
q*(q - 49)*(q + 1)**3/4
Let m(i) be the se