- 3*a**6/40 + 13*a**5/40 - 5*a**4/12 + a**2 + 279*a. Factor u(g).
-g*(g - 1)**2*(g + 20)/2
Let g(b) = -b**2 + 4*b + 398. Suppose -1672 = -3*j - 73*j. Let n be g(j). Factor 10/3*s**n + 35/3*s - 5*s**3 + 10/3.
-5*(s - 2)*(s + 1)*(3*s + 1)/3
Let p(u) be the second derivative of 10/11*u**2 - 1/66*u**4 + 0 + 1/11*u**3 + 22*u. Factor p(d).
-2*(d - 5)*(d + 2)/11
Let d(l) = -2*l**3 - 3*l**2 + l + 4. Let x be d(-1). Let u(a) be the first derivative of 3*a - 3/2*a**x + 12 + 3/4*a**4 - a**3. Factor u(k).
3*(k - 1)**2*(k + 1)
Let n(z) be the third derivative of z**6/120 - 16*z**5/15 - z**4/6 + 128*z**3/3 + 147*z**2 - 9*z. Factor n(t).
(t - 64)*(t - 2)*(t + 2)
Let x be (-3 - (3/(-24) + 1764/(-480)))/(36/30). Factor 16 - 2*a**2 - 20/3*a + x*a**3.
2*(a - 4)*(a - 2)*(a + 3)/3
Factor -234005779872 + 180839088*d - 61110*d**2 + 1212*d**3 - 1208*d**3 + 14526*d**2.
4*(d - 3882)**3
Let r be ((-2)/(-8))/((-3)/(-204)). What is y in -195*y + 55*y**2 + 129 + r - 81 - 5*y**3 + 160 = 0?
3, 5
Let v(j) = -j**3 + 19*j**2 + 2. Let r be v(19). Determine a so that 3 + 0 - a**r - 2*a - 6*a + 6*a = 0.
-3, 1
Factor 1388/3*j - 824/3*j**2 + 464/3 + 7/3*j**3.
(j - 116)*(j - 2)*(7*j + 2)/3
Let t(o) be the second derivative of o**4/36 - 34*o**3/9 - 70*o**2/3 - 46*o - 10. Suppose t(i) = 0. What is i?
-2, 70
Let a(c) = c**2 - 2*c - 26566. Let o be a(-162). Let 1/3*k**o - k + 0 = 0. Calculate k.
0, 3
Determine y, given that -92*y**2 - 37268*y**3 + 4*y**5 + 37232*y**3 + 12*y**4 - 9 + 153 + 96*y = 0.
-3, -1, 2
Find i, given that 94*i**4 - 2145*i + 3170*i**2 - 847*i + 968 - 1238*i**3 + 21*i**5 - 23*i**5 = 0.
1, 22
Suppose 5*c + 4*v - 20 = 0, -6*v - 78 = -2*c - 108. Let o(d) be the first derivative of -1/21*d**3 + c*d - 15 - 1/7*d**2. Factor o(b).
-b*(b + 2)/7
Let a be ((-28)/(-8) - 8) + ((-4)/(-14))/((-216)/(-4914)). Suppose 4*l + 19/5 + 1/5*l**a = 0. Calculate l.
-19, -1
Solve 920 - 3685*h + 710*h**2 + 14705/4*h**3 + 35/4*h**5 - 1630*h**4 = 0.
-1, 2/7, 1, 2, 184
Let 60*d**2 + 5/3*d**3 + 400*d - 8000/3 = 0. What is d?
-20, 4
Let z(s) be the first derivative of 0*s**2 + 0*s + 95 + 16/5*s**3 + 1/10*s**4. Factor z(n).
2*n**2*(n + 24)/5
Let k(i) = 18*i + 182. Let t be k(-10). Suppose -4*w - c + 34 - 1 = 0, -w + t*c - 3 = 0. Factor -1/2*v**2 + w*v - 49/2.
-(v - 7)**2/2
Let p(d) be the first derivative of 10/3*d**3 + 16*d + 18 - 1/3*d**4 - 8*d**2. Let c(l) be the first derivative of p(l). Suppose c(q) = 0. Calculate q.
1, 4
Let i be (3 - 6)*(-1 - -1 - (-756)/(-81)). Let w(f) be the second derivative of 0 + 1/6*f**5 - 7/18*f**4 + 1/3*f**3 + 0*f**2 + i*f - 1/45*f**6. Factor w(r).
-2*r*(r - 3)*(r - 1)**2/3
Let y(q) be the first derivative of 3*q**4/4 + 450*q**3 + 101250*q**2 + 10125000*q - 3454. Factor y(o).
3*(o + 150)**3
Let w(n) be the second derivative of -n**5/200 + 47*n**4/40 + n**3/60 - 141*n**2/20 + 10391*n. Factor w(b).
-(b - 141)*(b - 1)*(b + 1)/10
Suppose 0 = -2*k - 5*c + 34, -2*k + 16*c - 11*c = -74. Let t be 3 + k/(-18) + (-4)/24. Factor 4/3*m**5 - 8/3*m**3 + 0 + 0*m**2 + 0*m + t*m**4.
4*m**3*(m - 1)*(m + 2)/3
Suppose -3*q + 564520 - 12736 = 0. Factor -62461 - 16335*j + 66704 - 5*j**3 - 495*j**2 - q.
-5*(j + 33)**3
Let t be 1*-37*2/2. Let v = t + 39. What is c in -9*c**4 + 0*c**3 + 5*c**4 + 8 - 4*c**v + c**3 + 2*c**5 + 14*c - 17*c**3 = 0?
-1, 1, 4
Let g = -188927/71 - -2661. Let h = g - -485/213. Factor -h*o - 2 - 1/3*o**2.
-(o + 1)*(o + 6)/3
Suppose -78 = 3*s + 3*l, 0 = -3*s + 2*l - 32 - 26. Let z be (s/77)/(36/(-140)). Find k, given that -4/3 - 2/9*k**2 + z*k = 0.
2, 3
Let m be 4/(-16)*183/(-122). Factor 243/8 - 27/4*k + m*k**2.
3*(k - 9)**2/8
Let q be 144/(-224)*14/(-804). Let i = q + 1063/804. Factor -i + 2/3*z**2 + 2/3*z.
2*(z - 1)*(z + 2)/3
Factor -t**4 + 11992*t**3 + 55*t**2 - 47*t - 27*t - 126*t - 11990*t**3.
-t*(t - 5)**2*(t + 8)
Let a = -63 - -63. Suppose 0 = -4*r - a*r + f + 820, -r = -3*f - 205. Suppose -r + 6*l - 21*l**2 + 205 = 0. Calculate l.
0, 2/7
Let l(c) be the second derivative of 17/36*c**3 + 0 - 187*c - 19/6*c**2 + 1/72*c**4. Factor l(d).
(d - 2)*(d + 19)/6
Let a be (-916739)/(-55710) + ((-2)/(-36))/(-1). Factor a*r - 8/5*r**2 - 4.
-2*(r - 10)*(4*r - 1)/5
Let z be 2*(122/(-32) - -4) + (-3374)/(-560). Find k, given that -2/5*k**2 - 128/5 + z*k = 0.
8
Let l be ((-72)/22)/((-225)/11880). What is i in -3968/5*i**3 - 1232/5*i**4 + 544/5*i + l*i**2 - 128/5 + 294*i**5 = 0?
-4/3, -2/5, 2/7, 2
Factor -1059*k**2 - 8*k**3 + 160 + 5*k**3 + 107 + 1020*k - 216*k - 9*k**3.
-3*(k - 1)*(k + 89)*(4*k + 1)
Suppose -18*s - 13 = -67. Find j such that 37*j**2 + 4*j**s + 3*j**2 + 44*j + 56*j - 16*j = 0.
-7, -3, 0
Let k be (2*(-2)/(-4))/(-3*(-6)/288). Suppose 2 + 0 = j. Solve k*r + 5*r**j + 6*r - r - r = 0.
-4, 0
Factor 2/3*l**3 - 18 + 10*l + 22/3*l**2.
2*(l - 1)*(l + 3)*(l + 9)/3
Let o(v) = -50*v**2 + 155*v - 40. Let n(r) = 22. Let s(k) = -10*n(k) - o(k). Factor s(h).
5*(h - 4)*(10*h + 9)
Suppose 6335 - 6506 = -57*f. Factor -f*y**2 + 15/4 - 6*y.
-3*(2*y - 1)*(2*y + 5)/4
Let l(n) = -2*n**2 + 4*n + 6. Let t(d) = -3*d**2 + 8*d + 11. Let v(f) = -f - 3. Let k be v(2). Let a(w) = k*l(w) + 2*t(w). Suppose a(x) = 0. What is x?
-1, 2
Let y(q) be the second derivative of -5*q**4/12 - 395*q**3/6 - 195*q**2 - 1025*q - 3. Factor y(k).
-5*(k + 1)*(k + 78)
Let i = 2018 + -6053/3. Let h be 16*3/21*(-14)/(-12). Factor h - i*f**2 + 2/3*f.
-(f - 4)*(f + 2)/3
Let h = 973 + -970. Suppose -2*p + 16 = 6*m, h*p - 14*m = -11*m. Find a such that 8/7 + 4*a - 36/7*a**p = 0.
-2/9, 1
Let g = 45152/25 + -1806. Let z(h) be the second derivative of 0*h**3 + g*h**6 + 3/100*h**5 + 0*h**2 + 0 + 23*h - 1/30*h**4 + 1/30*h**7. Solve z(w) = 0.
-1, 0, 2/7
Let t = 6528 - 6478. Let p(n) be the third derivative of 1/35*n**7 + 0*n**4 + 1/40*n**6 + t*n**2 + 0 + 0*n**5 + 0*n + 1/112*n**8 + 0*n**3. Factor p(s).
3*s**3*(s + 1)**2
Suppose -5*f - 5*p + 20 = 0, -5*f + 4*p + 0*p = -2. Let u(o) = -o**2 + 12*o - 30. Let m be u(4). Let -9*g - m*g**f + g + 8*g + g**4 + g**3 = 0. What is g?
-2, 0, 1
Let r(q) = 4*q**2 - 2021*q + 2027. Let c(m) = -14*m**2 + 7073*m - 7093. Let g(p) = -5*c(p) - 17*r(p). Factor g(o).
2*(o - 503)*(o - 1)
Solve -8558163*m**2 - 19272983076*m - 1689*m**3 - 16276034207682 - 1/8*m**4 = 0.
-3378
Let z(i) be the second derivative of -3*i**5/40 + 21*i**4/8 + 45*i**3/4 + 69*i**2/4 - i - 519. Factor z(h).
-3*(h - 23)*(h + 1)**2/2
Suppose 0 = 11*w - 65 + 10. Suppose -7*p**2 + 5*p**3 - 4*p**2 + 10*p**4 + p**2 + 5*p**5 - 10*p**w = 0. Calculate p.
-1, 0, 1, 2
Let v(y) be the second derivative of -y**5/300 - 13*y**4/120 - 2*y**3/5 + 16*y**2 - 88*y. Let l(q) be the first derivative of v(q). Find s, given that l(s) = 0.
-12, -1
Let k(o) = 16*o - 34. Let j be k(4). Factor -j*t**2 - 167 + 167 + 5*t**4 - 25*t**3.
5*t**2*(t - 6)*(t + 1)
Suppose -4*k + 2 = -6*k, -102 = -5*h - 3*k. Let i be (1/(-3))/((-175)/h + 7). Determine p, given that 0*p + i*p**5 - 1/4*p**2 - 3/4*p**4 + 0 + 3/4*p**3 = 0.
0, 1
Suppose 23*w = 59*w + 34*w + 27*w. Let u(m) be the third derivative of 3/40*m**6 + w - 5/4*m**5 + 0*m - 8*m**3 - 6*m**2 + 7*m**4. Factor u(g).
3*(g - 4)**2*(3*g - 1)
Let l(b) be the first derivative of -b**6/108 - 7*b**5/48 + 5*b**4/8 - 31*b**3/3 - b**2 - 84. Let z(s) be the third derivative of l(s). Solve z(a) = 0 for a.
-6, 3/4
Suppose 127 - 42 = 5*i + 5*j, 0 = -4*i - 5*j + 68. Factor 1 + i*v + v**5 + 7 - 7*v**3 - 27*v - 2*v**2 + 22*v.
(v - 2)**2*(v + 1)**2*(v + 2)
Factor 0*h**2 - 13/4*h**3 + 0 + 0*h + 3/4*h**4.
h**3*(3*h - 13)/4
Let w(q) be the third derivative of -20/3*q**3 - 25/48*q**8 + 68/21*q**7 - 155/24*q**6 + 0*q - 16*q**2 + 17/6*q**5 + 35/6*q**4 + 1. Solve w(y) = 0.
-2/5, 2/7, 1, 2
Determine z so that 4/3*z**2 - 1216/3 + 40*z = 0.
-38, 8
Suppose -12 = -5*c - 42. Let o be (9/c)/(3 - 108/32). Factor -45*z + 43*z + 2*z**3 + 2 - o + 2*z**2.
2*(z - 1)*(z + 1)**2
Suppose 0 = 3*a - 4*o - 31, -2*o + 116 = -4*a + 144. Let n = -2 - -4. Solve -2*h**3 + 5*h**3 - 22*h**4 - 4*h**n + 9*h**2 - h**a + 21*h**4 + 2*h = 0.
-1, 0, 2
Factor 3*x**2 + 4*x**2 + 3*x**2 - 6*x**2 - 1474*x - 502*x.
4*x*(x - 494)
Let y(h) be the third derivative of -77*h**5/45 - 389*h**4/36 - 10*h**3/9 - 1819*h**2. Factor y(a).
-2*(2*a + 5)*(77*a + 2)/3
Factor 0*l + 0*l**2 - 4/3*l**3 + 0 + 2/3*l**4.
2*l**3*(l - 2)/3
Let f(a) be the third derivative of -4*a**3 + 56*a**2 + 0*a +